Method and system for detecting diffused single particles

Abstract

There is provided a method for detecting diffusion particles, comprising introducing a sample comprising diffusion particles into an optical microcavity; coupling the probe light into the optical microcavity such that the probe light resonates with the optical microcavity, wherein the diffusion particles diffuse into an optical mode volume defined by the coupled probe light; and detecting the output light from the optical microcavity as a function of time while maintaining the resonance, wherein the diffusion particles produce a change in the detected output light. A system for performing the method is also provided.

Description

[0001] Cross - Reference to Related Applications

[0002] This application claims priority to U.S. Provisional Patent Application No. 63 / 521,919, filed on June 20, 2023, and U.S. Provisional Patent Application No. 63 / 424,642, filed on November 11, 2022, the entire contents of both of which are incorporated herein by reference.

[0003] Reference to Government Rights

[0004] This invention was made with government support under GM136981 awarded by the National Institutes of Health and DE - AC02 - 06CH11357 awarded by the U.S. Department of Energy. The government has certain rights in the invention.

[0005] The project leading to this application has received funding from the Marie Sklodowska - Curie grant agreement No 886216 under the Horizon 2020 research and innovation programme of the European Union. Background Art

[0006] Neurodegenerative diseases are incurable protein - misfolding disorders characterized by a progressive loss of neuronal function. For example, the misfolding and aggregation of intrinsically disordered proteins are undoubtedly associated with neuronal death in Parkinson's disease. The formation of protein inclusions occurs by the misfolding of soluble monomeric proteins into intermediate oligomers, which ultimately form insoluble amyloid deposits in the brain, mainly composed of the protein alpha - synuclein (αSyn). Neuronal amyloid deposits (Lewy bodies) are a pathological hallmark of Parkinson's disease and are generally considered a protective mechanism against the oligomers themselves, which are thought to be the main pathogens. The term "oligomer" is commonly used to describe a variety of pre - fibrillar aggregates that are highly variable in size, shape, and structure, with varying degrees of β - sheet architecture. Some biophysical techniques have been used to study these properties of amyloid proteins specifically, and of biomolecules in general. However, the low abundance (<1%) of these substances in biological fluids, their instability, and heterogeneity make it almost impossible to observe them with existing techniques. Summary of the Invention

[0007] Methods for detecting diffusing particles, including diffusing single - protein molecules, are provided. Systems for performing the methods are also provided.

[0008] As illustrated in the examples below and compared to existing technologies, the present method and system can be used to detect extremely small single particles, including single proteins as small as about 1 kDa, where the signal-to-noise ratio is about 100, even when the particles are freely diffusing in solution. The present method and system can be used to determine the size of such particles and to distinguish between mixtures of different types of particles, including molecular isomers having the same molecular weight but different shapes. Unlike other existing biophysical techniques, the present method and system do not require (e.g., with fluorescent probes or other types of probes) labeling of the particles and do not require the particles to interact with any surface, thus providing a non-invasive, label-free method for analyzing biomolecules, including those linked to pathological diseases. Such information is extremely useful for elucidating the role of these substances in these pathological diseases and thus in the development of diagnostic tools and therapeutic interventions. However, the present method and system are not limited to such applications and more broadly include sample characterization as well as revealing the mechanisms underlying protein oligomerization, biomolecular interactions, and macromolecular assembly.

[0009] In Example 1, a method for detecting diffusing particles includes: (a) introducing a sample comprising diffusing particles into an optical microcavity; (b) coupling probe light into the optical microcavity such that the probe light resonates with the optical microcavity, wherein the diffusing particles diffuse into the optical mode volume defined by the coupled probe light; and (c) detecting the output light from the optical microcavity as a function of time while maintaining resonance, wherein the diffusing particles produce a change in the detected output light.

[0010] Example 2 is the method of Example 1, wherein the optical microcavity is an open-entry optical microcavity configured such that the maximum intensity region of the optical mode volume can be entered by the diffusing particles.

[0011] Example 3 is the method of any one of Examples 1-2, wherein the optical microcavity is a Fabry-Perot microcavity having a cavity, wherein the optical mode volume is defined within the cavity.

[0012] Example 4 is the method of any one of Examples 1 - 3, wherein the resonance in step (b) is associated with the maximum transmission of the probe light through the optical microcavity or the minimum intensity of the back - reflected probe light from the optical microcavity. Example 5 is the method of Example 4, wherein the probe light is coupled such that it experiences constructive interference to form a standing wave in the optical microcavity and the maximum transmission of the probe light or the minimum intensity of the back - reflected probe light is obtained by adjusting one or more of the following: the power of the probe light, the gain of the Pound - Drever - Hall (PDH) servo loop that couples the source of the probe light to the optical microcavity, and the offset of the PDH servo loop. Example 6 is the method of Example 5, wherein the standing wave is achieved by satisfying mλ = 2nL, where m is an integer, λ is the wavelength of the probe light, n is the refractive index of the sample, and L is the length of the optical microcavity. Example 7 is the method of Example 6, further comprising adjusting λ, adjusting L, adjusting the power of the probe light, adjusting the gain of the PDH servo loop, adjusting the offset of the PDH servo loop, or a combination thereof during step (c) to maintain resonance.

[0013] Example 8 is the method of any one of Examples 1 - 7, wherein the sample comprises water. Example 9 is the method of Example 8, wherein the optical microcavity is a Fabry - Perot microcavity having a cavity, and the optical mode volume is defined within the cavity.

[0014] Example 10 is the method of any one of Examples 1 - 9, wherein the sample has a certain concentration of diffusing particles such that the probability that the diffusing particles occupy the optical mode volume is less than one.

[0015] Example 11 is the method of any one of Examples 1 - 10, wherein the detected output light is the transmitted probe light containing recesses or the detected output light is the back - reflected probe light containing spikes, and the method further comprises measuring the time width of each recess or spike. Example 12 is the method of Example 11, further comprising generating a plot of intensity versus the time width of each recess or spike.

[0016] Example 13 is the method of any one of Examples 1 - 11, wherein the detected output light is the transmitted probe light containing recesses or the detected output light is the back - reflected probe light containing spikes, and the method further comprises measuring the autocorrelation function (ACF) from the recesses or spikes and calculating the hydrodynamic radius based on the measured ACF.

[0017] In Example 14, the system for detecting diffusing particles includes: (a) an optoelectronic component configured to couple probe light into an optical microcavity such that the probe light resonates with the optical microcavity; (b) an optical microcavity into which a sample containing diffusing particles is introduced to diffuse into the optical mode volume defined by the coupled probe light; (c) a detector configured to detect the output light from the optical microcavity as a function of time; and (d) an optoelectronic component configured to maintain resonance while using the detector to detect the output light from the optical microcavity as a function of time, wherein the optoelectronic component (d) provides a Pound-Drever-Hall (PDH) servo loop that couples the source of the probe light and the optical microcavity.

[0018] Example 15 is the system of Example 14, wherein the optical microcavity is an open-entry optical microcavity configured such that the region of maximum intensity of the optical mode volume can be entered by diffusing particles.

[0019] Example 16 is the system of any one of Examples 14-15, wherein the optical microcavity is a Fabry-Perot microcavity having a cavity, and wherein the optical mode volume is defined within the cavity.

[0020] Example 17 is the system of any one of Examples 14-16, further comprising an actuator operatively coupled to the optical microcavity and the PDH servo loop, the actuator being configured to adjust the cavity length L of the optical microcavity.

[0021] Example 18 is the system of any one of Examples 14-17, further comprising a controller that includes a processor and a non-transitory computer-readable medium operatively coupled to the processor, the non-transitory computer-readable medium including instructions that, when executed by the processor, cause the controller to perform operations including: receiving a signal from the detector; based on the received signal, satisfying mλ = 2nL, where m is an integer, λ is the wavelength of the probe light, n is the refractive index of the sample, and L is the cavity length of the optical microcavity; and based on the received signal, adjusting one or more of the power of the probe light, the gain of the PDH servo loop, the offset of the PDH servo loop, or a combination thereof.

[0022] Example 19 is the system of any one of Examples 14-18, further comprising a controller that includes a processor and a non-transitory computer-readable medium operatively coupled to the processor, the non-transitory computer-readable medium including instructions that, when executed by the processor, cause the controller to perform operations including: receiving a signal from the detector; processing the signal to determine the time width of the signal; and outputting the determined time width. Example 20 is the system of Example 19, wherein the operations further include processing the signal to calculate the hydrodynamic radius of the diffusing particles and outputting the calculated hydrodynamic radius to the system.

[0023] After reviewing the following drawings, detailed description, and the appended claims, other principal features and advantages of the present disclosure will become apparent to those skilled in the art. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Exemplary embodiments of the present disclosure will be described hereinafter with reference to the drawings.

[0025] Figure 1A is a schematic diagram of a portion of a Fabry - Perot (FP) microcavity 100 according to an exemplary embodiment. The FP microcavity 100 is an exemplary open - access optical microcavity that can be used in the present method and system.

[0026] Figure 1B is after a sample 116 including diffusing particles has been introduced into the cavity 110 of the FP microcavity Figure 1A schematic diagram of the FP microcavity 100. The particles (denoted by reference numeral 118) diffuse into the optical mode volume defined by the coupled probe light (schematic of the standing wave 114). Such a diffusion event results in a change in the detected output light from the FP microcavity. It is believed that this is due to the particles 118 increasing the local refractive index within the optical mode volume, thereby triggering a rapid cooling cascade. Elastic scattering of the coupled probe light can contribute to the cooling. The present method and system are capable of detecting such single - particle diffusion events as a function of time, for example, by an avalanche photodiode (APD), thereby generating a plot such as Figure 1B shown in the figure. It is not possible to detect such single - particle diffusion events using existing dynamic light - scattering methods and systems.

[0027] Figure 2 is a system 200 for performing the present method according to an exemplary embodiment.

[0028] Figure 3 is Figure 2 block diagram of the system 200.

[0029] Figures 4A - 4C shows signals from a detector 222 (which detects the probe light transmitted through the FP microcavity) of the system 200 obtained from three samples ( Figure 4A , streptavidin; Figure 4B , carbonic anhydrase; and Figure 4C , aprotinin) obtained from Figure 2 . The diffusion events appear as dips in the transmitted probe light.

[0030] Figure 5A shows a plot of the average full - width at half - maximum (FWHM) of the dips measured from each of the corresponding plots in Figures 4A - 4C and another plot obtained from a sample including the protein c - Myc. Figure 5BIt is a graph of the average FWHM of the spikes measured in a similar graph obtained from the detector 220 that detects the probe light of the retroreflection.

[0031] Figure 6A Fig. shows a simplified schematic diagram of a single-molecule sensing instrument based on a fiber optic Fabry-Perot cavity (FFPC) used in Example 2. A laser (660 - 760 nm) with a spectral width of 1 MHz passes through a linear polarizer (||) and a half-wave plate (λ / 2), is selectively attenuated by a variable optical attenuator (VOA), and is phase-modulated by a lithium niobate electro-optic modulator (EOM) driven by a 200 MHz voltage-controlled oscillator (VCO). Then the light is coupled into the cavity via an optical fiber splitter to enable collection of the reflected light, and is also coupled into the input fiber, where the transmitted intensity is detected on a photodiode. To maintain the resonance between the cavity and the laser, Pound-Drever-Hall (PDH) cavity length stabilization is achieved using frequency sidebands generated by the EOM driven by a VCO at 200 MHz. An error signal is generated by applying a low-pass filter to the mixed VCO reference signal and the photodiode signal. Then this signal is fed into a proportional-integral (PI) controller, which drives a ceramic piezoelectric actuator to stabilize the cavity length to maintain resonance. Protein diffusion events are monitored in two channels (reflection and transmission) on separate photodiodes. Figure 6B Fig. shows a wavelength scan for determining the spectral linewidth of the cavity mode to be probed. The cavity finesse is 37450 in water.

[0032] Figure 7A Fig. shows the perturbation of the locked resonance cavity mode originating from a single protein diffusion event. The locked signals are monitored in both transmission and reflection, and these events appear as transient decreases in the transmitted signal intensity and increases in the reflected intensity. Figure 7B Fig. shows a 2D plot of the time width and the extracted prominence of the reflected signal and the accompanying histogram.

[0033] Figure 8A Fig. shows the ensemble autocorrelation of hundreds of single protein diffusion events. Figure 8B Fig. shows the relationship between the autocorrelation time and the protein radius at an autocorrelation threshold of 40%, showing a distinct linear correlation.

[0034] Figures 9A - 9B Fig. shows for ( Figure 9A ) a mixed protein sample of aprotinin (6.5 kDa, 1.45 nm) and Myc tag (1.2 kDa, 0.75 nm) and for ( Figure 9B ) a 2D plot of the peak prominence versus the time width of a mixed DNA structure sample of duplex (16.6 kDa, 9 nm) and Y-junction (16.6 kDa, 5 nm) and the subsequent separate histograms, where multiple populations are clearly resolved.

[0035] Figure 10A A figure is shown that depicts the frequency noise spectral density in water, the locked bandwidth (LBW) characteristics, and the mean squared displacement power spectral density (MSDPSD) of proteins (streptavidin, aprotinin, carbonic anhydrase, and Myc tag). The noise spectral density of the locked cavity in water rapidly converges to the detector-limiting noise (off-resonance noise), thereby highlighting the high passive stability. The 5 kHz locked bandwidth defined by the 0 dB feedback gain crossover controls the lower frequency limit of the velocity filter. The upper limit of the velocity filter is defined by the optothermal bandwidth (21 kHz). The molecular MSDPSD can be integrated within this filter bandwidth to determine the root mean square MSD. Figure 10B A cartoon is shown that illustrates the key processes and their frequency bandwidths. Noise below 5 kHz is suppressed by PDH. The upper limit of the LBW and the lower limit of the optothermal bandwidth define the molecular diffusion velocity observation window. Figure 10B A schematic diagram is shown that describes the mechanism of dynamically thermally induced (see Example 2 for details).

[0036] Figure 11 A schematic diagram is shown of a system for measuring the locked bandwidth (LBW) of the cavity used in Example 2, which is measured by adding a harmonic perturbation (F h ) from a function generator (Fxn generator) of known frequency and amplitude to the PI input (error input) together with the error signal (e) using a voltage adder (V+).

[0037] Figure 12 A figure is shown of the frequency noise spectral density of the mechanical motion of the cavity assembly used in Example 2 extracted from a finite element simulation of the mechanical mode. The resonant mechanical mode lies outside the velocity filter bandwidth, indicating that the cavity is highly stable within the observation window. The amplitude of the resonant mechanical mode is below the detector noise limit and less than the calculated resonant shift for <1 nm molecules.

[0038] Figure 13A A figure of the transmitted intensity of the locked cavity of Example 2 is shown, depicting the perturbation of the lock when a 1 mV voltage pulse is applied to the piezoelectric element at a frequency of 1 Hz. Figure 13B A figure is shown of how the applied pulse, input power, and cavity lock parameters can be optimized to mimic the signal caused by diffusing molecules. Due to the optothermal effect, the step-down voltage (bottom trace) produces a sharp drop (a) in the locked transmission signal (top trace), which is then briefly restored to the locked state (b) by the PI feedback loop, and then the transmission signal drops a second time (c) because the step-up voltage of the pulse offsets the cavity in the opposite direction, and finally the PI control restores the locked state (d).

[0039] Figure 14Shows the optothermal-induced broadening of the transmission cavity resonance in water, collected at cavity length tuning at two different pump wavelengths as described in Example 2. The rightward shift of the pump wavelength shifts the resonance position to a lower piezoelectric ramp voltage, demonstrating that the increased piezoelectric ramp voltage corresponds to an increased cavity length. Additionally, the direction of the broadening indicates a negative thermo-optic coefficient of the medium, as expected for water. Despite the low circulating power (5.5 mW), the optothermal broadening is evident and enables the high sensitivity of this measurement. The smaller peaks originate from polarization splitting due to the birefringence of the cavity mode. Data was collected using cavity four.

[0040] Figure 15A Shows the experimental determination of the optothermal bandwidth (PBW) as described in Example 2. The calculated bandwidth is 21 kHz, defining the upper limit of the molecular velocity filter (data was collected using cavity four). For comparison, Figure 15B Shows the theoretical quantification of PBW based on finite element simulations of the cooling rate in the cavity.

[0041] Figure 16 Shows a comparison of the signal-to-noise ratios obtained from the system used in Example 2 and from an existing system. Single molecule diffusion data was from Figure 7A and was collected in cavity one.

[0042] Figure 17A Shows the calculated velocity distribution plots for Myc tag, aprotinin, carbonic anhydrase, and streptavidin. Figure 17B Shows the mean squared displacement power spectral density plot (MSDPSD), with the upper and lower bounds replicated in Figure 10A . Integration within the bandwidth of the velocity filter observation window (5 kHz - 21 kHz) provides an approximation of the MSD of the molecule.

[0043] Figure 18 Plots the time width of carbonic anhydrase diffusion events as a function of the locking bandwidth of PDH determined by the proportional gain of PI control. This relationship can be explained by the inverse relationship between the molecular velocity filter bandwidth and the proportional gain value. As the gain increases, the velocity filter bandwidth narrows, resulting in the detection of a distribution of faster moving molecules with a narrower peak width. Data was collected at a proportional gain setting > -50 dB, where the average time width is no longer affected by the locking bandwidth. Error bars represent the standard deviation of the time width across all analyzed peaks. Data was collected using cavity three. Detailed Description

[0044] Provides methods for detecting diffusing particles, including diffusing single molecules. Also provides systems for performing these methods.

[0045] Regarding methods, in some embodiments, such methods include: introducing a sample containing diffusing particles into the cavity of an optical microcavity; coupling probe light into the optical microcavity such that the probe light resonates with the optical microcavity; and detecting the output light from the optical microcavity as a function of time while maintaining resonance. The diffusing particles diffuse into the optical mode volume defined by the coupled probe light in the cavity, and this "diffusion event" produces a change in the detected output light as a function of time. Without wishing to be bound by a particular theory, it is believed that such a diffusion event causes a local increase in the refractive index within the optical mode volume, thereby triggering a rapid cooling cascade that manifests as a shift in the resonance of the optical microcavity. Elastic scattering of the coupled probe light can contribute to the cooling. The optothermal distortion of the resonance of such an optical microcavity, combined with actively maintaining resonance during detection (e.g., using a Pound-Drever-Hall (PDH) servo loop as further described below), provides a surprisingly large amplification of the detector signal and thus enables easy observation of the change in the detected output light as a function of time. As further described below, these changes can be analyzed to extract information about the diffusing particles, including their size. These changes can also be analyzed to separate different populations of particles, including isomeric molecules having the same molecular weight but different shapes.

[0046] A variety of optical microcavities can be used with this method. Optical microcavities that confine light in a small volume by means of distributed Bragg reflection from a periodic structure within the optical microcavity can be used. However, suitable optical microcavities are those configured such that diffusing particles can enter the optical mode volume that is created within the optical microcavity that resonates with the probe light, including the region of maximum intensity of the optical mode. This ensures spatial overlap between the diffusing particles and the optical mode. Such optical microcavities can be referred to herein as "open-access" optical microcavities.

[0047] Certain Fabry-Perot (FP) microcavities are open-access optical microcavities that can be used in this method, including those configured to confine light within a cavity defined by two relatively facing, spaced-apart reflective surfaces. Figures 1A - 1BAn exemplary such FP microcavity 100 is shown. The FP microcavity 100 includes an input optical fiber 102 (e.g., a single-mode optical fiber) and an output optical fiber 106 (e.g., a multi-mode optical fiber). The input optical fiber 102 has a reflective end face 104, and the output optical fiber 106 has a reflective end face 108. The input optical fiber 102 and the output optical fiber 106 are oriented and aligned relative to each other such that the first reflective end face 104 and the second reflective end face 108 face each other and are spaced apart to define a cavity 110 therebetween having a cavity length L. In this embodiment, the FP microcavity 100 is bi-concave because both reflective end faces 104, 108 are concave. The reflective end faces 104, 108 may be provided by a reflective material (e.g., a dielectric material) coated or otherwise mounted on the respective ends of the input optical fiber 102 and the output optical fiber 106. Other FP microcavities having other configurations compared to the FP microcavity 100 may be used. For example, the FP microcavity need not be fiber-based. However, suitable FP microcavities generally include those having a high Q factor (e.g., at least 10 6 ) and a high finesse (F) value (e.g., at least 10 4 ). The materials, dimensions, reflective surfaces (shape, material), and alignment can be adjusted to achieve these Q factor and F values.

[0048] In some embodiments, the optical microcavity is not a ring optical microcavity (which may be referred to as a ring microresonator, etc.) or a whispering gallery mode optical microcavity.

[0049] The reflective surfaces of the optical microcavity can be cleaned to enhance or extend performance. Such cleaning procedures can include exposure to acids, bases, solvents, plasmas, particles, gases, or combinations thereof. A cleaning treatment using a base can include exposing the optical microcavity to hydroxides, aqueous solvents, or organic solvents. A gaseous cleaning treatment can include exposing the optical microcavity to ozone or carbon dioxide. A plasma cleaning treatment can include exposing the optical microcavity to a plasma of air, oxygen, argon, or nitrogen.

[0050] As mentioned above, the method includes coupling probe light into the optical microcavity such that it resonates with the optical microcavity. The conditions for achieving resonance depend on the type of optical microcavity being used and the medium within the cavity of the optical microcavity, but generally refer to ensuring that the probe light and the optical microcavity spectrally overlap with each other (i.e., overlap in frequency), and furthermore, ensuring that the overlap is maximized. (As used herein, "maximized" encompasses but does not require perfect overlap. That is, "maximized" encompasses "almost maximized". The method and system exhibit sufficient sensitivity in detecting diffusive single-particle events, including at the signal-to-noise ratios disclosed herein (see Figure 16), it can be demonstrated that sufficient overlap is achieved. This can be accomplished by using a Pound-Drever-Hall (PDH) servo loop operatively coupled to the probe light and the optical microcavity, as further described below. The probe light can be resonant with any desired optical mode of the optical microcavity, such as the fundamental spatial mode. The resonance conditions described herein generally refer to the loaded optical microcavity, i.e., the optical microcavity is experiencing all of the losses and non-linearities associated with the experimental operating conditions, including filling the optical mode volume of the optical microcavity with a medium in which particles diffuse and operating at typical pump powers.

[0051] For an optical microcavity such as the FP microcavity described above, resonance is achieved by coupling the probe light into the optical microcavity such that it experiences constructive interference to form a standing wave within the cavity of the optical microcavity. More specifically, for an FP optical microcavity such as Figures 1A - 1B the FP optical microcavity 100, resonance can be achieved by satisfying mλ = 2nL (Equation A), where m is an integer, λ is the wavelength of the probe light coupled into the optical microcavity, L is the cavity length of the optical microcavity, and n is the refractive index of the medium within the cavity. For a fixed cavity length L, resonance can be achieved by using a probe light having a wavelength λ that satisfies Equation A. Similarly, for a probe light having a fixed wavelength λ, resonance can be achieved by using a cavity length L that satisfies Equation A. As further described below, the present method allows for adjustment of either the probe light wavelength λ, the cavity length L, or both, in order to ensure that Equation A is satisfied and thus resonance is achieved during the coupling step and maintained during the detection step. In Figure 1A and Figure 1B the process of achieving resonance is illustrated, showing the probe light 112 entering via the input optical fiber 102 and undergoing multiple back-and-forth reflections at the reflective end faces 104, 108. When Equation A is satisfied, a standing wave 114 is formed within the cavity 110. The shape and size of the standing wave 114 determine the optical mode volume into which diffusing particles can enter. It should be noted that, Figure 1A and Figure 1B illustrate a schematic of the standing wave 114, which can be further characterized as consisting of a series of nodes and antinodes through which diffusing particles can pass.

[0052] As further illustrated in the examples below, resonance is further achieved by selecting additional conditions that ensure that the probe light transmitted through the optical microcavity is maximized (alternatively, the probe light retroreflected from the optical microcavity is minimized). "Maximized" ("minimized") has a meaning similar to that described above. These additional conditions include the power of the probe light, the gain of the PDH servo loop, the offset of the PDH servo loop, and the finesse of the optical microcavity. For example, for a selected probe light power, a selected PDH gain, and a selected optical microcavity, the PDH offset can be selected to achieve maximum sensitivity to incident diffusing particles. The examples below relate to an optical microcavity in "resonance" with a probe light that is both "locked" and "ready to fire". (See Figure 10C , drawing board 2.)

[0053] The probe light coupled into the optical microcavity is typically a laser beam. The laser can produce probe light at a fixed wavelength. In such an embodiment, the optical microcavity has a tunable cavity length L so as to ensure that resonance can be achieved and maintained as described above. However, in other embodiments, the laser can produce probe light with a tunable wavelength. Such an embodiment is useful for an optical microcavity with a fixed cavity length L, in which case the probe light wavelength can be tuned so as to ensure that resonance can be achieved and maintained as described above.

[0054] Whether fixed or tunable, the specific wavelength(s) of the probe light being used typically depends on the optical microcavity being used. For example, the use of a silica mirror reflective surface in the optical microcavity typically limits the wavelength to a range of about 300 nm to about 2000 nm. The probe light wavelength(s) also depends on the medium in which the diffusing particles are dispersed. For example, the use of water as the medium typically precludes the use of wavelengths above about 900 nm. Additionally, the wavelength(s) of the probe light typically is independent of the specific particles being analyzed, since the interaction with the particles is non-resonant.

[0055] The method also includes detecting the output light from the optical microcavity as a function of time while maintaining resonance. Under such conditions, diffusing particles entering the optical mode volume (including diffusing particles passing through the nodes / antinodes of the standing wave therein) cause a change (i.e., perturbation) in the detected output light. Compared to existing techniques, the method enables these changes to be detected with an unexpectedly high signal-to-noise ratio (see Figure 16 ). The detected output light can be the probe light transmitted through the optical microcavity (e.g., via Figures 1A - 1B the output optical fiber 106 of the FP optical microcavity 100) or the probe light retroreflected from the optical microcavity (e.g., via Figures 1A - 1B(input optical fiber 102 of the FP optical microcavity 100). Maintaining resonance during detection means using the above resonance conditions during the detection step (i.e., using the cavity length L and the probe light wavelength λ that satisfy Equation A and using additional conditions that should achieve maximum detection transmission, including the PDH offset (at the selected power, the selected PDH gain, and the selected optical microcavity)). In this way, the resonance perturbation caused by the diffusing particles appears as a large, detectable change in the output light of the detection. Maintaining resonance during detection can include adjusting the cavity length L to satisfy Equation A, adjusting the probe light wavelength λ to satisfy Equation A, adjusting the PDH offset, or a combination thereof. Such adjustment can occur during the step of detecting the output light (i.e., simultaneously). Such adjustment can be performed via a PDH servo loop operably coupled to the probe light and the optical microcavity, as further described below.

[0056] Thus, the present method and system relate to detecting output light as a function of time under conditions of continuous resonance between the probe light and the optical microcavity. This is different from methods and systems such as those described in L. Kohler et al. in Nature Communications 12.1 (2021): 1-7, where the probe light and the optical microcavity are intentionally detuned during detection via periodic modulation of the cavity length L.

[0057] The present method can be used to analyze various samples. Samples typically include a liquid medium and particles diffusing throughout the liquid medium. The term "particle" encompasses single molecules such as monomers, oligomers, polymers (and their domains), proteins (and their domains), nucleic acids such as DNA or RNA, and enzymes (and their domains). Proteins, nucleic acids, and enzymes can be collectively referred to as "biomolecules". Particles can also include collections of atoms or chemical molecules, such as metal nanoparticles, inorganic nanoparticles, etc. Samples can include a single type of particle or multiple different types of particles. The liquid medium is not particularly limited and can depend on the nature of the particles in the sample. In some embodiments, the liquid medium is essentially aqueous (i.e., includes water), although non-aqueous liquids can be present. Samples can be biological fluids from mammalian subjects, such as cerebrospinal fluid.

[0058] Depending on the type of particle, particles can be characterized by various sizes and masses. However, as noted throughout this disclosure, the present system and method are capable of determining the size of individual particles that are extremely small. This includes particles having a size of no more than 50 nm, no more than 25 nm, no more than 15 nm, no more than 10 nm, no more than 5 nm, no more than 1 nm, and in the range from 1 nm to 10 nm. This size can be referred to as the hydrodynamic diameter or radius of the particle. These sizes include significantly smaller sizes that cannot be analyzed using existing techniques. Regarding mass, this includes particles having a mass of no more than 100 kDa, no more than 75 kDa, no more than 50 kDa, no more than 25 kDa, no more than 10 kDa, and in the range from 1 kDa to 15 kDa. The present system and method are also capable of distinguishing particles having different sizes / masses and particles having the same size / mass but different shapes.

[0059] Samples analyzed using this method are characterized by having a relatively low concentration of diffusing particles. Generally, the concentration is low enough such that the probability of a single particle occupying the optical mode volume (e.g., see the standing wave 114 in Figure 1A and 1B ) is less than 1. Exemplary concentrations include concentrations in the range from 1 fM to 20 pM. As mentioned above, this method does not require the particles to be labeled with a probe (e.g., a fluorescent probe) that interacts with light. Thus, the particles can be characterized as unlabeled or non-labeled.

[0060] Once introduced into the interior of the optical microcavity (e.g., the cavity 110 of the FP microcavity 100) and while performing the steps of this method, the particles of the sample generally continue to diffuse throughout the cavity, including into the optical mode volume defined by the coupled probe light (e.g., the standing wave 114 of the FP microcavity 100). Although in some embodiments, the diffusing particles can adsorb to the surface of the optical microcavity, this is not a requirement of this method. That is, different from existing techniques, this method and system are configured to detect changes in the output light caused by diffusing particles, which are distinct from surface-bound or surface-adsorbed particles. In some embodiments, the particles can be characterized as not being adsorbed or unadsorbed relative to the surface of the optical microcavity. Additionally, the material of the optical microcavity (or coated surface) can be selected to prevent particle absorption on the surface of the cavity in contact with the sample. Such an optical microcavity can be referred to as non-absorbing or non-absorptive relative to diffusing particles.

[0061] Refer to Figure 1B , this figure shows the Figure 1A FP microcavity 100 after a sample 116 including a liquid medium 117 and diffusing particles (including diffusing particle 118) has been introduced into the cavity 110. As Figure 1AAs in [description in another context], the probe light 112 has been coupled into the microcavity 100 such that it resonates with the FP microcavity 100, thereby forming a standing wave 114 that provides maximum transmission through the microcavity 100. As mentioned above, diffusing particles entering the optical mode volume (whose shape and size are determined by the standing wave 114) constitute diffusing events that produce changes in the detected output light. Specifically, the probe light 112 transmitted via the output optical fiber 106 of the FP microcavity 100 can be detected by a detector (here an avalanche photodiode APD) as a function of time. An exemplary signal from the APD detector is shown in a plot 120 of intensity (or power or voltage) versus time. As shown in FIG. 120, the diffusing events of individual diffusing particles appear as depressions. Similarly, the probe light 112 retroreflected back via the input optical fiber 102 of the FP microcavity 100 can be detected as a function of time, thereby producing a plot of intensity (or power or voltage) versus time. However, compared to FIG. 120, in the case of detecting the retroreflected light, the diffusing events will appear as spikes. Other embodiments may include intermediate phases or inverted spikes and depressions. Other plots of intensity versus time are shown in Figures 4A - 4C (see Example 1) and Figure 7A (Example 2).

[0062] The analysis of the signal associated with the detected output light may include measuring the time width of each depression (spike) in a plot such as FIG. 120. These time widths are related to the transit time (and thus, velocity) of the particles in the optical mode volume, which in turn can be used to calculate the diffusion constant of the particles and ultimately the hydrodynamic radius of the particles. As part of the signal analysis, various data processing techniques can be applied to extract such information. Such techniques may include measuring the full width at half maximum (FWHM) of each depression (spike) in the detector signal plot. The data processing techniques can be used to provide a two-dimensional (2D) plot of the intensity and time width of each depression (spike) in plots such as Figures 4A - 4C and Figures 7A - 7B . An exemplary such 2D plot is shown in Figure 7A . The 2D plot of Figures 9A - 9B further demonstrates the ability of the present method and system to distinguish different particles in a mixture of such particles. Other techniques may include measuring the time autocorrelation function (ACF), which can be used to calculate the diffusion constant of the particles and ultimately the hydrodynamic radius of the particles in a manner consistent with fluorescence correlation spectroscopy. The ACF analysis is further described in Example 2 and is illustrated in Figures 8A - 8B . The analysis may involve using a calibration plot of detector signals obtained from a sample comprising diffusing particles of known size / mass.

[0063] Also provided is a system for detecting diffusing particles, which can be used to perform any of the methods in this method. The system is configured to detect a change in the detected output light caused by diffusing particles that diffuse into the optical mode volume defined by the coupled probe light within the cavity of the optical microcavity. In some embodiments, such a system includes: an optoelectronic component configured to couple the probe light into an optical microcavity that defines a cavity (e.g., an FP microcavity) such that the probe light resonates with the optical microcavity; an optical microcavity that defines a cavity into which a sample including diffusing particles can be introduced to diffuse into the optical mode volume defined by the coupled probe light; a detector configured to detect the output light from the optical microcavity as a function of time; and an optoelectronic component configured to maintain resonance during detection.

[0064] As used herein, the term "optoelectronic component" encompasses various types of optical devices and / or electrical devices for guiding, manipulating, changing, processing, etc. optical and electrical signals. Individual optoelectronic components can be shared among other components of the system, such as the source of the probe light, the optical microcavity, and the detector(s).

[0065] As described further below, such optoelectronic components can include one or more PDH servo loops operatively coupled to the probe light and the optical microcavity. The system can also include one or more actuators operatively coupled to the optical microcavity to tune its cavity length L. The system can also include a sample delivery assembly (e.g., a microfluidic device) operatively coupled to the optical microcavity and configured to introduce a sample into the cavity. The system can also include a light source (e.g., a laser) configured to generate the probe light. Although multiple light sources can be used, in some embodiments, the system includes only a single light source, i.e., the light source that provides the probe light. The system can also include a second detector. One detector can be configured to detect the probe light transmitted through the optical microcavity, while the other detector can be configured to detect the probe light reflected backward from the optical microcavity. The system can also include components configured to mechanically stabilize the optical microcavity, e.g., by absorbing or blocking mechanical noise. Such components include fiber supports (e.g., ferrules) for fiber-based optical microcavities and floating optical tables.

[0066] Figure 2 A schematic diagram of an exemplary system 200 configured to perform this method is shown. System 200 includes Figures 1A - 1B an FP microcavity 100 that includes an input fiber 102 and an output fiber 106. The enlarged box 204 shows a cavity 110 defined by the opposing, spaced-apart reflective end surfaces 104, 108 of the input fiber 102 and the output fiber 106. In this embodiment, the input fiber 102 and the output fiber 106 are aligned to promote Figures 1A - 1BThe basic spatial mode of the FP microcavity 100. To increase passive stability, the input optical fiber 102 and the output optical fiber 106 are supported by a glass ferrule 202 that defines an internal channel into which the input optical fiber 102 and the output optical fiber 106 are inserted. In other embodiments, other supports may be used instead of ferrules. In still other embodiments, such a support is not required. One or both of the input optical fiber 102 and the output optical fiber 106 are held movably within their respective ferrule channels. A ceramic piezoelectric actuator 206 is mounted to the glass ferrule 202 to move the input optical fiber 102 and / or the output optical fiber 106 relative to each other, thereby allowing adjustment of the cavity length L of the FP microcavity 100. In this embodiment, a sample containing a liquid medium and diffusing particles 207 is introduced into the cavity 110 by placing a droplet 208 of the sample such that it contacts and fills the cavity 110.

[0067] The system 200 further includes a laser source 210 (in this embodiment, a fixed-wavelength laser source) configured to provide probe light 211. The system 200 also includes components for manipulating the probe light 211, including a polarizer 212, a variable optical attenuator (VOA) 214, and a phase modulator 216. The thus-manipulated probe light 211 is delivered to the input optical fiber 102 via one or more additional optical fibers (alternatively, free-space optics may be used). An optical fiber beam splitter 218 allows the probe light 211 to be coupled into the input optical fiber 102. The optical fiber beam splitter 218 also allows any backscattered light traveling via the input optical fiber 102 from the FP microcavity 100 to be detected by one of the detectors (detector 220) in the system 200. The light transmitted from the FP microcavity 100 and traveling via the output optical fiber 106 is detected by another detector (detector 222) in the system 200. In this embodiment, both detectors 220 and 222 are high-bandwidth avalanche photodiodes.

[0068] A voltage-controlled oscillator (VCO) 224 generates a reference signal 226 that is used to drive a phase modulator 216 to generate a phase-modulated probe light that includes a carrier frequency and sidebands. The same reference signal 226 is also mixed with a signal 228 from a detector 222. The mixed signal 230 is input into a proportional-integral-derivative (PID) controller 232 to provide an error signal 234 that provides feedback to at least one of the piezoelectric actuators in the piezoelectric actuator 206 to allow adjustment of the cavity length L for a certain probe light wavelength λ (here 660 nm) to satisfy the above equation A. A low-pass passive filter (LP) may be included to suppress high-frequency electrical noise. Thus, each of these components in this paragraph, such as the phase modulator 216, VCO 224, PID controller 232, etc., may be considered to provide a part of a PDH servo loop 236 that is operatively coupled to both the probe light 211 and the FP microcavity 110. As further described in an example below, the PDH servo loop 236 is characterized by its PDH offset, which can be adjusted (depending on the selected power of the probe light 211, the selected PDH gain, and the selected optical microcavity) to ensure that the probe light transmitted through the FP microcavity 100 is maximized. Thus, the PDH servo loop 236 is configured to achieve and maintain resonance between the probe light 211 and the FP microcavity 110 during coupling / detection. Modifications to the PDH servo loop 236 or inclusion of another PDH servo loop may be used to allow adjustment of the probe light wavelength λ to ensure that resonance for a certain cavity length L can be achieved and maintained.

[0069] System 200 further includes a controller 238 that is configured to control one or more components of system 200. This may include control of the components of the PDH servo loop 236 described above. This may also include displaying and processing signals 240 from detector 220 and signals 242 from detector 222 of system 200. Such signals 240, 242 may be recorded by a data acquisition card (DAQ) operating at 50 kHz, which may be part of controller 238.

[0070] More generally, a controller of the system (such as controller 238) may be integrated into the system as part of a single device, or its functionality may be distributed over one or more devices that are directly connected or connected via a network, which may be wired or wireless, to other system components. A database, a data repository of the system, may also be included and operatively coupled to the controller.

[0071] As Figure 3As shown in the exemplary embodiments, the controller 300, which can be included in any system (including system 200) of the present system, can include an input interface 302, an output interface 304, a communication interface 306, a computer-readable medium 308, a processor 310, and an application 312. The controller 300 can be a computer of any form factor, including a circuit board.

[0072] The input interface 302 provides an interface for receiving information into the controller 300. The input interface 302 can interact with various input technologies, including, for example, a keyboard, a display, a mouse, a keypad, etc., to allow a user to input information into the controller 300 or make selections presented in a user interface displayed on the display. The input interface 302 can also provide an electrical connection that provides a connection between the controller 300 and other components of the system 200.

[0073] The output interface 304 provides an interface for outputting information from the controller 300. For example, the output interface 304 can interact with various output technologies, including, for example, a display or a printer, for outputting information for a user to review. The output interface 304 can also provide an interface for outputting information to other components 314 of the system 200.

[0074] The communication interface 306 provides an interface for receiving and sending data between devices using various protocols, transmission technologies, and media. The communication interface 306 can support communication using various transmission media that can be wired or wireless. Data and messages can be transmitted using the communication interface 306 between the controller 300, a database, other components of the system 200, and / or other external devices.

[0075] The computer-readable medium 308 is an electronic holding place or memory for information such that the information can be accessed by the processor 310 of the controller 300. The computer-readable medium 308 can include any type of random access memory (RAM), any type of read-only memory (ROM), any type of flash memory, etc., such as magnetic storage devices, optical discs, smart cards, flash memory devices, etc.

[0076] The processor 310 executes instructions. The instructions can be executed by a special-purpose computer, logic circuits, or hardware circuits. Thus, the processor 310 can be implemented in hardware, firmware, or any combination of these methods and / or in combination with software. The term "execute" is the process of running the application 312 or performing the operations invoked by the instructions. The instructions can be written using one or more programming languages, scripting languages, assembly languages, etc. The processor 310 executing the instructions thus means that it performs / controls the operations invoked by the instructions. The processor 310 is operatively coupled to the input interface 302, the output interface 304, the computer-readable medium 308, and the communication interface 306 to receive, send, and process information. The processor 310 can retrieve a set of instructions from a permanent storage device and copy the instructions in an executable form into a temporary storage device, which is typically some form of RAM.

[0077] The application 312 performs operations associated with the components of the system 200. Some of these operations can include receiving, processing, and / or outputting signals when using the system 200. Other of these operations can include controlling the components of the system 200 based on the received, processed, and / or output signals. Other of these operations can include receiving and / or processing detector signals generated when using the system 200. This processing can include generating graphs from the detector signals and / or extracting information about the diffusing particles being analyzed from the graphs / detector signals, including their size as described above. Other of these operations can include outputting such extracted information, for example, outputting to a display of the system 200. Some or all of the operations described in this disclosure can be controlled by instructions implemented in the application 312. The operations can be implemented using hardware, firmware, software, or any combination of these methods. Referring Figure 3 to the exemplary embodiments, the application 312 is implemented in software (including computer-readable and / or computer-executable instructions) that is stored in the computer-readable medium 308 and accessible by the processor to execute the instructions implementing the operations of the application 312. The application 312 can be written using one or more programming languages, assembly languages, scripting languages, etc.

[0078] Note that a device including the processor 310 and the computer-readable medium 308 operatively coupled to the processor 310, having computer-readable instructions stored thereon that, when executed by the processor 310, cause the device to perform any of the above operations (or various combinations thereof), is covered by this disclosure. The computer-readable medium 308 is similarly covered.

[0079] The system can also include other components and devices, such as a high-performance liquid chromatography (HPLC) device operatively coupled to the cavity of the optical microcavity.

[0080] Figure 6A A schematic diagram of another exemplary system configured to perform the present method is shown. Figure 6A The system of Figure 2 System 200 of

[0081] Any system (including Figure 2 and Figure 6A the systems shown in

[0082] This system can be configured to allow cleaning or replacement of the optical microcavity, the optical fiber, or both.

[0083] This system can be calibrated using various methods (including internal calibration). Internal calibration can enable absolute determination of sample physical parameters (including size / mass and diffusion constant). Exemplary internal calibration methods can rely on applying a perturbation to the optical microcavity (e.g., pulse - modulating the cavity length L) to cause a standardized response (i.e., resonance shift for particles of known size / mass and diffusion constant). As mentioned above, this system and method can be characterized by the signal - to - noise ratio (SNR) achieved when detecting diffusing particles of a specific size / mass. (See Figure 16 .) In some embodiments, for diffusing particles with a molecular weight of no more than 100 kDa, no more than 75 kDa, no more than 50 kDa, no more than 30 kDa, no more than 15 kDa, or no more than 1 kDa, the SNR is at least 75, at least 80, at least 90, at least 100, or at least 120. This includes achieving an SNR range (e.g., from 80 to 130) for diffusing particles with a molecular weight between any values in this paragraph (e.g., from 1 kDa to 80 kDa).

[0084] Figure 10A and Figure 10B Further illustrates the PDH servo loop 236 of system 200 ( Figure 2 ) and Figure 6AThe PDH servo loops of the systems shown are each configured as high-pass filters that suppress frequencies below their respective locking bandwidths (LBWs), enabling the detection of higher-frequency perturbations caused by diffusing particles. The frequency upper limit is set depending on the material of the optical microcavity and the optical bandwidth (PBW) of the medium therein. The LBW and PBW together determine the range of detectable frequencies and thus the bandwidth of each system (which can be referred to as a "molecular velocity filter"). Since the LBW and PBW are tunable (e.g., via the PDH servo loop (LBW) and the optical microcavity and the medium therein (PBW)), the bandwidth of the molecular velocity filter is also tunable.

[0085] The present system can be adjusted to improve or change performance, sensitivity, and dynamic range. Exemplary methods for adjusting performance include changing the frequency and bandwidth of the molecular velocity filter, which can be achieved via a proportional-integral-derivative (PID) controller or by changing the thermo-optic coefficient. Exemplary methods for changing the sensitivity and dynamic range of the system include changing the input laser power, coupling efficiency, thermo-optic coefficient, cavity finesse, and cavity length.

[0086] Exemplary embodiments of the present method and system are provided below.

[0087] In Example 1, a method for detecting diffusing particles includes (a) introducing a sample comprising diffusing particles into the cavity of an optical microcavity; (b) coupling probe light into the optical microcavity such that the probe light resonates with the optical microcavity, wherein the diffusing particles diffuse into the optical mode volume defined by the coupled probe light in the cavity; and (c) detecting the output light from the optical microcavity as a function of time while maintaining resonance, wherein the diffusing particles produce a change in the detected output light.

[0088] Example 2 is the method of Example 1, wherein the optical microcavity is a Fabry - Perot microcavity. Example 3 is the method of any one of Examples 1 - 2, wherein resonance is achieved by satisfying mλ = 2nL, where m is an integer, λ is the wavelength of the probe light, n is the refractive index of the sample, and L is the cavity length of the optical microcavity. And Example 4 is the method of Example 3, further comprising adjusting λ, adjusting L, or adjusting both during step (c) to maintain resonance. Example 5 is the method of any one of Examples 1 - 4, wherein the probe light resonates with the fundamental spatial mode of the optical microcavity. Example 6 is the method of any one of Examples 1 - 5, wherein the sample has a concentration of diffusing particles such that the probability of a diffusing particle occupying the optical mode volume is less than one. Example 7 is the method of any one of Examples 1 - 6, further comprising analyzing the detected output light to calculate the hydrodynamic radius of the diffusing particles. Example 8 is the method of Example 7, wherein the diffusing particles have a hydrodynamic radius of less than 10 nm. Example 9 is the method of any one of Examples 1 - 8, wherein the detected output light is transmitted probe light including a recess or the detected output light is back - reflected probe light including a spike, and the method further comprises measuring the full width at half maximum (FWHM) of each recess or spike and calculating the hydrodynamic radius based on the measured FWHM. Example 10 is the method of any one of Examples 1 - 8, wherein the detected output light is transmitted probe light including a recess or the detected output light is back - reflected probe light including a spike, and the method further comprises measuring the autocorrelation function (ACF) based on the recess or spike and calculating the hydrodynamic radius based on the measured ACF.

[0089] In Example 11, a system for detecting diffusing particles comprises: (a) an optoelectronic component configured to couple probe light into an optical microcavity defining a cavity such that the probe light resonates with the optical microcavity; (b) an optical microcavity defining a cavity into which a sample including diffusing particles can be introduced to diffuse into the optical mode volume defined by the coupled probe light; (c) a detector configured to detect output light from the optical microcavity as a function of time; and (d) an optoelectronic component configured to maintain resonance while using the detector to detect output light from the optical microcavity as a function of time.

[0090] Example 12 is the system of Example 11, where the optical microcavity is a Fabry - Perot microcavity. Example 13 is the system of any one of Examples 11 - 12, where the optoelectronic component (d) provides a Pound - Drever - Hall (PDH) servo loop that couples the source of the probe light and the optical microcavity. Example 14 is the system of any one of Examples 11 - 13, further comprising an actuator operably coupled to the optical microcavity and configured to adjust the cavity length L of the optical microcavity. Example 15 is the system of Example 14, where the PDH servo loop is coupled to the actuator. Example 16 is the system of any one of Examples 11 - 15, where the system does not include an optoelectronic component associated with any other light source other than the source of the probe light. Example 17 is the system of any one of Examples 11 - 16, where the optical microcavity is non - adsorptive with respect to the diffusing particles. Example 18 is the system of any one of Examples 11 - 17, further comprising a controller that includes a processor and a non - transitory computer - readable medium operably coupled to the processor, the non - transitory computer - readable medium including instructions that, when executed by the processor, cause the controller to perform operations including: receiving a signal from a detector; processing the signal to calculate the hydrodynamic radius of the diffusing particles; and outputting the calculated hydrodynamic radius to the system.

[0091] Example

[0092] Example 1

[0093] Figure 2 The system 200 is constructed and then used to analyze samples containing different proteins, including streptavidin (a tetrameric protein with a mass of 66 kDa and a diameter of 5 nm); carbonic anhydrase (an enzyme with a mass of 30 kDa and a diameter of 4.6 nm); aprotinin (a globular polypeptide with a mass of 6.5 kDa and a diameter of 2.7 nm); and c - Myc (a peptide with a mass of 1.2 kDa and a diameter of 0.75 nm).

[0094] Separate samples at a low enough concentration are prepared by dispersing the molecules in water to ensure that the probability of a single molecule occupying the optical mode volume is less than 1.

[0095] The experiment is conducted by placing droplets of the separate samples in the cavity of the FP microcavity 100. The probe light 211 is coupled into the FP microcavity 100 such that it resonates with the fundamental spatial mode of the FP microcavity 100 (as ensured by the PDH servo loop 236). While maintaining resonance (as ensured by the PDH servo loop 236), the output light as a function of time is detected using a detector 222 (which detects the probe light 112 transmitted via the output optical fiber 106). Figures 4A - 4C An exemplary plot of the signal from the detector 222 as a function of time for each sample is shown (Figure 4A , streptavidin; Figure 4B , carbonic anhydrase; and Figure 4C , aprotinin). These results demonstrate the ability of the present method and system to detect diffusion events from single protein molecules having extremely small sizes (e.g., only a few nm). In Figures 4A - 4C 's figure, the diffusion events appear as depressions in the transmitted probe light. The output light as a function of time is also detected using detector 220 which detects the probe light 112 retroreflected through input fiber 102. In those figures (not shown), the diffusion events appear as spikes.

[0096] In addition, as Figure 5A and Figure 5B shown, system 200 can be used to resolve differences in mass and thus differences in hydrodynamic radius. Specifically, Figure 5A is a plot of the average FWHM of the depressions measured from each corresponding figure of Figures 4A - 4C and another figure obtained from a sample including the protein c-Myc. Figure 5B is a plot of the average FWHM of the spikes measured from the corresponding figures obtained from detector 220.

[0097] Example 2

[0098] Introduction

[0099] Tools for measuring the properties of individual molecules included in heterogeneous solutions have become the cornerstone of modern molecular and biomolecular research. Almost all single-molecule methods use extrinsic labels, and while these labels provide important contrast and specificity, the dye-labeling procedures are difficult and interfere with the native function of biomolecules. Most single-molecule methods, including all current label-free methods, also rely on surfaces for immobilization, which is an expensive compromise since measurements may be biased towards detecting subpopulations in a mixed sample, disrupting native molecular interactions, altering kinetics, and generally excluding quantification of valuable solution-phase properties such as diffusion constants.

[0100] In this example, enhanced light-molecule interactions in a high-finesse fiber Fabry–Pérot microcavity are used to detect individual biomolecules as small as 1.2 kDa with a signal-to-noise ratio of >100, even when the molecules are freely diffusing in solution. The method described herein provides 2D intensity and time maps, enabling discrimination of subpopulations in a mixed sample. Notably, a linear relationship between time and molecular radius is observed, enabling the ability to collect key additional information on diffusion and solution-phase conformation. Additionally, mixtures of biomolecular isomers of the same molecular weight can be resolved. Detection is based on a novel molecular velocity filtering and dynamic thermal triggering mechanism that utilizes both photothermal bistability and Pound–Drever–Hall cavity locking. The results presented below were achieved in the absence of an external surface-based signal multiplier such as plasmon enhancement and include a SNR far exceeding the highest reported for label-free single-molecule sensing. Most importantly, the method operates without surface interactions, allowing interrogation of unperturbed label-free solution-phase molecules and assessment of molecular diffusion maps, a carrier of key information on biomolecular conformation and binding. This technology has broad applications in the life and chemical sciences and represents a significant advancement in label-free in vitro single-molecule techniques.

[0101] Materials and Methods

[0102] Experimental setup

[0103] Mirror Fiber Fabrication

[0104] First, a copper-coated fiber (IVG Fiber, Cu600) with a 125-μm cladding diameter was etched using nitric acid (70%). This etching process removed the copper coating, leaving a carbon coating above the cladding. The carbon coating was removed with a small amount of diamond paste on a cloth; however, this step was removed for subsequent fiber fabrication due to significant contamination from the diamond paste. The fiber was flat cut (<0.2–1°) using an automated cutter (AFL Fujikura, CT-106).

[0105] An 18W CO2 laser (Synrad, 48-1KAM) generates an ablation laser beam, which is guided and modified using polarization, phase delay, and other associated reflective and ZnSe focusing optics. An arbitrary waveform generator (Agilent, 33220A) controls the beam characteristics, and a digital optical power meter head (Thorlabs, S314C) with an attached console (Thorlabs, PM100D) is used to measure the beam power. The fiber substrate is mounted on top of a fiber fixture (Thorlabs, HFF003) that is located on a 3-axis translation stage (Thorlabs, MTS50-Z8; MTS50B-Z8; MTS50C-Z8) driven by a DC servo motor controller (Thorlabs, KDC101), which is fixed to a long-range single-axis translator (Thorlabs, LNR502( / M)) driven by a motor controller (Thorlabs, BSC201) for inspection-ablation positioning. A CCD camera (Thorlabs, CS165MU) is coupled to a long working distance microscope system (Navitar, 160-10) with a 20× magnification, 0.42NA infinity-corrected objective lens (Mitutoyo, 378-804-3), which is illuminated by a 635nm LED source (Thorlabs, LEDD1B) for imaging the fiber position. Optimizing the ablation alignment is facilitated by illuminating the core with an optical fault finder (VFLTOOL, HGB30). The laser is set to have a power of 0.28W, and the exposure time of 250ms is controlled using a shutter in front of the fiber. These exposure parameters produce a fiber with an average radius of curvature (ROC) of 48μm at the base of the ablation and an average diameter of 21μm calculated by a 2-σ Gaussian fit to the ablation profile (interferometric profiles and the resulting 2D depth profiles were obtained but not shown).

[0106] A ZYGO interferometer is used to characterize the fiber. Two perpendicular slices of the surface profile are analyzed. To calculate the ROC, the center of the ablation is assumed to be the minimum. Then a polynomial fit is performed, and the successive derivatives are averaged to calculate the ROC. For the diameter, a Gaussian fit is performed, and the diameter is taken as twice the standard deviation of the fit. The ellipticity of the ablation is calculated by comparing both the ROC and diameter values of the perpendicular slices. The eccentricity of the ablation is also measured by coupling the fault finder through the core of the fiber and then comparing it to the center of the ablation. The eccentricity, ROC, diameter, and ellipticity are all used to determine the viability of the fiber.

[0107] The fiber optic substrate is commercially coated at the wavelength of maximum reflectivity at 635 nm (LASEROPTIK GmbH, Germany) or 780 nm (LAYERTEC GmbH, Germany), where alternating layers of Ta2O5 and SiO2 are deposited using ion beam sputtering (IBS). The resulting distributed Bragg reflector surfaces have a transmission loss <20 ppm, an absorption loss <10 ppm, and a scattering loss <16 ppm.

[0108] Ferrule Assembly Preparation

[0109] The cavity bridge assembly is prepared using a fused silica ferrule (VitroCom, 8×1.25×1.25 mm) with an inner hole of 131 μm. The glass ferrule is cleaned using an air plasma cleaner (Harrick Plasma, PDC-001-HP) for 10 minutes. A thin layer of UV curable adhesive (Dymax, 9037-F) is placed on two 150 V piezoelectric elements (Thorlabs, PA4DG), which are aligned flush with the ferrule, thus ensuring that the direction of translation is aligned with the long axis of the ferrule. The adhesive is then cured using a UV lamp (Rolence Enterprise, Q6 UV). The assembly of the ferrule and the two piezoelectric elements is then fixed to a glass block approximately 20×7×3 mm in size. This assembly is then placed in an oven at 65 - 75 °C for 2 - 3 hours for additional curing of the adhesive. After this, wires are soldered to the piezoelectric elements. Two cuts are made in the ferrule to facilitate cavity length transition: a full cut to divide the ferrule into two parts to maximize cavity length transition, and a half cut to maintain fiber alignment along the inner hole. A diamond wire fixed in a jeweler’s saw is used to make these cuts. The full cut is made off-center, and the half cut is made near the center of the ferrule. After the full cut, a small piece of wire is placed in the hole to indicate when the cut reaches the hole. During the cutting process, canned air is used to remove glass dust.

[0110] The ferrule is cleaned after cutting by first moving it in deionized water for 5 minutes. Visualized using a digital microscope, micropore water (Millipore water) is suctioned through the hole of the ferrule and a section of fiber is moved through the hole to remove any residual glass dust. This process is repeated until no visible dust remains. The ferrule is then rinsed under micropore water, and a few drops of methanol (≥99.9%) are passed through the ferrule, and then the ferrule is thoroughly dried using a nitrogen gas line.

[0111] Fiber Optic Cavity Construction

[0112] The aforementioned high-reflectivity, mirror-coated optical fiber was fusion spliced to a connectorized jumper (Thorlabs, P3-630Y-FC-2) using a fusion splicer (Fujikura, FSM-100P). The optical fiber was aligned using a 6-axis piezoelectric actuator stage (Thorlabs, MAX602D). The input optical fiber was mounted onto this stage using a tapered v-groove fiber holder (Thorlabs, HFV002). The output optical fiber was held by a v-groove fiber holder fixed to an XYZ translation stage. For visual alignment of the optical fibers, two cameras were aligned perpendicular to the fiber axis. The top-down view used a CMOS camera (Thorlabs, DCC1545M) connected to a zoom lens (Navitar, 1-50487). This imaging system was used to both align and estimate the distance between the optical fibers. The second perpendicular axis used a digital microscope (Dino-Lite, AM4113ZT) for visualization. Using the two camera axes, the optical fibers were then visually and roughly aligned with each other using the 6-axis stage. The next step was to finely align the optical fibers by recording resonances. For this, a ramp signal from a data acquisition board (DAQ, NI, BNC-2120) was applied to a piezoelectric controller (Thorlabs, MDT693B), which drove the piezoelectric element to align with the fiber axis. Then a laser (635 - 760 nm) was injected into the input optical fiber and collected through the output optical fiber to an avalanche photodiode (APD, Thorlabs, APD430A). The resonances were measured in transmission and optimized by adjusting all the parameters of the 6-axis stage. The cavity finesse was characterized by using a wavelength-tunable external cavity diode laser (Newport, TLB-6704) or by introducing sidebands at a known frequency (2.6 GHz) via an electro-optic phase modulator (EOM, EOSpace, PM-0S5-10-PFA-PFA-633, PM-0S5-01-PFA-PFA-765 / 781) and extracting the linewidth via Lorentzian fitting.

[0113] The optical fibers were guided into the fabricated ferrule using top-down and parallel views, and a cavity was formed at the center of the half-cut. To fix the optical fibers inside the ferrule, 2 μL of low-viscosity UV-curing glue (Masterbond, UV16) was deposited sequentially on each optical fiber at the left entrance of the non-slotted ferrule and the right entrance of the slotted ferrule. The glue was drawn onto the optical fiber using capillary action and UV-cured (Rolence Enterprise, Q6 UV) after entering the ferrule by ~2 mm. Then the piezoelectric element on the bridge was attached to a piezoelectric actuator (nPoint, D.200) and the piezoelectric element was driven to evaluate the resonances under constant cavity translation.

[0114] Optical setup

[0115] Experiments were conducted on a custom-built setup (seeFigure 6A )。A single-frequency continuous-wave diode laser with a <1 MHz linewidth (660 nm, Cobolt Flamenco, 90261, 300 mW) or a tunable Ti-Saph cavity laser with a <100 kHz linewidth operating at a single frequency (760 or 780 nm, MSquared, SolsTiS) passes through a linear polarizer and a half-wave plate, and then is fiber-coupled into an electronically variable optical attenuator (Thorlabs, V600), and then enters an EOM (EOSpace, PM-0S5-10-PFA-PFA-633, PM-0S5-01-PFA-PFA-765 / 781) driven by a voltage-controlled oscillator (VCO, Mini-Circuits, ZX95-209-S+, 200 MHz). Then the light is coupled into the input fiber of the cavity through a fiber-based beam splitter (Thorlabs, TW670R3A1), and the power injected into the cavity is between 5 - 35 μW. The circulating power (P circ ) is calculated using Equation 1:

[0116]

[0117] where P inis the input power, η is the mode-matching overlap integral. T is the transmission loss of the mirror coating (10 ppm), and F is the cavity finesse. This expression is valid for cavity systems affected by absorption losses. The remaining path of the beam splitter is collimated and then focused (Thorlabs, C560TME-B) onto the active area of the APD (Thorlabs, APD430A), enabling the collection of reflected resonant light. The reflected signal voltage is sent to a DAQ board (NI, BNC-2120), and the reflected signal voltage is monitored using custom software. The transmitted light is collected through the output fiber of the cavity, collimated, and focused (Thorlabs, C560TME-B) onto the active area of the APD (Thorlabs, APD430A). The transmitted signal voltage is sent to a duplexer (Mini-Circuits, ZDPLX-2150-S+), and the low-frequency component (DC-10 MHz) is then routed to the DAQ board (NI, BNC-2120) to monitor the transmitted signal. The high-frequency component (50-2150 MHz) is amplified and sent to a mixer (Mini-Circuits, ZP-1MH-S+), where the high-frequency component is multiplied by the sine signal of the VCO in the homodyne detection scheme. The resulting frequency component is low-pass filtered (Mini-Circuits, SLP-1.9+) to extract the DC error signal and routed to the error input of the Pound-Drever-Hall lock box (PDH, Vescent, D2-125). The locking feedback is supplied to the piezoelectric element driving the cavity length via the servo output of the PDH lock box.

[0118] Hardware control and data acquisition software

[0119] Experiments were conducted using code written in Python 3 for the laboratory to handle both instrument control and data acquisition. The code interacts with the DAQ board (NI, BNC-2120) and the oscilloscope (Rigol, DS1104). For DAQ and oscilloscope connections, control was established using the PyLabLib package (doi.org / 10.5281 / zenodo.7324876) released under the GPL-3.0 license. The control code was written with a graphical user interface (GUI) to streamline user control. The GUI and interactive elements of the program are bound using PySide2 and use the Qt framework under the GPLv2 license. A copy of the control software is available under the GPLv3 license for free use.

[0120] Sample preparation

[0121] Lyophilized streptavidin (MilliporeSigma, 189730), carbonic anhydrase (MP Biomedicals, 0215387910), aprotinin (MilliporeSigma, A6106) and c-Myc peptide (MilliporeSigma, M2435) were dissolved in phosphate-buffered saline (pH 7.4) to 1 mg / ml -1 , aliquoted to appropriate volumes and stored at -20 °C. For experiments, samples were thawed on ice and diluted to working concentrations (0.25 pM - 15 pM) in filtered ( Whatman Anotop, WHA68091002) ultrapure micropore water (18 MΩ, pH 7). To ensure that measurements would be at the single-molecule level, the optical mode volume was calculated to accommodate an average of 0.7 molecules at the highest working concentration (15 pM).

[0122] The DNA sequence of each construct was manually designed and verified by NUPACK (www.nupack.org). Commercially available oligonucleotides (Integrated DNA Technologies, error! Reference source not found.) were purchased and used without purification. To assemble each structure, the corresponding DNA strands (5 μM) were mixed in folding buffer (25 mM HEPES, 100 mM KCl, 10 mM MgCl2, pH 7.4), and then annealed in a PCR thermal cycler (Bio-Rad) from 95 °C to 20 °C over 2 hours by a linear cooling step ( - 0.1 °C every 10 s). The products were further purified on a pure system (Cytiva) using a size exclusion chromatography column (Superdex 200 increase 10 / 300) to remove extra strands and potential aggregates. The final concentration of each construct was determined by Nanodrop (Thermo Fisher Scientific). Samples were stored at 4 °C for less than 1 month before use.

[0123] Table 1. DNA structures and sequences

[0124]

[0125]

[0126] Experimental data collection

[0127] Single biomolecule diffusion experiments

[0128] Before introducing the protein, filtered ( Whatman Anotop, WHA68091002) MilliQ water (8 μL) was added to the cavity. The input power in the cavity was controlled with the voltage applied to the VOA (Thorlabs, V600A) to ensure that all comparable experiments were performed with consistent power. The fundamental transmission cavity mode was found under active cavity length transitions, and the PDH was locked with a proportional gain of -40 dB. The lock position was tuned to the maximum possible transmission using the relative voltage offset on the lock box (Vescent, D2-125). If a spurious event was detected during the lock, the cavity was unlocked and cleaned under a filtered MilliQ water flow and dried with N2. This process was repeated after the protein experiment to ensure that the cavity was clean. The transmission and reflection signals as a function of time were monitored at an acquisition frequency of 50 kHz or 500 kHz. The intensity-time traces containing single molecule events were saved as.csv files every 30 s using the custom software described above. The water control experiment was continued until 5 minutes of data were collected without spurious signals.

[0129] A protein solution (streptavidin, carbonic anhydrase, aprotinin, or Myc tag, 0.2 - 15 pM, 8 μL) or DNA (8 μL, 10 pM) in filtered MilliQ water was introduced into the cavity. The input power in the cavity was controlled with the voltage applied to the VOA to ensure that all comparable experiments were performed with consistent power. The fundamental cavity mode was found under active cavity length transitions, and the PDH was locked with a proportional gain of -40 dB. The transmission and reflection signals as a function of time were monitored at an acquisition frequency of 50 kHz or 500 kHz. The intensity-time traces containing single molecule events were saved as.csv files every 30 s using the custom software described above.

[0130] Locking bandwidth characteristics

[0131] The locking bandwidth (LBW) of the cavity was measured by adding a harmonic perturbation (F h ) of known frequency and amplitude together with the error signal (e) to the PI input using a voltage adder (see Figure 11 ). To maintain the linear relationship between the voltage of the error signal and the frequency detuning of the cavity during the lock, the amplitude of the perturbation was optimized to 0.2× the peak-to-peak amplitude of the error signal. When the cavity was locked, the sum of the perturbation signal and the error signal was recorded for perturbation signals at different frequencies. This allowed the measurement of the frequency at which the lock no longer effectively compensated for system perturbations to determine the 0 dB gain value and thus the LBW of ~5 kHz (see Figure 10A ).

[0132] Noise background experiment

[0133] Measure the noise distribution of the locking cavity according to the error signal data. Use the slope of the scanned error signal calibrated with a 2.6 GHz modulation sideband to convert the voltage amplitude of the error signal to its corresponding cavity frequency offset. Extract the RMS value of the cavity resonance frequency offset according to the Fourier transform of the calculated error signal. Perform this measurement for different proportional gain settings, where the maximum noise suppression is achieved at ~5 KHz for the maximum locking bandwidth. Measure the background noise according to the off-resonance error signal. This value, along with the cavity finesse and gain, determines the LBW. It is found that the PDH locking loop has effective noise suppression for external perturbations at the background noise level throughout the LBW. Although the source of low-frequency noise is mainly due to ambient acoustic waves (mechanical waves are coupled to the optical table through the cavity system via contact points), a low-pass passive filter is used before the piezoelectric connection to suppress the higher-frequency noise (above the LBW) inherent in the electronic control system. It is expected that the mechanical resonance of the cavity appears at frequencies above the LBW, but its amplitude is lower than the detector background noise, at the level of 10 3 HzHz -1 / 2 (see Figure 12 ). The high mechanical passive stability and active PDH of the cavity define the frequency region where the cavity can be more sensitive to internal perturbations, as further described below.

[0134] Voltage Pulse Experiment

[0135] To demonstrate the mechanism described below (and see Figure 10C ), a controlled perturbation is introduced into the locking cavity to simulate a molecular perturbation to the cavity. The entry of molecules into the cavity causes an increase in the average refractive index and thus a decrease in frequency. This frequency decrease is simulated by temporarily and slightly increasing the cavity length by applying a voltage pulse to the piezoelectric element. Based on the duration of the measured molecular migration events (from the representative signal traces of proteins obtained but not shown) and their prominence, the parameters of the pulse (including duration and amplitude) are initially selected to roughly cause a similar detuning amplitude and cavity transmission profile (see Figures 13A - 13B ). Specifically, as Figures 13A - 13BAs shown, a square wave pulse signal with a duration of 140 μs - 1 ms and a repetition rate of 1 Hz is generated to affect the cavity length while the cavity is locked. The pulse generated by a function generator (Keysight, DSOX1204G) is added to the servo output of the locking box; then this combined signal is directed to the piezoelectric element. The time-varying transmission signal of the locked cavity is recorded to ensure that all perturbation events and pulse signals are correlated. Due to the length of the cable driving the piezoelectric element, the response time of the transmission signal to the DAQ card and the electromechanical device, a small response delay is seen. The transmission plot is the result of a step-down voltage perturbation that causes a sharp decrease in the locked transmission signal due to the photothermal effect (a), followed by a brief recovery to the locked state through PI feedback (b), then as the step-up voltage of the pulse moves the cavity in the opposite direction, the transmission signal drops a second time (c), and finally the PI control restores the locked state (d). When a pulse is generated, the resulting perturbation has a distribution similar to the distribution of the cavity's transmission signal caused by molecular interactions, i.e., a shift to lower frequencies ( Figure 7A ).

[0136] Photothermal broadening and thermo-optic coefficient

[0137] Optical microcavities with small mode volumes are vulnerable to dynamic photothermal nonlinearities that originate from the gradual development of intense light fields, leading to a temperature increase in the cavity. The coupling between heat and the cavity resonance frequency can result in resonance frequency drift and cooling cascades.

[0138] These photothermal dynamics depend on the thermo-optic coefficient (dn / dT) of the medium that governs heat dissipation. Increasing the temperature of a medium with a negative dn / dT will result in a decrease in the refractive index and thus a lower cavity resonance wavelength (higher frequency). When scanning the cavity length or the laser frequency, the resonance may drift to higher or lower wavelengths depending on the direction of the scan and the cavity-laser detuning. When the cavity length is scanned to a longer length, optimizing the resonance condition (Equation 2),

[0139] mλ = 2nL Equation 2

[0140] where m is an integer, λ is the wavelength, n is the refractive index of the medium, and L is the cavity length, appears to change as n decreases, resulting in a need for further higher lengths and a distorted line shape (see Figure 14 ). This behavior is expected in FFPCs when the medium is air and heat dissipation is mainly dominated by the mirror coating, where the "effective" negative dn / dT due to thermal expansion results in a shorter cavity length. A negative dn / dT is also expected when the medium is water. As Figure 14As shown, the optothermal behavior in the FFPCs described herein is characterized with water by actively scanning the cavity to increase the length and observing the direction of optothermal broadening in water. A positive voltage gradient is applied to one of the piezoelectric elements, and the positive voltage corresponding to an increase in cavity length is confirmed by tuning the wavelength of the pump laser and observing the shift of the resonance position to higher voltages at lower pump wavelengths. The direction of the broadened resonance is observed to be towards longer cavity lengths and thus lower wavelengths, as expected for a system dominated primarily by a medium with a negative thermo-optic coefficient.

[0141] Optothermal bandwidth measurement

[0142] The optothermal broadening of the cavity line shape as a function of the applied ramp rate is recorded to quantify the optothermal bandwidth of the cavity in water (see Figures 15A - 15B ). The resonance in transmission as a function of time is recorded, and the cavity length is tuned using a ramp signal applied to the piezoelectric element from a function generator (Keysight, DSOX1204G). Phase modulation sidebands applied at a known frequency (2.6 GHz) are used as frequency calibration markers for each trace. Initially, the ramp frequency and amplitude are chosen to minimize the optothermal effects in the cavity. This is determined by matching the resonance line shapes during both the increase and decrease of the ramp voltage. This trace is used to measure the linewidth of the cavity. Thereby, both the ramp rate is scanned and the traces are recorded to obtain both the increase and decrease in the ramp voltage component of the ramp signal.

[0143] Data analysis

[0144] Single-molecule diffusion and autocorrelation analysis

[0145] Analysis of the transmitted and reflected signals caused by single biomolecular perturbations is performed using custom-written code in Python 3. First, the biomolecule and water control data collected at a single input power are normalized to the maximum signal intensity (for reflection) or minimum signal intensity (for transmission) such that all signal peaks at comparable powers can be selected using a single threshold between 0 - 1. Single events are identified and analyzed using the SciPy.signalfind_peaks package. Signal peaks are selected with a prominence threshold of 0.35. A 2 ms time filter is applied to ensure that only peaks separated by more than 2 ms in time are selected. The time width is determined at the full width at half maximum of the event, and the prominence is determined as the vertical distance between the maximum of the peak and the local background intensity.

[0146] Autocorrelation analysis is performed using custom code written in Python 3 to quantify the temporal behavior of single-molecule events in the intensity-time traces. A normalization function (Equation 3) is generated by comparing time offset values to each other:

[0147]

[0148] where k is the time step, N is the total number of points, Y i is the intensity at a specific time, and is the average intensity. Several 30 s intensity-time traces of diffusing proteins in the locked cavity were concatenated. To ensure that the background is approximately continuous between files, the minimum value of each file was found and then the minimum value was subtracted from each point. Events were identified using an intensity threshold that was 2.5 standard deviations from the mean and were used to generate autocorrelation traces. The function sm.tsa.acf from the package statsmodels.api was used to generate the autocorrelation function. These functions were plotted for four different proteins (streptavidin, carbonic anhydrase, aprotinin, and Myc tag, see Figure 8A ) and values of different decay times were extracted. The time to decay to 40% of the autocorrelation time was shown to be linearly related to the protein radius, Figure 8B . This linear trend was maintained for a wide range of decay values (data not shown), demonstrating the robustness of the analysis. A copy of the analysis software is available under the GPLv3 license for free use.

[0149] Locked bandwidth analysis

[0150] To extract the effective LBW of the system, the Fourier transform of the signal measured at point S for each perturbation frequency was calculated (see Figure 11 ). The magnitude at the perturbation frequency was extracted and normalized with respect to the input signal F h and converted to decibels. The result of the normalized values was shown as a function of the input frequency of the sine wave ( Figure 10A ). The corresponding LBW was determined to be ∼5 kHz at the 0 dB crossover point. At higher frequencies, the signal was amplified due to a change in the phase of the control circuit that is thought to be a servo bump. At even higher frequencies, the lock has no effect on the perturbation signal and the relative intensity remains at 0 dB.

[0151] Determination of signal-to-noise ratio

[0152] The data traces were smoothed using various bin sizes to generate a moving average, following:

[0153]

[0154] where n is the bin size and F i is the value of the function at index i. This smoothing process was performed for a series of different bin sizes from n = 1 to n = 250. After smoothing, the traces were normalized. Smoothing of the data was only performed for SNR calculations. Then, to calculate the signal-to-noise ratio (SNR): the background was taken from the longest background segment in the trace (σN ) standard deviation. Then calculate the signal (S) based on the peak amplitude, and calculate the SNR of the protein measured in this example (see Figure 16 ):

[0155]

[0156] Quantify the SNR of each peak at each smoothing bin size. Give the maximum average SNR, and use a bin size of 190 for all datasets.

[0157] As Figure 16 shown, for comparison with other techniques (when provided), the SNR values are directly taken from the following references: V.R. Dantham et al., Nano Lett. 13, 3347 - 3351 (2013); P. Zijlstra et al., Nat Nanotechnol. 7, 379 - 382 (2012); W. Yu et al., Nat Commun. 7, 12311 (2016); G. Young et al., Science. 360, 423 - 427 (2018); M. Dahmardeh et al., Nat Methods. 20, 442 - 447 (2023). For the reference N.P. Mauranyapin et al., Nat Photonics. 11, 477 - 481 (2017), use WebPlotDigitizer to extract the data from Figure 9A to.csv. Then calculate the SNR by taking the maximum value of the signal and dividing it by the standard deviation of the region without signal. For the reference J. Su et al., Light Sci Appl. 5, 1 - 6 (2016), the resonance shift is taken as 5 nm as a high estimate from Figure 10C , and divided by the reported noise level of 9.6×10 -4 fm. For the reference M.D. Baaske et al., Nat Nanotechnol. 9, 933 - 939 (2014), calculate the standard deviation of the noise by estimating 3σ from Figure 10B and dividing by 3. Then use the average reported value of 2.5 fm for the 8 - mer, and then divide by the previously calculated standard deviation to calculate the SNR.

[0158] Determination of the optical bandwidth

[0159] To determine the optothermal bandwidth, the frequency shift of the optothermal broadening peak is calculated for each corresponding ramp rate. For each ramp rate, the optothermal broadening peak has a large distance between the left sideband and the main peak, which is determined as the peak-to-peak distance. Using this information, the frequency shift for each ramp rate is then calculated by computing the difference between the optothermal broadening peak-to-peak distance and the optothermal narrowing peak-to-peak distance. The frequency shift as a function of the ramp rate (see Figure 14 ) is then fit to Equation 6.

[0160]

[0161] where β ad and τ correspond to the adiabatic thermal resonance shift and the thermal response time constant, respectively. β(x) is the frequency shift and x is the linewidth. β ad is calculated to be 8.28 linewidths and τ is calculated to be 23.7 linewidths per microsecond. Equation 7 is then used:

[0162]

[0163] τ is converted to f th (21 kHz), which is the bandwidth stable for the optothermal resonator length.

[0164] Simulation and calculation

[0165] The calculated resonance shift

[0166] The analytical expression can be used to determine the frequency shift from small objects. Basically, these are the shifts in the absence of any additional optothermal enhancement and can be considered as the shifts observed in a cavity with a minimal circulating power. Two methods are used. First, Equation 8 is applied following the method of L. Kohler et al. Here, the polarizability of the molecule is calculated via the Lorentz-Lorenz equation (Equation 9) for a mixture weighted by the overlap between the mode volume and the molecule and divided by the volume of the molecule:

[0167]

[0168] where

[0169]

[0170] The mode area and the Rayleigh length are accordingly:

[0171]

[0172] where L is the cavity length, λ m = λ0 / n water is the wavelength in the medium, and the cavity geometry parameter is Gi = 1 - L / R i , where R i is the radius of curvature of each mirror. The cavity frequency shift is:

[0173]

[0174] where c is the speed of light in vacuum and the mode volume is This method is different from that of Kohler et al. because the molecule is much smaller than the mode volume and thus the mode shape shift is negligible on the length scale of the molecule.

[0175] For the four proteins studied in this example, the corresponding resonance shifts (Δv) and losses caused by interaction with the cavity mode were calculated (Table 2).

[0176] Table 2. Calculated resonance shifts caused by the interaction of the proteins streptavidin, carbonic anhydrase, aprotinin, and Myc tag with the mode volume of the FP microcavity. This method is taken from Kohler et al.

[0177]

[0178]

[0179] The second method is adapted from J. Su et al. First, the polarizability is calculated using Equation 8 as shown previously. Then the wavelength shift is calculated according to Equation 14:

[0180]

[0181] where r is the particle radius, λ is the free space wavelength, is calculated to be 1 / 5.5 for the microring of J. Su et al. and 1 / 4.8 for the FP microcavity because the molecule can overlap with the mode maximum. To calculate the resonance shift expected from the interaction of the protein with the microring resonator, the mode volume V m is taken from J. Su et al. and is equal to 330 μm 3 . To compare with the expected resonance shift of the FP cavity used in this example, V m is calculated to be 80 μm 3 . Given these values, the calculated frequency shifts are shown in Table 3.

[0182] Table 3. Calculated resonance shifts caused by the interaction of the proteins streptavidin, carbonic anhydrase, aprotinin, and Myc tag with the optical mode of the microring cavity. This method compares the shifts calculated assuming the mode volumes of the microring cavity and our FP microcavity, and this method is taken from J. Su et al.

[0183] Protein Refractive index Protein radius (nm) Δv ring (kHz) Δv FP (kHz) Streptavidin 1.43 2.8 3.796 15.064 Carbonic anhydrase 1.43 2.1 1.601 6.355 Aprotinin 1.43 1.45 0.530 2.092 Myc tag 1.43 0.757 0.075 0.297

[0184] The magnitude of the resonance shift caused by the interaction between the protein and the modes of the ring microresonator is significantly smaller than the shift from the same interaction in the FP cavity. The confinement of the optical mode in the medium outside the dielectric material in the FP microcavity allows for a stronger overlap between the molecule and the mode compared to the ring, where the mode is confined within the dielectric material (see Table 2). Additionally, the smaller mode volume in the FP microcavity promotes a stronger light-matter interaction, which further results in a larger resonance shift compared to that achieved using a ring microcavity (see Table 3).

[0185] Molecular velocity distribution and molecular mean square displacement power spectral density

[0186] The velocity distribution of particles undergoing free Brownian motion in solution follows Equations 15 and 16 (17):

[0187]

[0188] For a particle of mass m p in solution of mass m f and solution temperature T. The effective mass is calculated to account for the effect of the solution on the acceleration of the particle. Using these equations, one can estimate the likelihood that a particle moves at a given velocity (see Figure 17A ). The smaller the particle, the broader the velocity distribution becomes.

[0189] The mean square displacement power spectral density (MSDPSD) of particles undergoing free Brownian motion can be calculated using Equation 20, which is derived as the solution to the Langevin equation:

[0190]

[0191] For particle radius r, particle mass m, solution density ρ f , solution viscosity η, and solution temperature T. The τ term is the time constant, τ f associated with the inertia of the surrounding fluid, and τ p associated with the inertia of the particle itself. It should be noted that this version of the equation is for free particles (not confined by an optical trap). This equation was plotted for four proteins, using known mass values and radius values for streptavidin, carbonic anhydrase, and aprotinin, and a calculated radius for the Myc tag ( Figure 10A and Figure 17B ). A range from 1 kHz to 1 MHz was used, and the integral was calculated over the range from 5 kHz to 21 kHz, giving 0.00875 μm for the Myc tag 2 , 0.00457 μm for aprotinin 2, for carbonic anhydrase is 0.00315 μm 2 and for streptavidin is 0.00237 μm 2 .

[0192] Simulation optical bandwidth determination

[0193] Finite element simulations were performed using COMSOL (version 6.0). The adiabatic model was used to solve for the stable equilibrium of the cavity resonance frequency / length / wavelength under high circulating power conditions. When the cavity is locked, the heat generated by the absorbed circulating power is dissipated by heat conduction into the surrounding medium. The cavity equilibrium resonance frequency is determined by the thermal conductivity (K) of the system (assuming no convection or radiation). The thermal conductivity of the system was calculated by considering the volume of water equivalent to the optical mode volume, which was heated according to Equation 22. If a water is the absorbed power in water:

[0194]

[0195] where F is the finesse in air / water respectively, and the total absorbed power is:

[0196] P abs = P circ a Equation 22

[0197] Here, P circ is defined in Equation 1 as the circulating cavity power. Thus, the total power flow on the Gaussian surface surrounding the mode volume of the cavity was measured on a 200 μs time scale. This integration time was arbitrarily chosen to be much longer than the measured optothermal time constant of the system (determined to be 7.57 μs). Based on the distribution of the optical modes of the geometry of cavity one (not shown), a water cylinder with a radius of 1.25 μm and a length of 19 μm was used as the heat source of the model. The water with a volume defined by a sphere (radius 25 μm) acts as the heat sink of the system. Glass cylinders with a diameter of 125 μm were placed tangentially on each circular face of the heat source representing the optical fiber. Using the heat transfer modules in solids and fluids, a constant power density of 42.2 GW / m 3 was applied to the cylinder. This power density was calculated based on the circulating power of the cavity and the absorption of water, giving an absorbed power of 3.93599 μW on the volume of the cylinder. The system was set to an initial temperature of 293.15 K, and the system was allowed to evolve with this power input to approach a temperature of 293.28 K.

[0198] To estimate the thermal relaxation time, the system was initialized at the equilibrium temperature and its characteristic temperature decay profile was studied. Then the temperature data varying with time was fitted with an exponential decay curve (see Figure 15B)。This results in a time constant of 7.57 μs, consistent with a tropical width of 66.05 kHz, approximately three times larger than the measured value of 21 kHz (see Figure 15A ). This small difference is due to non-idealities not considered in the simulation, such as additional contact points with the ferrule not being taken into account.

[0199] Optical fiber cavity mechanism

[0200] Finite element simulations of the mechanical fluctuations of the cavity were performed using COMSOL (version 6.0). The optical fiber cavity was modeled (schematic not shown), which includes an optical fiber (glass), a ferrule (glass), a piezoelectric element (lead zirconate titanate, with a Young's modulus of 82.1 GPa and a Poisson's ratio of 0.39), and a glass plate. The piezoelectric element (2.5 mm × 2.3 mm × 2.5 mm) is located on top of a glass block (20 mm × 7 mm × 3 mm). The slotted ferrule part has a left half (3.4 mm × 1.25 mm × 1.25 mm), separated from the right part (4.6 mm × 1.25 mm × 1.25 mm) by a gap of 125 μm. A hole is placed 0.833 mm from the bottom of the ferrule, with a radius of 65.5 μm. There is a semi-cut through the right ferrule for the entire gap of 0.5 mm between the left and right. The optical fibers are each placed inside the holes, tangent to the bottom, with a radius of 125 μm. The 19-μm spacing between the optical fibers defines the optical cavity. Water is modeled as an ellipsoid (1 mm × 0.6 mm × 1.25 mm), centered on the plane at the top of the ferrule, directly above the gap between the optical fibers. The part of this ellipsoid that clamps to the optical fibers and the ferrule is removed. The two modules used for this simulation are solid mechanics for all glass components and the piezoelectric element, and pressure acoustics, frequency domain for the water component. A multi-physics boundary between the two is included. The eigenfrequencies and eigenmodes of this system were calculated for both cases with and without water. The eigenmodes that appear in both the air simulation and the water simulation were used for further calculations.

[0201] The noise spectral density was calculated as described above. According to the simulation, the effective mass of the eigenmode was first calculated, following the equation:

[0202]

[0203] where V is the volume of the simulation, ρ(x,y,z) is the density at a given position, u(x,y,z) is the displacement field at a given position, and max V is the maximum value within the volume of the simulation. Then the zero-point motion of the mode was calculated, following the equation:

[0204]

[0205] where Ω mis the angular frequency of the eigenmode m. Then the optomechanical coupling rate is calculated as follows:

[0206]

[0207] where L cavity is the length of the cavity (here 19 μm), u x is the maximum displacement in the x direction (parallel to the cavity optical axis) for any perturbation, and v0 is the coupled optical frequency.

[0208] A linewidth of 1000 Hz (Γm = 6283.185) is used as an approximation for all modes. Using these linewidths, the frequency noise spectral density can be calculated according to the equation:

[0209]

[0210] where Ω is the noise angular frequency (Ω = 2πf), the temperature is T, and the Boltzmann constant is k B .

[0211] The background noise of the cavity within the molecular velocity bandwidth is one order of magnitude lower than the detector background noise (see Figure 12 ). The step-by-step integration of S 2 from the locking bandwidth (5 kHz) to the optical tropical bandwidth (21 kHz) is calculated, and then the square root is taken to give the integrated noise within the selected region. The integrated noise over the observation bandwidth is on the order of the expected resonance shift from the smallest molecular Myc tag (Table 2).

[0212] Finally, Table 4 collects the parameters of the cavity used in the experiment for this example.

[0213] Table 4. Parameters of the cavity used in this example. The cavity used for collecting data shown in some figures is indicated in this table, and the cavity used for collecting data shown in the supplementary figures is indicated in the corresponding figure captions.

[0214] Parameter Cavity 1 Cavity 2 Cavity 3 Cavity 4 <![CDATA[λ pump (nm)]]> 660 660 660 760 Finesse 37450 17909 21780 30000 Cavity length (μm) 19 19 24 20 Δv (MHz) 206.87 398.83 286.9 261 ROC mirror 1 (μm) 122.4 116.9 60.9 ~170 μm ROC mirror 2 (μm) 97.7 105.5 67.5 ~170 μm Figure 6A X Figures 7A - 7B X Figures 8A - 8B X Figures 9A - 9B X Figures 10A - 10C X

[0215] Results

[0216] As described above, the FFPC is assembled from two single-mode fibers, where the single-mode fibers have concave laser-ablated end faces that are subsequently coated with a high-reflectivity dielectric layer (interferometric images and the resulting 2D depth maps were obtained but not shown). The fiber mirrors are aligned and laterally fixed within the cut fused silica sleeve ( Figure 6A ), to increase the passive mechanical stability of the resonator. The optical mode is probed with a static-frequency laser at 660 - 760 nm, where the laser output is injected into the input fiber. The reflection channel and the transmission channel are independently monitored on a pair of photodiodes ( Figure 6A)。The mirror separation is about 20 μm, resulting in a Q factor of ~2×10 6 and a mode volume on the order of 80 μm 3 . Under ambient conditions, the cavity finesse ranges from 27,000 - 101,000 across multiple cavities and decreases to 17,000 - 37,450 in water ( Figure 6B ). Continuous detection of a single resonance mode is achieved via phase-sensitive Pound-Drever-Hall (PDH) frequency locking, where the cavity length is actively stabilized to a single frequency of the pump laser ( Figure 6A ).

[0217] This example demonstrates the ability to detect single unlabeled proteins and small peptides by introducing samples of various masses and radii into the FFPC. These include tetrameric streptavidin (66 kDa, 2.80 nm), carbonic anhydrase (30 kDa, 2.10 nm), aprotinin (6.5 kDa, 1.45 nm), and the c-Myc peptide (more commonly known as the Myc tag) (1.2 kDa, 0.75 nm). Protein samples were prepared at pM concentrations such that the average occupancy of the optical mode volume is much less than one molecule. The input power into the cavity is ~5 μW, resulting in a circulating power of 5.5 mW.

[0218] Intensity traces show high-amplitude, correlated signals in both the transmission and reflection detection channels from the transient interaction between single diffusing protein molecules and the locked cavity mode ( Figure 7A ), manifesting as a negative peak in transmission and a positive peak in reflection (the mechanism is discussed below). The sign of the event, positive in reflection and negative in transmission, is caused by a biomolecule-induced resonance shift that results in less light transmitted out of the cavity and more light reflected at the locked cavity wavelength.

[0219] Confirmation that the perturbation of the locked cavity originates from biomolecule diffusion rather than environmental noise was achieved using water background measurements taken before and after introducing the protein, during which no signal was observed (data obtained but not shown), and showing that the detected events increase linearly with protein concentration (data obtained but not shown). Time traces were recorded at a time resolution of 20 μs over 30 s intervals (the full 30 s time trace is not shown), where the time scale of single protein diffusion events is on the order of 1 - 2 ms ( Figure 7B ). An extremely high SNR of up to 123 was achieved for the Myc tag ( Figure 16)Contributes to high time resolution, where diffusion events can be observed at a sampling rate of at least 50 kHz. Independent of plasma enhancement mechanisms, conformational or chemical changes in surface-proximity or surface-supported docking molecules, and demonstrated up to 42 times higher SNR for molecules with comparable molecular weights compared to existing label-free biomolecular sensing techniques. This method also achieves a mass detection limit ~25 times smaller than direct mass photometry and, when compared to mass photometry using machine learning, an ~8 times smaller detection limit while providing an ~70 times higher SNR.

[0220] Each transmission event includes both time and intensity data. Plotting the distributions of the time parameter and the intensity parameter provides a 2D distribution signal map that contains unique information about molecular mass and diffusion ( Figure 7B ). Each protein molecule exhibits a distribution of time widths, which are determined by the full width at half maximum (FWHM) of events significantly above the noise, and the prominence increases with increasing protein molecular weight ( Figure 7B ). Due to the randomness of Brownian motion, a variety of widths are expected. The prominence of the peaks differs between the transmission detection channel and the reflection detection channel ( Figure 7B ); this behavior originates from the dispersion characteristic of the FFPC cavity (resonances in reflection and transmission under cavity length transitions were obtained but not shown). In the proportional-integral (PI) control of the PDH system, at a proportional gain value > -50 dB, the average time width of the events remains constant (see Figure 18 ), where higher proportional gain values constitute higher locking bandwidths (LBWs). Therefore, experiments were conducted at an LBW of ~5 kHz above this threshold (see Figures 10A - 10B ). Collectively, these data confirm that these high-amplitude signals originate from the perturbation of the cavity mode volume by single diffusing proteins.

[0221] To demonstrate the ability of this technique beyond simple detection, correlation analysis was used to extract time information from the data, exploring the potential of using this technique for characterization. Correlation spectroscopy is a common tool across time-sensitive biophysical methods, such as fluorescence correlation spectroscopy (FCS) and dynamic light scattering, and thus aims to extract information on the collective diffusion and hence size and mass of molecules. Autocorrelation analysis shows longer time-scale dynamics for proteins with increasing mass ( Figure 8A ). Importantly, the autocorrelation time is linearly proportional to the radius of the protein (data were obtained but not shown). This result confirms the versatility of this new single-molecule technique as a molecular characterization, thus demonstrating the ability to extract meaningful molecular information, including size and diffusion characteristics. Label-free methods for evaluating molecular dynamics have a great impact in biophysical applications.

[0222] Even for a Myc tag as short as a 10 - amino - acid peptide, the extremely high SNR of single - protein events highlights the ability of this technology to extend the dynamic range of applications to both smaller molecules and higher acquisition rates. To demonstrate this, transient events of Myc - tag diffusion with a 2 - μs time resolution were measured (500 kHz acquisition rate, data obtained but not shown). This high collection frequency facilitated the measurement of events as narrow as 26 μs. At a collection frequency of 500 kHz, even these high - speed events can be sampled well beyond the minimum Nyquist condition, highlighting the ability to study kHz processes such as enzyme kinetics and conformational changes without sacrificing SNR. Only the optical bandwidth limits the time resolution (discussed further below).

[0223] Having demonstrated single - molecule measurements of solution - phase, label - free proteins, the ability of this system to resolve simple bimolecular mixture populations is next demonstrated. The resolution of mixtures is crucial for identifying diagnostic biomarkers, understanding disease pathogenesis, and elucidating biomolecule - biomolecule and biomolecule - drug interactions. Techniques such as FCS, which is very valuable for inferring conformation, and fluorescence polarization anisotropy, which is very valuable for determining drug binding, are limited by fluorescence - labeling requirements. Ensemble label - free techniques such as dynamic light scattering can provide diffusion information of biomolecules, but the analysis is limited by the high dependence of scattering on the molecular radius (r 6 ), masking small particles among larger ones and thus requiring monodisperse samples for quantification. Mass photometry overcomes this obstacle via spatial discrimination but is limited by the detection limit and surface use. In contrast, this technology generates 2D maps that contain information about mass and diffusion and can be used as molecular tags ( Figure 7B ).

[0224] First, a mixture of aprotinin and Myc tag with a mass of 5.3 kDa and a radius difference of 0.7 nm was studied ( Figure 9A ). The 2D map of this mixture qualitatively resembles the component distribution. Although it would be difficult to resolve these two populations considering only peak prominence, two distinct populations are clearly evident: a fast - moving population with an average event FWHM of 0.49 ± 0.15 ms and a broader, slower - moving population with an average event FWHM of 1.68 ± 1.37 ms.

[0225] Beyond protein samples, the resolution ability was explored for a bimolecular mixture of DNA isomers with the same mass (16.6 kDa) and composition but different sequences ( Figure 9B):DNA duplex (9 nm) and Y-junction structure (5 nm). Here, the two populations are clearly resolved in both dimensions of the 2D plot. The event prominence is clearly divided into two populations, a low-intensity population with an average prominence of 1.35 ± 0.02 V and a high-intensity population with a lower abundance and a prominence of 1.46 ± 0.03 V. Two partially resolvable populations with similar relative amplitudes to those observed in the peak prominence can be seen in the time domain. Interestingly, the faster diffusing component of the mixture produces a larger amplitude perturbation to the cavity mode. As discussed below, the response of the FFPC to molecular perturbations is influenced by molecular properties as well as multiple dynamic cavity properties. The ability to clearly reveal the presence of two molecules with the same small mass but different conformational and diffusion behaviors indicates that this method provides complementary information that cannot be discerned from mass photometry.

[0226] Discussion

[0227] Detecting single freely moving unlabeled small biomolecules with a high SNR requires a reasonable mechanism by which small perturbations to the optical system can be discerned. The proposed mechanism begins with a change in refractive index as the biomolecule displaces the lower refractive index water molecules in the microcavity (commonly referred to as the "reaction mechanism"). Resonance shifts of 1 - 49 kHz due to the altered optical path length were estimated based on the protein molecular weight (data obtained but not shown). Note that these shifts are much larger (~20 times larger) at equivalent weights than those estimated in whispering gallery mode resonators because of the smaller mode volume and better spatial overlap between the molecule and the optical mode. Based on a combination of high passive stability, active low-frequency stabilization, creating a velocity discrimination window for molecular motion, and using the dynamic optothermal distortion of the resonance line shape, there is the ability to resolve resonance shifts that are small compared to the cavity linewidth (~200 MHz) with such a high SNR. In water, the optothermal effect occurs due to the absorption of some of the cavity circulating power, which changes the refractive index of the medium via the thermo-optic coefficient.

[0228] The combination of mounting the FFPC in a glass ferrule and PDH locking provides excellent stability to the optical system, thus suppressing mechanical and laser frequency noise to the detector limit level ( Figure 10A ). In addition, the mechanical stability of the cavity is extremely high, far below the detector background noise (see Figure 12 ). Importantly, the PDH LBW only suppresses fluctuations at temporal frequencies below 5 kHz (including molecular fluctuations) ( Figure 10A ). This is a key function of the PDH loop because low-frequency mechanical fluctuations can introduce appreciable resonance frequency shifts. This loop also suppresses perturbations generated by larger, slowly moving molecules or particles because most of their displacements will occur within the PDH LBW ( Figure 10A)。Importantly, small molecules undergoing Brownian motion, despite having a smaller overall resonance shift due to their reduced size, have a larger fraction of their mean squared displacement power spectral density (MSDPSD) outside the PDH suppression window ( Figure 10A , Figures 17A - 17B ). For the smallest protein (Myc tag, 0.75 nm), the integration of the MSDPSD between the ends of the locking bandwidth and the optothermal bandwidth (discussed below) yields a root mean square (RMS) displacement of 93 nm. This displacement is comparable to the ~250 nm distance between the nodes and antinodes of the cavity standing wave (simulated cavity standing wave obtained but not shown), indicating that due to diffusing molecules, the microcavity can experience nearly complete resonance shift outside the PDH LBW. When the molecule diffuses back to the node, the perturbation stops, causing the system to exhibit a dependence on the molecular diffusion constant ( Figures 8A - 8B ). Notably, the detection by transfer from node to antinode operates differently from the evanescent detection mode. The key is that the solution-phase label-free device allows this novel use of PDH as a high-pass filter to reduce mechanical noise while transmitting signals from fast-moving molecules ( Figure 10B ), which is the key difference compared to previous schemes.

[0229] The second element of the proposed mechanism relies on the optothermal-induced distortion of the resonance line shape ( Figure 10C ) and the dynamic optothermal triggering mechanism, which amplifies small resonance shifts. The FFPC spatially confines a relatively strong optical field, causing resonance temperature changes within the mode volume medium and subsequent thermo-optical resonance shifts. The presence of this thermal nonlinearity is clearly manifested as a broadened and asymmetric cavity line shape during an active scan of the cavity length or wavelength (see Figure 14 ). This optothermal nonlinearity originates from the mirror coating and the aqueous medium, without the need for light absorption by the molecules themselves. The optothermal bandwidth is experimentally determined to be 21 kHz (see Figure 15A ), thus defining the upper limit of the molecular observation window ( Figure 10B ). In a non-PDH-stabilized cavity, these optothermal nonlinearties lead to multiple different stable equilibria. However, with PDH stabilization, this nonlinearity can be used for additional signal amplification. By introducing an offset from the original, arbitrarily locked position to increase the cavity transmission ( Figure 10C , panel 1), the pump laser is brought to a frequency slightly below the cavity maximum ( Figure 10C , panel 2). In this triggering state, even the resonance shift of diffusing molecules can shift the cavity resonance into an unstable regime where the pump laser is at a higher frequency than the microcavity resonance ( Figure 10C, the drawing board 3). Here, the offset triggers a dynamic process through which the cavity cools faster than LBW, resulting in further resonance offset and more cooling, ultimately causing a significant reduction in transmission ( Figure 10C , the drawing board 4). Other molecule-induced mechanisms such as scattering can also contribute to cavity cooling. After the molecules have diffused out of the antinode, the cavity begins to warm up, and ultimately PDH restores the initial locked position at a rate defined by LBW ( Figure 10C , the drawing board 2). In the case of a smaller perturbation (such as having a Myc tag), the cavity cools less, resulting in a distribution of peak prominences. Evidence of this mechanism can be found in the controlled voltage pulses added to the output servo of PDH, thus providing a qualitative imitation of the internal perturbation caused by the molecules passing through ( Figure 13B ). Figure 13A ).

[0230] In summary, the proposed mechanism is characterized by the diffusion of molecules into the microcavity where their rapid motion exceeds the PDH locking bandwidth. The highly sensitive optothermal effect experienced by the cavity due to these rapid molecular perturbations causes the cavity to cool rapidly, resulting in enhanced offset and very strong signals. Both peak prominence and temporal width are expected to be affected by system parameters including the PDH LBW. However, while peak prominence is a complex function of biomolecule molecular weight (and thus refractive index) and diffusion parameters, the temporal width is expected to be more purely dominated by the diffusion parameters, resulting in a clear linear dependence ( Figures 8A - 8B ).

[0231] Conclusion

[0232] In the absence of surfaces, extrinsic labels, and plasmonic enhancers, this example has demonstrated outstanding sensitivity in observing single, diffusing biomolecules, achieving an SNR > 100 for sub-1nm peptides. This method utilizes the open-access geometry of the microscale FFPC to facilitate unobstructed biomolecule diffusion and maximize the overlap between biomolecules and the light field. The enhanced sensitivity relative to other label-free techniques originates from molecular velocity filtering and optothermal triggering, where two experimental challenges (rapid molecular motion and thermal nonlinearity) are transformed into advantages. Very similar to the distinctive feature regions of infrared spectroscopy, the resulting rich 2D intensity / time data can be used to distinguish unique, identifiable molecular tags and has the potential to provide quantitative mass and diffusion information without surface perturbation.

[0233] Mass photometry, a new method that can provide quantitative mass information of unlabeled biomolecules in a spatially resolved manner, has been commercialized and widely adopted, thus demonstrating the great potential of photon single-molecule assays. Although this solution-phase FFPC-based method sacrifices the spatial resolution of mass photometry, it offers significantly higher sensitivity with μs kinetics, a detection limit of ≤1 kDa, and 2D signal maps that provide a way to distinguish molecules based on conformation and mass alone, which affect diffusion characteristics. Additionally, FFPC provides convenient fiber-optic integration, enabling molecules to be easily examined via mass photometry after passing through the FFPC, thus making these methods truly complementary.

[0234] Increased suppression of external noise sources will result in further significant improvements, including the ability to detect biomolecules smaller than 1 kDa. Optimizing measurement parameters using quantitative modeling will enable tuning of the molecular map. For example, the configuration of the bandwidth of the velocity filter can be used to selectively collect information from different diffusion populations. As demonstrated by the experiments above, this FFPC method can be used to resolve rapid biomolecular conformational changes, elucidate the self-assembly of small molecules in complex samples, and provide a way for rapid screening of protein-protein and protein-drug interactions. By being label-free and single-molecule, this method alleviates some key experimental difficulties in two widely used biophysical techniques, FCS and dynamic light scattering. This direct and easily scalable device will bring many benefits to the fields of life science and chemical science, such as trace analysis, separation science, mechanistic insights, and clinical diagnosis.

[0235] As used herein, the term "exemplary" means serving as an example, instance, or illustration. Any aspect or design described herein as "exemplary" is not necessarily to be construed as preferred or superior to other aspects or designs. Additionally, for the purposes of this disclosure and unless otherwise specified, "a" or "an" means "one or more".

[0236] If not already included, the numerical values of all parameters in this disclosure begin with the term "about" meaning approximately. "Nearly", as in "nearly maximized", has a similar meaning. These terms are used to cover those variations inherent in the measurement / implementation of the relevant parameters as understood by a person of ordinary skill in the art. This covers within ±5%, ±4%, ±3%, ±2%, and ±1% of the disclosed numerical values (or maximum or minimum values). This also covers the exact values of the disclosed numerical values and values rounded to the disclosed numerical values.

[0237] The foregoing description of the exemplary embodiments of the present disclosure has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the present disclosure to the precise forms disclosed, and modifications and variations may be made in light of the above teachings or may be acquired from the practice of the present disclosure. Some embodiments have been selected and described in order to explain the principles of the present disclosure and as practical applications of the present disclosure, so that those skilled in the art can utilize the present disclosure in various embodiments and various modifications suitable for the specific purposes contemplated. The scope of the present disclosure is intended to be defined by the appended claims and their equivalents.

Claims

1. A method for detecting diffusing particles, the method comprising: (a) introducing a sample comprising diffusing particles into an optical microcavity; (b) coupling probe light into the optical microcavity such that the probe light resonates with the optical microcavity, wherein the diffusing particles diffuse into an optical mode volume defined by the coupled probe light; and (c) detecting output light from the optical microcavity as a function of time while maintaining resonance, wherein the diffusing particles cause a change in the detected output light.

2. The method according to claim 1, wherein the optical microcavity is an open-access optical microcavity configured such that a region of maximum intensity of the optical mode volume can be entered by the diffusing particles.

3. The method according to claim 1, wherein the optical microcavity is a Fabry - Perot microcavity having a cavity, wherein the optical mode volume is defined within the cavity.

4. The method according to claim 1, wherein the resonance in step (b) is associated with maximum transmission of the probe light through the optical microcavity or minimum intensity of the probe light back - reflected from the optical microcavity.

5. The method according to claim 4, wherein the maximum transmission of the probe light or the minimum intensity of the back - reflected probe light is obtained by coupling the probe light such that the probe light undergoes constructive interference to form a standing wave within the optical microcavity and by adjusting one or more of: the power of the probe light, the source coupled to the probe light, the gain of the Pound - Drever - Hall (PDH) servo loop of the optical microcavity, and the offset of the PDH servo loop.

6. The method according to claim 5, wherein the standing wave is achieved by satisfying mλ = 2nL, where m is an integer, λ is the probe light wavelength, n is the refractive index of the sample, and L is the optical microcavity length.

7. The method according to claim 6, further comprising adjusting λ, adjusting L, adjusting the power of the probe light, adjusting the gain of the PDH servo loop, adjusting the offset of the PDH servo loop, or a combination thereof during step (c) to maintain resonance.

8. The method according to claim 1, wherein the sample comprises water.

9. The method according to claim 8, wherein the optical microcavity is a Fabry - Perot microcavity having a cavity, wherein the optical mode volume is defined within the cavity.

10. The method according to claim 1, wherein the sample has a certain concentration of diffusing particles such that the probability that the diffusing particles occupy the optical mode volume is less than one.

11. The method according to claim 1, wherein the detected output light is transmitted probe light comprising a notch, or the detected output light is back - reflected probe light comprising a spike, and the method further comprises measuring the time width of each of the notch or spike.

12. The method according to claim 11, further comprising generating a plot of the intensity versus time width of each of the notch or spike.

13. The method according to claim 1, wherein the detected output light is transmission detection light including a recess, or the detected output light is back-reflection detection light including a spike, and the method further includes measuring an autocorrelation function (ACF) based on the recess or the spike and calculating a hydrodynamic radius based on the measured ACF.

14. A system for detecting diffusing particles, the system comprising: (a) an optoelectronic component configured to couple detection light into an optical microcavity such that the detection light resonates with the optical microcavity; (b) an optical microcavity into which a sample including diffusing particles is introduced to diffuse into an optical mode volume defined by the coupled detection light; (c) a detector configured to detect output light from the optical microcavity as a function of time; and (d) an optoelectronic component configured to maintain resonance while using the detector to detect output light from the optical microcavity as a function of time, wherein the optoelectronic component (d) provides a Pound-Drever-Hall (PDH) servo loop coupling a source of the detection light and the optical microcavity.

15. The system according to claim 14, wherein the optical microcavity is an open-access optical microcavity configured such that a region of maximum intensity of the optical mode volume can be entered by the diffusing particles.

16. The system according to claim 14, wherein the optical microcavity is a Fabry-Perot microcavity having a cavity, wherein the optical mode volume is defined within the cavity.

17. The system according to claim 14, further comprising an actuator operably coupled to the optical microcavity and the PDH servo loop, the actuator configured to adjust a cavity length L of the optical microcavity.

18. The system according to claim 14, further comprising a controller including a processor and a non-transitory computer-readable medium operably coupled to the processor, the non-transitory computer-readable medium including instructions that, when executed by the processor, cause the controller to perform operations including: receiving a signal from the detector; based on the received signal, satisfying mλ = 2nL, where m is an integer, λ is a detection light wavelength, n is a refractive index of the sample, and L is a cavity length of the optical microcavity; and based on the received signal, adjusting one or more of a power of the detection light, a gain of the PDH servo loop, an offset of the PDH servo loop, or a combination thereof.

19. The system according to claim 14, further comprising a controller including a processor and a non-transitory computer-readable medium operably coupled to the processor, the non-transitory computer-readable medium including instructions that, when executed by the processor, cause the controller to perform operations including: receiving a signal from the detector; processing the signal to determine a time width of the signal; and outputting the determined time width.

20. The system according to claim 19, wherein the operation further includes processing the signal to calculate the hydrodynamic radius of the diffusing particles and outputting the calculated hydrodynamic radius to the system.

Images