Single molecule state analysis method based on photon-by-photon means

Abstract

The invention provides a single molecule state analysis method based on a photon-by-photon means. The method comprises the following steps: observing a donor photon by photon based on a fluorescence resonance energy transfer principle, and recording microscopic time and macroscopic time corresponding to a single photon to generate a photon-by-photon observation sequence; taking a photon-by-photon observation sequence as an observation sequence of a hidden Markov model, taking a target sequence containing single-molecule fluorescence lifetime and macroscopic time corresponding to the single-molecule fluorescence lifetime as a hidden state sequence of the hidden Markov model, and calculating the target sequence from the observation sequence, wherein initial probability distribution, state transition probability distribution and observation probability distribution are obtained according to a photon-by-photon observation sequence by using an EM algorithm, and the observation probability distribution has a convolution form of an instrument response function and ideal observation probability distribution. According to the photon-by-photon observation sequence and the model parameters, a fluorescence lifetime-macroscopic time function is obtained through a Viterbi algorithm, and the target biomolecule state is analyzed. According to the method, the time resolution for observing the service life of the fluorescent molecules is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of using fluorescence lifetime microscopy to detect the dynamic behavior of biological molecules, and in particular to a single molecule state analysis method based on a photon-by-photon approach. Background Art

[0002] The function and conformation of biomolecules are closely related. Linking conformational states with changes in biochemical functions is a prominent goal of biology, which requires the ability to accurately analyze the structure and dynamics of biological systems. Studying the structure and function of biomolecules at the single-molecule level can help people clearly understand the truth of life activities from the level of molecular operation mechanism. At present, the technologies for detecting biomolecular conformation information in the time dimension mainly include fluorescence resonance energy transfer technology (FRET), fluorescence correlation spectroscopy (FCS) and its derivative technologies (such as fluorescence lifetime correlation spectroscopy (FLCS), two-dimensional fluorescence lifetime correlation spectroscopy (2DFLCS), etc.).

[0003] Fluorescence resonance energy transfer (FRET) known in the prior art has become an important tool for studying the conformation and structural dynamics of biomolecules at the ensemble and single-molecule levels. FRET refers to when two fluorescent groups are close enough, only one of the fluorescent groups A is excited, and the other fluorescent group B will receive non-radiative energy. The distance between the two fluorescent groups A and B can be determined from the fluorescence intensity and fluorescence lifetime of A, and its spatial resolution can reach the sub-nanometer level. FRET is generally used in combination with electron multiplying CCD (EMCCD) and confocal microscopy, and the real-time time resolution can be sub-millisecond level.

[0004] Figure 1 Schematic diagram showing the acquisition of single-molecule fluorescence lifetime data using confocal fluorescence microscopy.

[0005] Fluorescence lifetime refers to the average time that a fluorescent molecule remains in its excited state before emitting a photon, and is an intrinsic property of the fluorophore. At the single-molecule level, fluctuations in fluorescence lifetime reflect the heterogeneity and fluctuations of the local environment and have higher stability than fluorescence intensity. In the presence of fluorescence resonance energy transfer, the fluorescence lifetime decreases as the FRET efficiency increases, reflecting the conformational changes of the biomolecule. Based on the relationship between fluorescence lifetime and FRET efficiency, the lifetime-based single-molecule FRET method has been developed and applied to study the conformational dynamics of biomolecules.

[0006] Among the existing known technologies, SIFA, lipo-FRET and Queen-FRET technologies developed from FRET provide methods for in situ observation of the conformation and position changes of living cell membranes and nearby biomolecules. The principle is that the fluorescence intensity and fluorescence lifetime of the fluorophore labeled on the biomolecule change with the distance between the fluorescence and the quencher. Compared with FRET, only one fluorescent molecule needs to be labeled at the site of interest of the biomolecule. The time resolution of SIFA, lipo-FRET and Queen-FRET is at the second level, and it is impossible to accurately observe the dynamic process with a time scale of milliseconds and below. The main factors limiting its time resolution are: 1) The time resolution of observing the change of fluorescence intensity using EMCCD is affected by the time resolution of EMCCD, which is generally at the level of 50 milliseconds; 2) The existing fluorescence lifetime FRET method requires more photons to fit a relatively accurate lifetime, which limits the resolution. The dynamic process of the research object is generally at the sub-second level and longer time scale.

[0007] Therefore, a method for analyzing the state of a single biomolecule and its rapid kinetic behavior with higher time resolution and a device for implementing the method are needed. Summary of the invention

[0008] The present invention is based on the principle of fluorescence resonance energy transfer, obtains the fluorescence lifetime-real time measurement value, and analyzes it based on the hidden Markov model and EM algorithm in the photon-by-photon framework, such as the Baum-Welch algorithm. The energy transfer efficiency E between the donor and the acceptor in fluorescence resonance energy transfer is defined as:

[0009]

[0010]

[0011]

[0012] Where R is the distance between the two fluorescent probes, R0 is the characteristic quenching distance, and R0 is the distance corresponding to the transfer efficiency E of 50%. Since the distance R between the donor and the acceptor is inversely proportional to the sixth power, E is very sensitive to the spatial distance, which is why fluorescence resonance transfer can be used to measure nanometer-scale distances. R0 is calculated by the dipole approximation, where Q D is the donor quantum yield, n is the refractive index of the medium, κ 2 is the dipole orientation factor between the two fluorescent molecules, ε A is the maximum extinction coefficient of the acceptor, J(Λ) is the normalized donor emission spectrum F D The absorption spectrum of the receptor E A The spectral overlap coefficient.

[0013] Figure 2 Schematic diagram showing the relationship between the microscopic time of a single fluorescent molecule and the lifetime state of the fluorescent molecule.

[0014] The fluorescence lifetime is the characteristic value of the relaxation time of fluorescence in the excited state. When a fluorescent molecule absorbs a photon and transitions from the ground state to the excited state, after a time t, it returns to the ground state through spontaneous radiation and emits a photon. After the fluorescent molecule absorbs a photon, the electrons in the molecule will transition from the ground state to the excited state. After a period of vibrational relaxation (generally between picoseconds and nanoseconds), it will return to the ground state by radiating a photon with a longer wavelength and lower energy. Among them, vibrational relaxation occupies most of the time from excitation to emission. For the same fluorescent molecule, its vibrational relaxation time is not a fixed value, but a probability distribution with exponential decay. The longer the relaxation time, the lower the proportion of photons. The vibrational relaxation time is also called the microscopic time t, and the number of photons at the corresponding moment is I(t), which conforms to the relationship of formula 4. The curve of I(t) changing with t is called the fluorescence lifetime decay curve or the fluorescence intensity decay curve. Among them, A is the pre-exponential factor, which is equal to the number of photons at the microscopic time t=0, and is proportional to the total number of photons. τ D It is the characteristic value when the exponential decay function decays to 1 / e of the maximum value, called the fluorescence lifetime. It reflects the average residence time of a fluorescent molecule in the excited state. It is its inherent property, but is affected by many environmental factors, such as temperature, pH, etc.

[0015]

[0016]

[0017]

[0018] The fluorescence lifetimes determined by observing the donor in the presence and absence of the acceptor are denoted by τ DA and τ D , so here we can use τ D Assuming a single distance between the donor and acceptor fluorophores (i.e., no distance fluctuations), the FRET efficiency is given by Equation 5. The advantage of this approach is that no correction factors are required, since most correction factors affect the relative number of photons detected in the donor and acceptor channels but do not affect the fluorescence decay of the donor itself. The lifetime method can also be used for ensemble or imaging measurements under incomplete labeling conditions. Under stable external conditions, τ DA It reflects the relative distance between the donor and acceptor of the FRET pair, as shown in Formula 6.

[0019] Hidden Markov model (HMM) is widely used in life sciences to analyze the conformational dynamics of biomolecules. Hidden Markov model is a probabilistic model about time series, which describes a random sequence of unobservable states randomly generated by a hidden Markov chain, and then a random sequence of observations generated by each state generating an observation. The state sequence randomly generated by the hidden Markov random chain is called a state sequence; each state generates an observation, and the random sequence generated by this is called an observation sequence. Each position in the sequence can be regarded as a moment. The parameter Φ of the hidden Markov model is determined by three matrices: the initial probability distribution, the state transition probability distribution, and the observation probability distribution. The state transition probability is defined as the probability of transferring to another state at the next moment under the premise of being in a certain state at the current moment. The state transition probability can be fully described by the state transition probability matrix, which is an n-dimensional matrix, where n is the number of hidden states. The observation probability is defined as the probability that the observed value in a certain state is a predetermined value. For FRET data, the observation probability satisfies the Gaussian distribution.

[0020] Figure 3 The figure shows the statistical lifetime decay curve of the fluorescent molecule at the microscopic time. The value of the observation probability matrix is ​​the result of the normalization of the lifetime decay curve.

[0021] In order to solve the technical problem of low resolution in the prior art, the first aspect of the present invention provides a single molecule state analysis method based on a photon-by-photon approach, the method comprising:

[0022] Based on the principle of fluorescence resonance energy transfer, donors and acceptors composed of fluorescent molecules are respectively labeled on the target biological molecules;

[0023] observing the donor multiple times, wherein only a single photon emitted by the donor is received in each observation;

[0024] According to the multiple observations, the microscopic time and macroscopic time corresponding to a single photon are recorded to generate a photon-by-photon observation sequence, wherein the microscopic time refers to the time interval from when the donor is excited to when it emits a photon through spontaneous radiation, and the macroscopic time refers to the moment when a photon is observed;

[0025] The photon-by-photon observation sequence is used as the observation sequence of the hidden Markov model; a target sequence is constructed, wherein the target sequence includes the single-molecule fluorescence lifetime and its corresponding macroscopic time; the target sequence is used as the hidden state sequence of the hidden Markov model, and the hidden Markov model is used to calculate the target sequence from the observation sequence.

[0026] Preferably, in the method, calculating the target sequence from the observation sequence using a hidden Markov model comprises:

[0027] According to the photon-by-photon observation sequence, the number of hidden states of the hidden Markov and the corresponding hidden Markov model parameters are obtained using the EM algorithm: the initial probability distribution, the state transition probability distribution and the observation probability distribution; wherein the structure of the observation probability distribution that needs to be iterated in the EM algorithm is limited to a form having a convolution of an instrument response function and an ideal observation probability distribution, wherein the instrument response function gives a mapping between the real value and the measured value of the microscopic time in the photon-by-photon observation;

[0028] The target sequence is obtained according to the photon-by-photon observation sequence and the hidden Markov model parameters by using a Viterbi algorithm for determining the hidden state sequence.

[0029] Preferably, in the method, the instrument response function is obtained by a deconvolution algorithm based on the intrinsic lifetime decay curve of the fluorescent molecule and the original fluorescence lifetime.

[0030] Preferably, in the method, the obtaining of hidden Markov model parameters using the EM algorithm includes setting respective iteration initial values ​​of the state transition probability distribution and the observation probability distribution, wherein the iteration initial values ​​are limited to within 2 orders of magnitude of reference values ​​of the target biological molecules.

[0031] Preferably, in the method, the EM algorithm adopts the maximum expectation algorithm of variational Bayesian estimation.

[0032] Preferably, in the method, the EM algorithm adopts a forward algorithm, a backward algorithm or a forward-backward algorithm to reduce the computational time complexity.

[0033] Preferably, the method further comprises the following steps:

[0034] After obtaining the target sequence, obtaining the rapid kinetic information of the target biomolecule according to the multiple single-molecule fluorescence lifetimes and their corresponding macroscopic times in the target sequence includes:

[0035] Calibrate the state of the target biomolecule according to the fluorescence lifetime corresponding to each observation;

[0036] Performing frequency distribution statistics on the residence time distribution of the target biomolecule in each state;

[0037] The obtained frequency distribution is statistically fitted into a single exponential decay distribution and a reaction rate constant is obtained according to its decay rate, wherein the reaction rate constant is used to calculate the free energy of the conformational change of the biomolecule.

[0038] Preferably, in the method, the obtained frequency distribution is subjected to single exponential fitting according to the least squares method to obtain the reaction rate constant.

[0039] Preferably, in the method, the structure of the observed probability distribution that needs to be iterated in the EM algorithm is defined as:

[0040]

[0041] Where IRF is the instrument response function, x is the observed value, and λ i is the observed probability value, is the ideal observation probability distribution, and bg is the noise constant associated with the instrument.

[0042] Preferably, in the method, the donor is selected so that the target biomolecule has only a single fluorescence lifetime peak; and

[0043] The diffusion rate of the target biomolecule is defined so that the donor freely diffuses through the laser focal volume and resides therein for at least 3 times the residence time of the target biomolecule in the state to be determined during the conformational state change.

[0044] The second aspect of the present invention provides a single molecule state analysis device based on a photon-by-photon approach, comprising a fluorescence lifetime microscope unit and a calculation unit, wherein the fluorescence lifetime microscope unit comprises:

[0045] a picosecond pulsed laser, which is used to excite the donor to an excited state;

[0046] Single-photon detectors, which are limited to receiving only a single photon during an observation period;

[0047] A time-correlated single photon counter, which is used to record the microscopic time and macroscopic time associated with the single photon; and

[0048] The computing unit is configured to implement the single-molecule state analysis method described in any one of the first aspects of the present invention according to the microscopic time and macroscopic time associated with the single photon recorded by the fluorescence lifetime microscope unit.

[0049] The single-molecule rapid kinetic analysis change method based on fluorescence lifetime and the device for implementing the same according to the present invention can significantly improve the temporal resolution of dynamic observation of fluorescent molecule lifetime; in addition, this method provides an effective and feasible way to improve the temporal resolution of SIFA, lipo-FRET and Queen-FRET technologies in the future. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The embodiments of the present invention are further described below with reference to the accompanying drawings, in which:

[0051] Figure 1 A schematic diagram showing the collection of single-molecule fluorescence lifetime data using confocal fluorescence microscopy;

[0052] Figure 2 A schematic diagram showing the relationship between the microscopic time of a single fluorescent molecule and the lifetime state of the fluorescent molecule;

[0053] Figure 3 A schematic diagram of the statistical lifetime decay curve of the fluorescent molecule microscopic time is shown, where the value of the observation probability matrix is ​​the result of normalization of the lifetime decay curve;

[0054] Figure 4 A schematic diagram showing how to connect the observation sample to the vesicle surface to reduce the diffusion rate and increase the observation time. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described in combination with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Those skilled in the art can make appropriate adjustments to the components, parameters, etc. in the embodiments of the present invention based on the concept of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention. In other cases, well-known methods, devices, implementations or operations are not shown or described in detail to avoid blurring various aspects of the present invention.

[0056] In addition, the described features, structures or characteristics may be combined in one or more embodiments in any suitable manner. In the following description, many specific details are provided to provide a full understanding of the embodiments of the present invention. However, those skilled in the art will appreciate that the technical solution of the present invention can be practiced without one or more of the specific details, or other methods, components, devices, steps, etc. may be adopted. In other cases, known methods, devices, implementations or operations are not shown or described in detail to avoid blurring the various aspects of the present invention. The flow in the embodiment is only an exemplary description, does not necessarily include all the content and operations / steps, and does not necessarily perform in the described order. For example, some operations / steps can also be decomposed, and some operations / steps can be merged or partially merged, so the order of actual execution may change according to actual conditions.

[0057] For FRET experiments, in the case of a known model, given the observation model, it is necessary to find the HMM model parameters and the hidden state sequence. Using the EM algorithm, for example, the Baum-Welch algorithm can be used to solve the model parameters according to the observation sequence, and according to the model parameters and the observation sequence, the Viterbi algorithm (also known as the dynamic programming algorithm or the viterbi algorithm) can be used to solve the most likely hidden state sequence. There are many methods for determining the data model, i.e. the number of hidden states, using the EM algorithm in actual experiments, and these methods are trying to avoid human bias. Preferably, the inventor uses variational Bayesian estimation (variational Bayesian inference) in this application to determine the data model, and variational Bayesian estimation can more efficiently match the application of using hidden Markov models to analyze biomolecules under the photon-by-photon framework.

[0058] The traditional HMM model for processing fluorescence signals ignores the calculation deviation caused by the time when the photons arrive at the detector. In order to optimize this problem, the present invention uses the maximum expectation algorithm of variational Bayesian estimation, combined with the photon-by-photon hidden Markov model, to process single-molecule fluorescence lifetime data. The inventors use single-photon detectors and single-photon counters to construct an observation framework for observing the change of fluorescence lifetime over time photon by photon. Specifically, by using a photoelectric avalanche diode to record the arrival time of photons, a photon-by-photon hidden Markov model analysis can be achieved. This method can be used for experimental data of FRET and lifetime of free-diffusing fluorescence, and can fully extract the information carried by each photon, so as to analyze the experimental data more accurately.

[0059] In the photon-by-photon framework, we first need to define a sufficiently short time unit Δt, during which at most one photon can be received. The time between adjacent photons is defined as Δt. n =t n -t n-1 , which is an integer multiple of Δt. The lifetime of the fluorescent molecule conforms to the random transition between different lifetime states of the system in the Markov process, and the hidden state sequence is z i ,z i+1 The time interval between them is Δt, and the observation sequence is in is time t i The observed value of the detected photon is the time from when the fluorescent molecule is excited by the laser to when it emits a photon spontaneously in the fluorescence lifetime experiment, which is called the microscopic time. i The microscopic time of the fluorescent molecule in the lifetime state satisfies the decay coefficient exponential distribution, where λ iis the observation probability value. Under the condition that the number of system model states is K, the probability distribution of the complete system data containing the parameters to be solved can be expressed as:

[0060]

[0061] Among them, the first item on the right is:

[0062]

[0063] And among them, is the reaction rate constant, and Represents the probability of the system transitioning to other states under the condition that it leaves the current state.

[0064] According to Bayesian variational estimation, the marginal likelihood function is:

[0065]

[0066] Take the logarithm of both sides of the equation and take the logarithm about expectations, get

[0067]

[0068] is the approximate or variational posterior of the model parameters and hidden variables, (10) has the following inequality relationship,

[0069]

[0070]

[0071] Equally and only if When the equality sign holds, the approximate variational posterior is equal to the true posterior. The purpose of variational Bayesian estimation is to adjust the variational posterior To make the right side of the inequality Maximize and keep approaching the marginal likelihood.

[0072] In the calculation process, the variational Bayesian theory will Factorization,

[0073]

[0074]

[0075] Among them, P(π), Satisfies the Dirichlet distribution, Satisfying the gamma distribution, taking Satisfies exponential decay distribution,

[0076]

[0077] The forward-backward algorithm is used in the variational EM calculation to reduce the computational time complexity from O(K T ) is reduced to O(K 2 T), making the computation faster. In addition to computing the marginal likelihood function, variational estimation also produces a probability distribution of the parameters given the data. The most likely parameters can be taken from these distributions and the most likely hidden state sequence can be computed using the Viterbi algorithm.

[0078] The present invention further develops the photon-by-photon hidden Markov method and uses it to analyze the smFRET experimental data obtained by confocal microscopy that contains fluorescence lifetime information. When the fluorescent molecules pass through the focal volume of the confocal microscope, they are excited by the picosecond pulse laser to emit fluorescent molecules. The instrument records the time T when each photon arrives at the detector and the microscopic time t. Under ideal conditions without considering the deviation caused by the instrument response function, the ideal observation probability distribution can be approximated to satisfy Distribution of forms.

[0079] In order to further correct the calculation to improve the accuracy, the inventors modified the observation probability distribution according to the instrument response function, so that the observation probability distribution is limited to the form of the convolution of the instrument response function and the ideal observation probability distribution, wherein the instrument response function gives the mapping between the real value and the measured value of the microscopic time in the photon-by-photon observation. In one example, the correction has the following form

[0080]

[0081] Where IRF is the instrument response function, and the denominator on the right side indicates that normalization has been performed. However, the correction is not limited to the above specific formula form, and can also be adjusted accordingly according to the characteristics of the observed target. For example, the ideal observation probability distribution can also be other forms of distribution (such as Gaussian distribution, Poisson distribution, gamma distribution, chi-square distribution, etc.), and the constant bg related to the instrument is not necessary. Similar local parameter corrections do not deviate from the protection scope covered by the concept of the present invention. f(x|λ i ) is corrected and applied to the second term on the right side of Formula 7, thereby the composition structure of the hidden Markov model containing the complete data of the system parameters to be solved is also updated, thus integrating the fluorescence lifetime information into the photon-by-photon hidden Markov model.

[0082] The steps are as follows:

[0083] The required fluorescent donor is used to label the biological molecules to be observed using FRET, and the lifetime decay curve I(t) of the freely diffusing fluorescent molecules is collected using a confocal fluorescence lifetime microscope. The original fluorescence lifetime τ is obtained by tail exponential fitting. D ;

[0084] Knowing I(t) and τ D , the instrument response function IRF(t) of the confocal fluorescence lifetime microscope can be analyzed by deconvolution;

[0085] The concentration of the biomolecules to be tested labeled with donor and acceptor fluorescence was diluted to ~50 pM, and the data of freely diffusing fluorescent molecules, namely the microscopic time and macroscopic time corresponding to a single photon, were collected using a confocal fluorescence lifetime microscope, and the data were constructed into an observation sequence.

[0086] The collected observation sequence is estimated by the lifetime-based photon-by-photon hidden Markov model EM algorithm to obtain the most likely number of states of the model as well as the kinetic parameters and state change sequence. The obtained instrument response function is needed to correct the hidden state model of the hidden Markov model in the calculation. Before using the EM algorithm to iterate the hidden Markov model to converge, the initial value of the transition probability distribution is set manually. as well as The selection of should not differ too much from the actual value range of the target molecule in advance, and should be within 2 orders of magnitude as much as possible (the initial value of the iteration refers to π, and The initial value of and The initial value of is not necessarily between 0 and 1. For example, for π, the values ​​of 0.1 and 0.001 are two orders of magnitude different. Generally speaking, appropriately setting the initial value of the iteration can effectively reduce the operation time of the EM algorithm and improve the accuracy of the result. However, it is only an optional step for more optimization and is not a limitation of the method of the present invention.) From the posterior distribution The probability distribution of the parameter Φ of the hidden Markov model is obtained, thereby determining the most likely parameter Φ and using the Viterbi algorithm to calculate the most likely hidden state sequence.

[0087] Obtaining the hidden state sequence means obtaining the mapping relationship between single-molecule fluorescence lifetime and macroscopic time, based on which other state information or fast kinetic behavior of the target biological molecule can be further analyzed.

[0088] Wherein, as an illustration but not limitation, in a further analysis step, after obtaining the target sequence, the rapid kinetic information of the target biomolecule is obtained according to the mapping relationship between the single-molecule fluorescence lifetime and the macroscopic time in the target sequence, including: calibrating the state of the target biomolecule according to the fluorescence lifetime corresponding to each observation; performing frequency distribution statistics on the residence time distribution of the target biomolecule in each state; fitting the obtained frequency distribution statistics to a single exponential decay distribution and obtaining a reaction rate constant according to its decay rate, wherein the reaction rate constant is used to analyze the free energy of conformational changes of the biomolecule. In a further calculation example, the decay rate is approximately considered to be the reaction rate constant.

[0089] The modified hidden Markov calculation method integrates the fluorescence lifetime information corresponding to the instrument response function, and fully utilizes the advantages of fluorescence lifetime FRET and photon-by-photon analysis. It can analyze the fluorescence lifetime of the system to be studied, and can accurately analyze the parameters of the dynamic changes between its lifetime states, thereby further analyzing the dynamic information of the system from the changes in fluorescence lifetime. At present, the detection of the dynamics of a single molecule can achieve a time resolution of sub-millisecond level.

[0090] Example 1

[0091] This example uses simulated data to verify the feasibility of the above method. Since there are many influencing factors in the real experimental data and the correct results cannot be directly obtained, in order to preliminarily verify the reliability of the algorithm, the simulated data is first obtained based on the Monte Carlo simulation model to preliminarily verify the reliability of the algorithm. The simulated data is consistent with the experimental data settings in signal intensity and signal-to-noise ratio. In this simulation program, it is assumed that the sample to be tested is a Holliday Junction (HJ) DNA structure (the bases at both ends can be complementary to each other), there are two conformations (A and B), open loop and closed loop, and different fluorescent molecules are labeled at both ends, and FRET will occur, resulting in a decrease in the donor fluorescence lifetime. The intrinsic fluorescence lifetime of the fluorescent molecule τ0 = 3.5ns, and each conformation corresponds to a different fluorescence lifetime of the donor τ A =1ns, τ B = 2.6ns. The DNA molecule switches between the two conformations and reaches a dynamic equilibrium. Five different initial reaction rate constants are set: k AB =1000s -1 , 500s -1 , 200s -1 , 100s -1 , 50s -1 ;k BA =1000s -1 , 500s -1 , 200s -1 , 100s-1 , 50s -1 The probability of molecular conformation change P can be calculated based on the initial reaction rate constant. AB =k AB ΔT,P BA =k BA ΔT. ΔT is the macroscopic time resolution, which is set to 1us. A random number generator (RNG) is used to generate a probability P between 0 and 1. When the molecule is in conformation A and P <P AB When the molecule is in the B conformation and P <P BA , it changes to conformation A, otherwise the conformation remains unchanged.

[0092] In the process of fluorescent molecules being excited by laser and received by the detector, the probability of fluorescent molecules being excited by laser and receiving photons by the detector is set according to the average intensity of the signal in the experiment. The random number generator is used to generate random numbers to determine whether the fluorescent molecules finally reach the detector. When recording photon information, it is necessary to record macroscopic time and microscopic time. Macroscopic time is the number of pulsed laser excitations, and microscopic time needs to be generated by random numbers. When the molecular state is s (s is A or B), its lifetime is τ s The microscopic time t of the photon is generated by a random number generator with an exponential decay distribution. According to the instrument conditions in the experiment, only the photon data with a microscopic time less than 25ns are saved.

[0093] Due to the existence of scattered light, detector dark counts and other reasons, there will be a lot of background noise in the photons actually detected, which is characterized by a uniform distribution of microscopic time instead of exponential decay. Set the probability of background noise according to the experimental conditions. First, use a random number generator to generate a random number, and compare it with the probability generated by the background noise to determine whether background photons are detected. If background photons are detected, a randomly distributed microscopic time t is generated by a random number generator. Since a real single-photon detector has dead time, only one photon signal can be recorded in a very short time (tens of nanoseconds), that is, only one photon can be recorded in one pulse cycle. Therefore, before recording new photon information, it is also necessary to determine whether a photon has been recorded at the same macroscopic time, and the microscopic time is smaller than the new photon (the photon with a smaller microscopic time is detected first).

[0094] The microscopic time of the photon detected by the instrument in the experiment is affected by the instrument response function IRF compared with the real microscopic time. For a photon with a real microscopic time of t′, the microscopic time detected by the instrument is t″, which satisfies the probability distribution function:

[0095]

[0096] Where α is the normalization coefficient. Where IRF is set according to the parameters of the instrument in the experiment.

[0097] According to the above simulation process, the total detection time of each set of state transition parameters is set to 2s, and the total number of photons is about 4×10 5 .

[0098] According to the above simulation process, the following data can be obtained: 1) The intrinsic lifetime decay curve of the fluorescent molecule I(t); 2) The delay(T) curve of the Holliday Junction microscopic time-macroscopic time of the fluorescent marker. The above data are subjected to photon-by-photon hidden Markov analysis of lifetime:

[0099] By fitting the tail of the intrinsic lifetime decay curve I(t) of the fluorescent molecule, that is, only fitting the data with t>4ns. The least squares method is selected as the fitting method, and the single exponential decay function is selected as the fitting function y(t), as shown in Formula 18, to obtain the original fluorescence lifetime τ0. In order to obtain a more accurate fluorescence lifetime and subsequent deconvolution to obtain IRF, I(t) requires the number of photons to be approximately 1×10 7 ;

[0100]

[0101] By using I(t) and the fluorescence lifetime τ0, the instrument response function IRF is obtained through the deconvolution algorithm (Formula 19). According to the characteristics of the observed target biomolecules in this embodiment, it can be expressed as:

[0102]

[0103] Where Δt is the resolution of microscopic time t, Δt = 0.016ns.

[0104] The variational Bayesian estimation of the microscopic time-macroscopic time curve delay(T) based on the lifetime-based photon-by-photon hidden Markov model is used to obtain the most likely state number of the model as well as the dynamic parameters and state change sequence. Artificially set the initial value of the transition probability distribution as well as The selection of should not be too different from the true value, and should be within 2 orders of magnitude as much as possible. It is an approximation of the posterior distribution of the model parameters, from the distribution The most likely parameters are obtained from the microscopic time-macroscopic time curve delay(T) and the Viterbi algorithm is used to solve the life state-macroscopic time curve τ(T). The Viterbi algorithm is used to calculate the most likely hidden state sequence.

[0105] The residence time of biomolecules in different states is counted according to the life state-macroscopic time curve τ(T). The residence time is subjected to frequency distribution statistics, and for example, the least square method is used to perform single exponential fitting to obtain the reaction rate constant, which is basically consistent with the reaction rate constant obtained in the real experiment.

[0106] Example 1 verifies the concept of the present invention by constructing a simulated data set through simulation. The data set is constructed based on the real fluorescence lifetime observation data of known biomacromolecules and the real data of rapid kinetic experiments, so the simulated data set has high authenticity and accuracy. Using the model provided by the present invention, the calculated reaction rate constant has a small error compared with the reaction rate constant obtained by the real experiment, indicating that the model of the present invention has high accuracy.

[0107] Example 2

[0108] This embodiment uses the photon-by-photon hidden Markov method of fluorescence lifetime to analyze the conformational dynamics changes of real biomolecules. In this embodiment, a special biomolecule is selected, namely the Holliday Junction DNA structure or HJ structure or HJ, which has two different conformations, and the biomolecule as a whole changes between the two conformations at a certain rate. The state reaction rate of the HJ structure is regulated by the concentration of magnesium ions in the solution, and the relationship with the magnesium ion concentration has been well analyzed, which can be used as a good example to verify this method. Fluorescent dyes Alexa Fluor 488 and Alexa Fluor647 can undergo FRET, in which the lifetime of the donor fluorescence Alexa Fluor 488 changes with the change of the distance between the two fluorophores, satisfying formula 6. The above two fluorescent markers are placed on the two arms of HJ, and the lifetime of Alexa Fluor 488 will change with the conformational changes of HJ. In this example, fluorescence lifetime confocal microscopy was used to observe free HJ in solution. A 488nm picosecond pulsed laser was used as the laser light source to collect the fluorescence signal when HJ freely diffused into the laser focal volume. The fluorescence lifetime was analyzed by photon-by-photon hidden Markov method to resolve the real-time conformational change information of HJ.

[0109] For a biological sample of interest, when it freely diffuses through the observation volume, the time it is excited and observed in the observation volume needs to be at least on the same order of magnitude as the time scale of the kinetic process; at the same time, the photon collection rate should also be ensured to match the scale of the kinetic process as much as possible, and the fluorescent molecules should collect a minimum of about 40 photons in each latent state; in order to minimize the impact of noise, the signal-to-noise ratio of the fluorescence signal should be greater than 15.

[0110] For HJ samples, HJ was linked to artificially prepared liposomes (such as Figure 4 ) Extend the observation time by reducing the diffusion rate, and use fat-soluble vitamin E and cysteamine to increase the fluorescence intensity and reduce fluorescence blinking to improve the fluorescence signal intensity and signal-to-noise ratio.

[0111] Step 1: Label one of the arms of HJ with fluorescent Alexa Fluor 488, and use a fluorescence lifetime confocal microscope to measure the intrinsic fluorescence lifetime τ0 of Alexa Fluor 488. The concentration of HJ is ~10 nM. The experiment collects approximately 1×10 7 photons to obtain the fluorescence lifetime decay curve I(t). The intrinsic fluorescence lifetime τ0 of Alexa Fluor 488 is obtained by fitting I(t) using the same method as in Step 1 of Example 1.

[0112] Step 2: Use I(t) and the fluorescence lifetime τ0 to obtain the instrument response function IRF through a deconvolution algorithm (Equation 16), with a microscopic time resolution of Δt = 0.016 ns.

[0113] Step 3: Collect fluorescence molecule data of freely diffusing HJ labeled with Alexa Fluor 488 and Alexa Fluor 647 through a confocal fluorescence lifetime microscope. This step includes:

[0114] 1) The current laboratory instruments are limited by the detection efficiency and can detect approximately 20 photons per millisecond. To keep the conformational change process of HJ within our detection range (1 ms < dwell time < 10 ms), multiple sets of different magnesium ion concentrations are set.

[0115] 2) To ensure that each HJ molecule can collect enough photons for analysis, we need to reduce the free diffusion speed of HJ and extend the time it stays in the laser focus volume. To achieve this, we connect HJ molecules to vesicles with a diameter of hundreds of nanometers through biotin-streptavidin interactions to reduce the diffusion speed of HJ. When preparing the vesicle sample, a certain proportion of phospholipid molecules with biotin-labeled heads is incorporated. In the experiment, the biotinylated HJ sample and streptavidin are incubated in a certain proportion to ensure that each HJ is connected to streptavidin as much as possible, while each streptavidin is connected to no more than 1 HJ. Then, the mixed solution of HJ and streptavidin is mixed with the vesicle solution in a certain proportion and incubated to ensure that each HJ is connected to the vesicle as much as possible, while each vesicle is connected to no more than 1 HJ. Through this method, the diffusion rate of vesicle HJ can be reduced by approximately 2 orders of magnitude.

[0116] Figure 4 A schematic diagram showing the connection of the observation sample to the vesicle surface to reduce the diffusion rate and increase the observation time is shown.

[0117] 3) Dilute the HJ connected to the vesicles to a suitable concentration, which requires that the HJ concentration is high enough to observe enough HJ molecules per unit time, and low enough to make the probability of more than one HJ molecule entering the focal volume at the same time low enough to ensure that the fluorescence signal is a single molecule signal. The generally accepted concentration is 50-100pM.

[0118] 4) Observe HJ using fluorescence lifetime confocal microscopy. A Nikon confocal microscope equipped with the fluorescence lifetime microscopy component PicoQuant was used in the experiment. A 60× oil objective lens was used in the experiment, with a numerical aperture of NA=1.42 and a laser focal volume of approximately 1fL. The laser light source uses a picosecond pulse laser, and the appropriate pulse excitation frequency is set according to the fluorescence lifetime. The frequency needs to be high enough to excite as many photons as possible, and the interval between two fluorescences is long enough to obtain a good enough lifetime decay curve to obtain a more accurate light intensity. The laser excitation frequency was set to 40MHz in the experiment. In order to obtain more accurate results, it is necessary to collect enough photons. Currently, about 4×10 5 photons.

[0119] Step 4, calculate the microscopic time-macroscopic time curve delay(T) (i.e., the photon-by-photon observation sequence) using the lifetime-based photon-by-photon hidden Markov model EM algorithm to obtain the most likely state number of the model as well as the hidden Markov model parameters and hidden state sequence.

[0120] The maximum expectation algorithm of variational Bayesian estimation is used as a more suitable special case of the EM algorithm in this embodiment, and the initial value of the transition probability distribution is artificially set. as well as The selection of should not be too different from the true value, and should be within 2 orders of magnitude as much as possible. It is an approximation of the posterior distribution of the model parameters, from the distribution The most likely hidden Markov model parameters are obtained: initial probability distribution, state transition probability distribution and observation probability distribution, wherein the structure of the observation probability distribution that needs to be iterated in the EM algorithm is defined as a convolution of an instrument response function and an ideal observation probability distribution, wherein the instrument response function gives a mapping between the true value and the measured value of the microscopic time in photon-by-photon observation.

[0121] For the microscopic time-macroscopic time curve delay(T) and the determined hidden Markov model parameters, the Viterbi algorithm is used to solve the life state-macroscopic time curve τ(T) as a hidden state sequence. Thus, the most likely life state-macroscopic time curve τ(T) is obtained by the Viterbi algorithm.

[0122] According to the life state-macroscopic time curve τ(T), the residence time of HJ molecules in different states is counted. The residence time is subjected to frequency distribution statistics, and the obtained frequency distribution statistics are fitted to a single exponential decay distribution and the reaction rate constant is obtained according to its decay rate, wherein the reaction rate constant is obtained by single exponential fitting using the least squares method. The determination of the reaction rate constant of the two-state conformational change of HJ at different magnesium ion concentrations (1mM~10mM) by this method is basically consistent with the data in previous literature, and the difference is about 10% or less, so it is believed that this method is reliable for determining the conformational kinetic parameters of HJ.

[0123] In Example 2, real biological molecules were selected, and fluorescence lifetime-real time measurement values ​​were obtained based on the principle of fluorescence resonance energy transfer. The measurement values ​​were analyzed based on the method of the present invention, and the reaction rate constant was calculated. Verification showed that it has higher credibility, indicating that the model of the present invention has higher accuracy.

[0124] In other embodiments of the present invention, the forward-backward algorithm may not be used in the variational EM calculation to avoid sacrificing accuracy, or other similar methods may be used to compromise between calculation accuracy and calculation, such as using a forward algorithm or a backward algorithm.

[0125] In other embodiments according to the present invention, the variational posterior factorized by the variational Bayesian theory is used according to the determined state of the target biomolecule. Each factor in may have other types of distribution forms instead of being limited to the Dirichlet distribution, gamma distribution and exponential decay distribution mentioned above, so its distribution form should be adjusted according to the actual model to be iterated.

[0126] In other embodiments according to the present invention, the instrument response function IRF may also be a parameter given in advance by a specific instrument and does not need to be calculated based on the fluorescence lifetime decay curve actually measured.

[0127] In other embodiments of the present invention, the method of the present invention can also be used to analyze the state or rapid kinetic behavior of other biological macromolecules, such as hairpin structure or G4 structure, wherein it is necessary to adjust the instrument response function IRF or the probability distribution model of each factor in the hidden state process according to the characteristics of the observation instrument and the observation target.

[0128] Although the present invention has been described through preferred embodiments, the present invention is not limited to the embodiments described herein but includes various changes and modifications that may be made without departing from the scope of the present invention.

Claims

1. A single molecule state analysis method based on a photon-by-photon approach, the method comprising: Based on the principle of fluorescence resonance energy transfer, donors and acceptors composed of fluorescent molecules are respectively labeled on the target biological molecules; observing the donor multiple times, wherein only a single photon emitted by the donor is received in each observation; According to the multiple observations, the microscopic time and macroscopic time corresponding to a single photon are recorded to generate a photon-by-photon observation sequence, wherein the microscopic time refers to the time interval from when the donor is excited to when it emits a photon through spontaneous radiation, and the macroscopic time refers to the moment when a photon is observed; The photon-by-photon observation sequence is used as the observation sequence of the hidden Markov model; a target sequence is constructed, wherein the target sequence includes the single-molecule fluorescence lifetime and its corresponding macroscopic time; the target sequence is used as the hidden state sequence of the hidden Markov model, and the hidden Markov model is used to calculate the target sequence from the observation sequence.

2. The method according to claim 1, wherein: The calculating the target sequence from the observation sequence using a hidden Markov model comprises: According to the photon-by-photon observation sequence, the number of hidden states of the hidden Markov and the corresponding hidden Markov model parameters are obtained using the EM algorithm: the initial probability distribution, the state transition probability distribution and the observation probability distribution; wherein the structure of the observation probability distribution that needs to be iterated in the EM algorithm is limited to a form having a convolution of an instrument response function and an ideal observation probability distribution, wherein the instrument response function gives a mapping between the real value and the measured value of the microscopic time in the photon-by-photon observation; The target sequence is obtained according to the photon-by-photon observation sequence and the hidden Markov model parameters by using a Viterbi algorithm for determining the hidden state sequence.

3. The method according to claim 2, wherein: The instrument response function is obtained according to the intrinsic lifetime decay curve of the fluorescent molecule and the original fluorescence lifetime through a deconvolution algorithm.

4. The method according to claim 2, wherein: The method of obtaining the hidden Markov model parameters by using the EM algorithm includes setting initial iteration values ​​of the state transition probability distribution and the observation probability distribution, respectively. The initial iteration values ​​are limited to within two orders of magnitude of the reference values ​​of the target biomolecules.

5. The method according to claim 2, wherein: The EM algorithm adopts the maximum expectation algorithm of variational Bayesian estimation.

6. The method according to claim 5, wherein: The EM algorithm adopts a forward algorithm, a backward algorithm or a forward-backward algorithm to reduce the computational time complexity.

7. The method according to any one of claims 1 to 6, further comprising the following steps: After obtaining the target sequence, obtaining the rapid kinetic information of the target biomolecule according to the multiple single-molecule fluorescence lifetimes and their corresponding macroscopic times in the target sequence includes: Calibrate the state of the target biomolecule according to the fluorescence lifetime corresponding to each observation; Performing frequency distribution statistics on the residence time distribution of the target biomolecule in each state; The obtained frequency distribution is statistically fitted into a single exponential decay distribution and a reaction rate constant is obtained according to its decay rate, wherein the reaction rate constant is used to calculate the free energy of the conformational change of the biomolecule.

8. The method according to claim 7, wherein: The obtained frequency distribution was subjected to single exponential fitting according to the least squares method to obtain the reaction rate constant.

9. The method according to claim 1, wherein: The structure of the observed probability distribution that needs to be iterated in the EM algorithm is defined as: Where IRF is the instrument response function, x is the observed value, and λ i is the observed probability value, is the ideal observation probability distribution, and bg is the noise constant associated with the instrument.

10. The method according to claim 1, wherein: Selecting the donor so that the target biomolecule has only a single fluorescence lifetime peak; and The diffusion rate of the target biomolecule is defined so that the donor freely diffuses through the laser focal volume and resides therein for at least 3 times the residence time of the target biomolecule in the state to be determined during the conformational state change.

11. A single molecule state analysis device based on a photon-by-photon approach, comprising a fluorescence lifetime microscope unit and a calculation unit, wherein the fluorescence lifetime microscope unit comprises: a picosecond pulsed laser, which is used to excite the donor to an excited state; Single-photon detectors, which are limited to receiving only a single photon during one observation period; A time-correlated single photon counter, which is used to record the microscopic time and macroscopic time associated with the single photon; and The computing unit is configured to implement the single-molecule state analysis method according to any one of claims 1 to 10 according to the microscopic time and macroscopic time associated with the single photon recorded by the fluorescence lifetime microscope unit.

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