Single molecule state analysis method based on a photon-by-photon approach

Abstract

The application provides a single-molecule state analysis method based on a photon-by-photon approach, which is based on the principle of fluorescence resonance energy transfer, observes a donor photon by photon, records micro time corresponding to a single photon and macro time to generate a photon-by-photon observation sequence, takes the photon-by-photon observation sequence as an observation sequence of a hidden Markov model, takes a target sequence containing a single-molecule fluorescence lifetime and corresponding macro time as a hidden state sequence of the hidden Markov model, and calculates the target sequence from the observation sequence, wherein an initial probability distribution, a state transition probability distribution and an observation probability distribution are obtained according to the photon-by-photon observation sequence and by using an EM algorithm, and the observation probability distribution has a convolution form of an instrument response function and an ideal observation probability distribution. According to the photon-by-photon observation sequence and model parameters, a fluorescence lifetime-macro time function is obtained by using a Viterbi algorithm, and a target biomolecule state is analyzed. The method significantly improves the time resolution of fluorescence molecule lifetime observation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of detecting the dynamic behavior of biomolecules using fluorescence lifetime microscopy, and in particular, the present application relates to a single-molecule state analysis method based on a photon-by-photon approach. BACKGROUND

[0002] The function and conformation of biomolecules are closely related, and linking the conformation state to the transformation of biochemical function 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 and understand the truth of life activities from the level of molecular operation mechanism. Currently, the techniques 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] The 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 level. FRET refers to when two fluorescent groups are close enough, only one fluorescent group 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 judged from the fluorescence intensity and fluorescence lifetime of A, and the spatial resolution can reach sub-nanometer level. FRET is generally used in combination with an electron multiplying CCD (EMCCD) and a confocal microscope, and the real-time time resolution can reach sub-millisecond level.

[0004] Figure 1 A schematic diagram of acquiring single-molecule fluorescence lifetime data using a confocal fluorescence microscope is shown.

[0005] Fluorescence lifetime refers to the average time that a fluorescent molecule maintains its excited state before emitting a photon, which is an inherent property of a fluorophore. At the single-molecule level, the fluctuation of fluorescence lifetime reflects the heterogeneity and fluctuation of the local environment, and has higher stability than fluorescence intensity. When fluorescence resonance energy transfer exists, the fluorescence lifetime decreases with the increase of FRET efficiency, reflecting the conformational change of the biomolecule. On the basis of the relationship between fluorescence lifetime and FRET efficiency, the lifetime-based single-molecule FRET method is developed and applied to the study of biomolecular conformation dynamics.

[0006] The SIFA, lipo-FRET and Queen-FRET technologies developed from the FRET in the prior art known technologies provide a method for observing in situ the conformation and position changes of biomolecules near the membrane of living cells, and the principle is that the fluorescence intensity and the fluorescence lifetime of the fluorescent group labeled on the biomolecule change with the distance between the fluorescent group and the quencher. Compared with the FRET, only one fluorescent molecule needs to be labeled at the site of interest of the biomolecule. The time resolution of the SIFA, lipo-FRET and Queen-FRET is in the order of seconds, and the dynamic process in the time scale of milliseconds and below cannot be accurately observed. The main factors limiting the time resolution are: 1) the EMCCD is used to observe the change of the fluorescence intensity, and the time resolution is affected by the time resolution of the EMCCD, which is generally in the order of 50 milliseconds; 2) in the existing fluorescence lifetime FRET method, more photons are needed to fit the relatively accurate lifetime, which limits the resolution, and the dynamic process of the research object is generally in the sub-second and longer time scale.

[0007] Therefore, there is a need for an analysis method of the state and fast dynamic behavior of a single biomolecule with higher time resolution and a device for implementing the same. SUMMARY

[0008] The present application 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, such as the Baum-Welch algorithm, in the per-photon framework. The energy transfer efficiency E between the donor and the acceptor in the fluorescence resonance energy transfer is defined as:

[0009]

[0010]

[0011]

[0012] wherein 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 of E, E is very sensitive to the spatial distance, which is the reason why the fluorescence resonance transfer can be used to measure the nanoscale distance. R0 is calculated by the dipole approximation, wherein Q D is the quantum yield of the donor, 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, and J(Λ) is the spectral overlap coefficient of the normalized donor emission spectrum F D and the acceptor absorption spectrum E A .

[0013] 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.

[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 to transition from the ground state to the excited state, after a time t, the fluorescent molecule absorbs a photon, and the electron in the molecule will transition from the ground state to the excited state. After a vibration relaxation time (usually between picoseconds and nanoseconds), the molecule will return to the ground state by emitting a photon with a longer wavelength and lower energy. The vibration relaxation time accounts for the vast majority of the time from excitation to emission. For the same fluorescent molecule, the vibration 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 vibration relaxation time is also called the microscopic time t, and the number of photons at the corresponding time is I(t), which satisfies formula 4. The curve of I(t) changing with t is called the fluorescence lifetime decay curve or the fluorescence intensity decay curve. Where A is the pre-exponential factor, equal to the number of photons at t = 0, proportional to the total number of photons. τ D is the characteristic value of the decay to 1 / e of the maximum value of the exponential decay function, called the fluorescence lifetime, reflecting the average residence time of a certain fluorescent molecule in the excited state, which is an inherent property, but is affected by various environmental factors such as temperature, pH, etc.

[0015]

[0016]

[0017]

[0018] The fluorescence lifetime determined by observing the donor in the presence and absence of the acceptor is denoted as τ DA and τ D respectively, so τ D can be regarded as the original fluorescence lifetime here. Assuming there is a single distance (i.e. no distance fluctuation) between the donor and acceptor fluorophores, the FRET efficiency is given by formula 5. The advantage of this method is that no correction factor is needed, because 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. τ DA reflects the relative distance between the FRET donor and acceptor, as shown in formula 6.

[0019] Hidden Markov model (HMM) is widely used in life science to analyze the conformational dynamics of biomolecules. HMM is a probabilistic model about time series, which describes a hidden Markov chain randomly generating a sequence of unobservable states, and then generating an observable sequence by generating an observation from each state. The sequence of states randomly generated by the hidden Markov chain is called state sequence, and the sequence randomly generated by generating an observation from each state is called observation sequence. Each position of the sequence can be regarded as a time. The parameters Φ of the HMM are determined by three matrices, namely the initial probability distribution, the state transition probability distribution and the observation probability distribution. The state transition probability is defined as the probability of transitioning to another state at the next time under the premise of being in a certain state at the current time. The state transition probability can be completely 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 of observing a certain predetermined value under a certain state. For FRET data, the observation probability satisfies the Gaussian distribution.

[0020] Figure 3 A schematic diagram of the statistical lifetime decay curve of the fluorescence molecular micro-time is shown. The numerical value of the observation probability matrix is the result of normalizing 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 application provides a single molecule state analysis method based on a photon-by-photon approach, which comprises:

[0022] Based on the principle of fluorescence resonance energy transfer, a donor and an acceptor composed of fluorescence molecules are respectively labeled on a target biomolecule;

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

[0024] The micro-time corresponding to the single photon and the macro-time are recorded according to the multiple observations to generate a photon-by-photon observation sequence, wherein the micro-time refers to the time interval from the excitation of the donor to the emission of the spontaneous radiation photon, and the macro-time refers to the time when a certain photon is observed;

[0025] The photon-by-photon observation sequence is taken as the observation sequence of the hidden Markov model; a target sequence is constructed, wherein the target sequence comprises a single molecule fluorescence lifetime and the corresponding macro-time; the target sequence is taken as the hidden state sequence of the hidden Markov model, and the target sequence is calculated from the observation sequence by using the hidden Markov model.

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

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

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

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

[0030] Preferably, in the method, the obtaining the hidden Markov model parameters using the EM algorithm comprises setting the respective iterative initial values of the state transition probability distribution and the observation probability distribution, which are limited within 2 orders of magnitude of the reference value of the target biomolecule.

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

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

[0033] Preferably, in the method, the following steps are further included:

[0034] After obtaining the target sequence, the fast kinetic information of the target biomolecule is obtained according to the single-molecule fluorescence lifetimes in the target sequence and the corresponding macro-time, comprising:

[0035] According to the fluorescence lifetime of the target biomolecule corresponding to each observation, the state in which the target biomolecule is located is calibrated;

[0036] The residence time distribution of the target biomolecule in each state is subjected to frequency distribution statistics;

[0037] The obtained frequency distribution statistics is fitted to a single-exponential decay distribution and the reaction rate constant is obtained according to the 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 fitted with a single exponential according to least square method to obtain the reaction rate constant.

[0039] Preferably, in the method, the structure of the observation 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 observation value, λ i is the observation probability value, is the ideal observation probability distribution, and bg is the instrument related noise constant.

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

[0043] The diffusion rate of the target biomolecule is defined so that the time for the donor to freely diffuse through the laser focus volume and stay therein is at least 3 times the residence time of the target biomolecule conformation state change in the state to be determined.

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

[0045] a picosecond pulsed laser for exciting the donor to an excited state;

[0046] a single photon detector limited to receiving only a single photon in one observation period;

[0047] a time-correlated single photon counter for recording the micro-time and macro-time associated with the single photon; and

[0048] The computing unit is configured to implement the single molecule state analysis method according to any one of the first aspect of the present application according to the micro-time and macro-time associated with the single photon recorded by the fluorescence lifetime microscope unit.

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

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

[0051] Figure 1 A schematic diagram showing the acquisition of single-molecule fluorescence lifetime data using a confocal fluorescence microscope is shown.

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

[0053] Figure 3 A schematic diagram showing the statistical lifetime decay curve of a fluorescent molecule microscopic time, where the values of the observation probability matrix are the result of the lifetime decay curve normalization is shown.

[0054] Figure 4 A schematic diagram showing the attachment of observation samples to the vesicle surface to reduce the diffusion rate and increase the observation time is shown. DETAILED DESCRIPTION

[0055] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based upon the embodiments in the present application, those skilled in the art can make other embodiments without creative effort, which are also within the scope of protection of the present application. In other cases, well-known methods, devices, implementations or operations are not shown or described in detail in order to avoid obscuring the aspects of the present application.

[0056] In addition, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the application. One skilled in the relevant art will recognize, however, that the application can be practiced without one or more of the specific details, or with other methods, components, devices, steps, etc. In other instances, well-known methods, devices, implementations, or operations are not shown or described in detail to avoid obscuring aspects of the present application. The described flow diagrams merely illustrate one example of how to implement the process and are not all inclusive or required. For example, some operations / steps can be split into multiple operations / steps, and some operations / steps can be combined or partially combined, and thus the actual order can vary from what is described. The order of the steps can be changed, for example, depending on the implementation.

[0057] For FRET experiment, given the observation model, the HMM model parameters and the hidden state sequence need to be found in the case of known model. Using EM algorithm, such as using Baum-Welch algorithm, the model parameters can be solved according to the observation sequence, and according to the model parameters and the observation sequence, the most likely hidden state sequence can be solved using Viterbi algorithm (also known as dynamic programming algorithm or viterbi algorithm). There are many methods for determining the data model, i.e. the number of hidden states, using EM algorithm in actual experiments, and these methods all try to avoid artificial bias. Preferably, the inventors use variational Bayesian inference to determine the data model in the present application, which can more efficiently match the application of using hidden Markov model to analyze biomolecules under the photon-by-photon framework.

[0058] The traditional HMM model processing fluorescence signal ignores the calculation bias caused by the process of photon arrival time to the detector. In order to optimize this problem, the present application 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 a single photon detector and a single photon counter to construct an observation framework of fluorescence lifetime changing with time in a photon-by-photon observation. Specifically, the photon-by-photon hidden Markov model analysis can be realized by using photoelectric avalanche diode to record the photon arrival time. This method can be used for FRET and lifetime experimental data of free diffusion fluorescence, can fully extract the information carried by each photon, and can more accurately analyze the experimental data.

[0059] In the photon-by-photon framework, a short enough time unit Δt is first defined, in which at most one photon can be received, and 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 is a system that randomly jumps between different lifetime states in accordance with the Markov process, and the hidden state sequence is z i ,z i+1 The time between adjacent photons is Δt, and the observation sequence is wherein is the observed value of the photon detected at time t i In the fluorescence lifetime experiment, it is the time from the excitation of the fluorescent molecule by the laser to the spontaneous emission of the photon, which is called micro time. In the case of τ i The micro time of the fluorescent molecule in the lifetime state satisfies the exponential distribution with decay coefficient , wherein λ iTo observe the probability value. In the system model state number K conditions, including the system complete data of the to-be-solved parameter probability distribution can be expressed as:

[0060]

[0061] Where the right side of the first term:

[0062]

[0063] And where, is the reaction rate constant, and represent the probability of the system leaving the current state and moving to other states.

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

[0065]

[0066] Taking the logarithm of both sides and taking the expectation with respect to , we get

[0067]

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

[0069]

[0070]

[0071] and only when the equality holds, that is, the approximate variational posterior is equal to the true posterior, and the purpose of variational Bayesian estimation is to maximize the right side of the inequality by adjusting the variational posterior , and continuously approaches the marginal likelihood.

[0072] In the calculation process, the variational Bayesian theory factorizes ,

[0073]

[0074]

[0075] where P(π), satisfies the Dirichlet distribution, satisfies the Gamma distribution, and satisfies the exponential decay distribution,

[0076]

[0077] The use of the forward-backward algorithm in the variational EM computation reduces the computational time complexity from O(K T ) to O(K 2 T), thus speeding up the computation. In addition to computing the edge likelihood function, the variational estimation also yields a probability distribution over the parameters given the data. The most likely parameters can be obtained from these distributions and the most likely hidden state sequence can be computed using the Viterbi algorithm.

[0078] The present application further develops the photon-by-photon hidden Markov method to analyze smFRET experimental data obtained by a confocal microscope, which contains information of fluorescence lifetime. When a fluorescent molecule passes through the focal volume of the confocal microscope, it is excited by a picosecond pulsed laser to emit fluorescence. The instrument records the time T and the micro-time t of each photon reaching the detector. In the ideal state without considering the deviation caused by the instrument response function, the ideal observation probability distribution can be approximated as a distribution satisfying .

[0079] To further correct the computation to improve the accuracy, the inventors modify the observation probability distribution according to the instrument response function, so that the observation probability distribution is limited to a form having a convolution of the instrument response function and the ideal observation probability distribution, wherein the instrument response function gives the mapping between the true value and the measured value of the micro-time in the photon-by-photon observation. In one example, the modification has the following form

[0080]

[0081] where IRF is the instrument response function, and the denominator part on the right side represents the normalization processing. However, the modification is not limited to the above specific formula form, and can be adjusted according to the characteristics of the observation 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 instrument-related constant bg is not necessarily present, and similar local parameter modification does not deviate from the protection scope covered by the concept of the present application. i After the modification, f(x|λ D ) is applied to the second term on the right side of formula 7, and thus the composition structure of the hidden Markov model of the complete data of the to-be-solved parameters is also updated, so that the fluorescence lifetime information is integrated into the photon-by-photon hidden Markov model.

[0082] The method steps are as follows:

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

[0084] I(t) is known and τ D The instrument response function IRF(t) of the confocal fluorescence lifetime microscope can be analytically resolved by deconvolution;

[0085] The concentration of the biological molecule to be measured, which is labeled with donor and acceptor fluorescence, is diluted to about 50 pM, and data of the freely diffusing fluorescent molecules, i.e. micro-time and macro-time corresponding to single photons, are collected by the confocal fluorescence lifetime microscope, and the data are constructed into observation sequences.

[0086] The EM algorithm estimation based on the lifetime-based per-photon hidden Markov model is performed on the collected observation sequences to obtain the most likely number of states of the model and the kinetic parameters and state change sequences. The instrument response function obtained is required to modify the hidden state model of the hidden Markov model in the calculation. Before the EM algorithm is used to iteratively converge the hidden Markov model, the initial value of the transition probability distribution is artificially set and The selection of the initial value of the transition probability distribution should not differ from the real value range of the target molecule by more than two orders of magnitude, and is preferably within two orders of magnitude (the initial value of the iteration refers to the initial value of π, and The initial value of π, and is not necessarily within 0-1. For example, the values 0.1 and 0.001 for π differ by two orders of magnitude. In general, a suitable setting of the initial value of the iteration can effectively reduce the calculation time of the EM algorithm and improve the accuracy of the results, but it is only an optional step for optimization and is not a limitation of the method of the present application). The probability distribution of the parameters Φ of the hidden Markov model is obtained from the posterior distribution , and the most likely parameters Φ are determined and the most likely hidden state sequence is calculated using the Viterbi algorithm.

[0087] The hidden state sequence is obtained, i.e. the mapping relationship of the single-molecule fluorescence lifetime-macro-time is obtained, and based on this, other state information or fast kinetic behavior of the target biological molecule can be further analyzed.

[0088] In a further analytical step, illustrative and not limiting, after obtaining the target sequence, rapid dynamic information of the target biomolecule is obtained based on the mapping relationship between single-molecule fluorescence lifetime and macroscopic time in the target sequence. This includes: determining the state of the target biomolecule based on its 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 the reaction rate constant based on its decay rate, wherein the reaction rate constant is used to resolve information such as the free energy of biomolecule conformational changes. In a further calculation example, the decay rate is approximated as the reaction rate constant.

[0089] The modified Hidden Markov Model (HMM) calculation method described above integrates fluorescence lifetime information corresponding to the instrument response function, fully utilizing the advantages of fluorescence lifetime FRET and photon-by-photon analysis. It can analyze the fluorescence lifetime count of the system under study and accurately resolve the parameters of dynamic changes between lifetime states, thereby further analyzing the system's dynamic information from the changes in fluorescence lifetime. Currently, the detection of single-molecule dynamics can achieve sub-millisecond time resolution.

[0090] Example 1

[0091] This example uses simulated data to verify the feasibility of the above method. Since real experimental data contains many influencing factors and the correct results cannot be directly obtained, simulated data was first obtained based on a Monte Carlo simulation model to preliminarily verify the algorithm's reliability. The simulated data had the same signal intensity and signal-to-noise ratio settings as the experimental data. In this simulation program, it is assumed that the sample to be tested is a Holliday Junction (HJ) DNA structure (with complementary base pairing at both ends), with two conformations (open-loop and closed-loop) (A and B), each end labeled with different fluorescent molecules, and FRET is generated, leading to a decrease in donor fluorescence lifetime. The intrinsic fluorescence lifetime of the fluorescent molecule τ0 = 3.5 ns, and each conformation corresponds to a different donor fluorescence lifetime τ A =1ns,τ B = 2.6 ns. DNA molecules interconvert between two conformations and reach dynamic equilibrium. Five different initial reaction rate constants were 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 change of molecular conformation P can be calculated according to the initial reaction rate constant AB = k AB ΔT, P BA = k BA ΔT. Where ΔT is the macroscopic time resolution, set to 1 us. The probability P of 0-1 is generated by a random number generator (RNG). When the molecule is in conformation A, and P < P AB , it becomes conformation B; when the molecule is in conformation B, and P < P BA , it becomes conformation A, otherwise the conformation remains unchanged.

[0092] In the process of exciting the fluorescent molecules by laser and accepting by the detector, the probability of exciting the fluorescent molecules by laser and accepting by the detector is set according to the average intensity of the signal in the experiment, and a random number is generated by a random number generator to determine whether the fluorescent molecules finally reach the detector. When recording the photon information, the macroscopic time and the microscopic time need to be recorded. The macroscopic time is the number of times of pulsed laser excitation, and the microscopic time needs to be generated by a random number. When the molecular state is s (s is A or B), the lifetime is τ s , and the microscopic time t of the photon is generated by an exponential decay distribution random number generator. According to the instrument conditions in the experiment, only the photon data with a microscopic time less than 25 ns is saved.

[0093] Due to the existence of scattered light, detector dark count and other reasons, there will be a lot of background noise in the actual detected photons, and the characteristic is that the microscopic time is not exponentially decaying distribution, but uniform distribution. According to the experimental condition, the probability of background noise is set. First, a random number is generated by a random number generator, and it is judged whether the background photon is detected by comparing the probability generated by the background noise. If the background photon is detected, a randomly distributed microscopic time t is generated by a random number generator. Since the real single photon detector has a 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 a pulse period. Therefore, before recording the new photon information, it is also necessary to judge whether a photon has been recorded in the same macroscopic time, and the microscopic time is smaller than the new photon (the photon with 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 instrument detects a microscopic time of t", which satisfies the probability distribution function:

[0095]

[0096] where a is a normalization factor. Where IRF is set according to the parameter setting of the instrument in the experiment.

[0097] According to the above simulation process, the total detection time of each group of state transition parameters is set to 2s, and the total number of photons is about 4x10 5 .

[0098] According to the above simulation process, the following data can be obtained: 1) fluorescence molecule intrinsic lifetime decay curve I(t); 2) fluorescence labeled Holliday Junction micro-time-macro-time curve delay(T). The above data are analyzed by lifetime per photon hidden Markov analysis:

[0099] By fitting the tail of the fluorescence molecule intrinsic lifetime decay curve I(t), that is, only the data of t>4ns are fitted. The fitting method is selected as the least square method, and the fitting function y(t) is selected as the single exponential decay function, as shown in formula 18, to obtain the original fluorescence lifetime τ0. In order to obtain more accurate fluorescence lifetime and subsequent deconvolution to obtain IRF, the number of photons of I(t) is required to be about 1x10 7 ;

[0100]

[0101] Using I(t) and fluorescence lifetime τ0, the instrument response function IRF is obtained by deconvolution algorithm (formula 19), which can be expressed as:

[0102]

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

[0104] The model most likely state number, kinetic parameters and state change sequence are obtained by performing variational Bayesian estimation based on lifetime per photon hidden Markov model on the micro-time-macro-time curve delay(T). The initial value of transition probability distribution is set artificially and The selection of the above should not differ too much from the true value, and should be within 2 orders of magnitude as much as possible. is the posterior distribution of the model parameters, and the most likely parameters are obtained from the distribution The lifetime state-macro-time curve τ(T) is solved by using the Viterbi algorithm on the micro-time-macro-time curve delay(T). The most likely hidden state sequence is calculated by using the Viterbi algorithm.

[0105] The residence time of biomolecules in different states is counted according to the lifetime state-macro time curve τ(T). The residence time is counted by frequency distribution statistics, and an example is shown in which a single exponential fitting is performed by using the least square method to obtain a reaction rate constant, which is basically consistent with the reaction rate constant obtained by real experiment.

[0106] Example 1 verifies the concept of the present application, and a simulation data set is constructed by simulation, which is constructed according to the real fluorescence lifetime observation data of known biological macromolecules and the real data of fast kinetics experiment, so the simulation data set has high authenticity and accuracy. The reaction rate constant obtained by using the model given in the present application has very small error compared with the reaction rate constant obtained by real experiment, indicating that the model of the present application has high accuracy.

[0107] Example 2

[0108] This example uses the photon-by-photon hidden Markov method of fluorescence lifetime to analyze the conformational dynamics of real biological molecules. In this example, a special biological molecule is selected, i.e. Holliday Junction DNA structure or HJ structure or HJ, which has two different conformations, and the whole biological molecule changes between the two conformations at a certain rate. The state reaction rate of HJ structure is regulated by the concentration of magnesium ions in the solution, and the relationship with the concentration of magnesium ions has been well analyzed, which can be a good example for verifying the method. The fluorescence dyes Alexa Fluor 488 and Alexa Fluor 647 can undergo FRET, in which the lifetime of the donor fluorescence Alexa Fluor 488 changes with the distance between the two fluorophores, satisfying formula 6. The above two fluorescent labels are placed on the two arms of HJ, and the lifetime of Alexa Fluor 488 will change with the conformational change of HJ. In this example, the fluorescence lifetime confocal microscope is used to observe the free HJ in the solution, a 488 nm picosecond pulsed laser is used as the laser light source, the fluorescence signal of HJ freely diffusing into the laser focusing volume is collected, and the photon-by-photon hidden Markov method of fluorescence lifetime is used for analysis to obtain real-time conformational change information of HJ.

[0109] For a biological sample of interest, when it freely diffuses through the observation volume, the time of being excited and observed in the observation volume needs to be at least in the same order of magnitude as the time scale of the kinetic process; at the same time, the photon collection rate should also be matched with the kinetic process scale as much as possible, and the fluorescence molecule should collect at least about 40 photons in each hidden state; in order to reduce the influence of noise as much as possible, the signal-to-noise ratio of the fluorescence signal should be greater than 15.

[0110] For HJ sample, HJ is connected to the artificial prepared liposome through biotin-streptavidin interaction (such asFigure 4 ) To extend the observation time to reduce the diffusion rate, we use fat-soluble vitamin E and cysteamine to increase the fluorescence intensity while reducing the fluorescence flicker to improve the fluorescence signal intensity and signal-to-noise ratio.

[0111] Step 1, One arm of HJ is labeled with fluorescent Alexa Fluor 488, and the intrinsic fluorescence lifetime of Alexa Fluor 488, τ0, is measured by fluorescence lifetime confocal microscopy with HJ concentration of ~10 nM. About 1 x 10 7 photons are collected to obtain the fluorescence lifetime decay curve I(t). The intrinsic fluorescence lifetime of Alexa Fluor 488, τ0, is obtained by fitting I(t) in the same way as Step 1 in Example 1.

[0112] Step 2, Using I(t) and the fluorescence lifetime τ0, the instrument response function, IRF, is obtained by the deconvolution algorithm (Equation 16) with a micro-time resolution of Δt = 0.016 ns.

[0113] Step 3, HJ labeled with Alexa Fluor 488 and Alexa Fluor 647 is used to collect free diffusion fluorescence molecule data by confocal fluorescence lifetime microscopy. This step includes:

[0114] 1) The current laboratory instrument used is limited by the detection efficiency, which can detect about 20 photons per millisecond. In order to make the conformational change process of HJ within our detection range (1 ms < dwell time < 10 ms), we set up multiple groups of different magnesium ion concentrations.

[0115] 2) In order to make each HJ molecule be able to collect enough photons for analysis, we need to reduce the free diffusion rate of HJ and extend its residence time in the laser focus volume. To achieve this purpose, we connect the HJ molecules to nanometer-diameter vesicles through biotin-streptavidin interaction to reduce the diffusion rate of HJ. When preparing the vesicle sample, a certain proportion of biotin-labeled phospholipid molecules are incorporated. In the experiment, the biotin-labeled HJ sample is incubated with streptavidin in a certain proportion to connect as many HJs as possible to each streptavidin, while each streptavidin is connected to no more than one HJ. Then the mixed solution of HJ and streptavidin is incubated with the vesicle solution in a certain proportion to connect as many HJs as possible to each vesicle, while each vesicle is connected to no more than one HJ. Through this method, the diffusion rate of the vesicle HJ can be reduced by about 2 orders of magnitude.

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

[0117] 3) Dilute the HJ with vesicles to an appropriate concentration, both high enough to observe a sufficient number of HJ molecules per unit time and low enough to ensure that the probability of more than one HJ molecule entering the focal volume simultaneously is sufficiently low to ensure that the fluorescence signal is a single molecule signal. A generally accepted concentration is 50-100 pM.

[0118] 4) Observe the HJ using fluorescence lifetime confocal microscopy. In the experiment, a Nikon confocal microscope was used, equipped with a fluorescence lifetime microscope module PicoQuant. In the experiment, a 60x oil objective was used, with a numerical aperture NA = 1.42, and the laser focal volume was about 1 fL. A picosecond pulsed laser was used as the laser light source, and the appropriate pulse excitation frequency was 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 fluorescence needs to be long enough to obtain a good lifetime decay curve to obtain a more accurate light intensity. In the experiment, the laser excitation frequency was set to 40 MHz. In order to obtain more accurate results, a sufficient number of photons need to be collected. In the experiment, about 4 x 10 5 photons were collected for each condition.

[0119] Step 4, calculate the EM algorithm of the lifetime-based per-photon hidden Markov model for the micro-time-macro-time curve delay(T) (i.e. the per-photon observation sequence) to obtain the most likely number of states of the model and the hidden Markov model parameters and the hidden state sequence.

[0120] In this embodiment, the maximum expectation algorithm using variational Bayesian estimation is a more suitable special case of the EM algorithm, and the initial values of the transition probability distribution and are set artificially to be not too different from the true values, and are preferably within two orders of magnitude. is an approximation of the posterior distribution of the model parameters, and the most likely hidden Markov model parameters: the initial probability distribution, the state transition probability distribution and the observation probability distribution are obtained from the distribution , wherein the structure of the observation probability distribution that needs to be iterated in the EM algorithm 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 true value and the measured value of the micro-time in the per-photon observation.

[0121] Using the micro-time-macro-time curve delay(T) and the determined hidden Markov model parameters, the Viterbi algorithm is used to solve the lifetime state-macro-time curve τ(T) as the hidden state sequence. Thus, the most likely lifetime state-macro-time curve τ(T) is obtained by the Viterbi algorithm.

[0122] The residence time of HJ in different states is counted according to the lifetime state-macro time curve τ(T). The frequency distribution statistics of the residence time is obtained, the single exponential decay distribution is fitted according to the obtained frequency distribution statistics, and the reaction rate constant is obtained according to the decay rate, wherein the reaction rate constant is obtained by single exponential fitting using the least square method. The reaction rate constant of the bimolecular conformation change of HJ under different magnesium ion concentrations (1 mM-10 mM) determined by the method is basically consistent with the data in the previous literature, and the difference is about less than 10%, so it is considered that the method is reliable for determining the conformation dynamics parameters of HJ.

[0123] In example 2, a real biological molecule is selected, the fluorescence lifetime-real time measurement value is obtained based on the principle of fluorescence resonance energy transfer, and the measurement value is analyzed based on the method of the application to calculate the reaction rate constant. It is proved that the reliability is higher, which shows that the model of the application has high accuracy.

[0124] In other embodiments according to the application, the forward-backward algorithm can also not be used in the variational EM calculation to avoid sacrificing accuracy, or other similar methods can 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 application, according to the determined state of the target biological molecule, the variational posterior Each factor in the variational posterior factorized according to the variational Bayesian theory can have other types of distribution forms instead of being limited to the Dirichlet distribution, the Gamma distribution and the exponential decay distribution described above, and therefore the distribution form should be adjusted according to the actual model to be iterated.

[0126] In other embodiments according to the application, the instrument response function IRF can also be a parameter given in advance by a specific instrument instead of being calculated according to the actually measured fluorescence lifetime decay curve.

[0127] In other embodiments according to the application, the method described in the application can also be used to analyze the state or fast kinetics behavior of other biological macromolecules, such as hairpin structure or G4 structure, wherein the probability distribution model of the instrument response function IRF or each factor in the process of solving the hidden state needs to be adjusted according to the observation instrument and the characteristics of the observation target.

[0128] Although the application has been described by preferred embodiments, the application is not limited to the embodiments described herein, and includes various changes and variations made without departing from the scope of the application.

Claims

1. A method for single-molecule state analysis based on a photon-by-photon approach, the method comprising: labeling a donor and an acceptor, both of which are composed of fluorescent molecules, on a target biomolecule, respectively, based on the principle of fluorescence resonance energy transfer; observing the donor multiple times, wherein only a single photon emitted by the donor is received in each observation; recording a micro-time corresponding to a single photon and a macro-time at which the photon is observed according to the multiple observations to generate a photon-by-photon observation sequence, wherein the micro-time refers to a time interval from the excitation of the donor to the emission of a photon by spontaneous radiation, and the macro-time is the time at which a photon is observed; taking the photon-by-photon observation sequence as an observation sequence of a hidden Markov model; constructing a target sequence, wherein the target sequence comprises single-molecule fluorescence lifetimes and corresponding macro-times; taking the target sequence as a hidden state sequence of the hidden Markov model, and calculating the target sequence from the observation sequence using the hidden Markov model; wherein the calculation of the target sequence from the observation sequence using the hidden Markov model comprises: obtaining the number of hidden states of the hidden Markov model and corresponding hidden Markov model parameters, i.e., an initial probability distribution, a state transition probability distribution and an observation probability distribution, using an EM algorithm according to the photon-by-photon observation sequence; 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 a true value of a micro-time in a photon-by-photon observation and a measured value; obtaining the target sequence by a Viterbi algorithm for determining the hidden state sequence according to the photon-by-photon observation sequence and the hidden Markov model parameters.

2. The method of claim 1, wherein, The instrument response function is obtained from a fluorescence molecule intrinsic lifetime decay curve and an original fluorescence lifetime according to a deconvolution algorithm.

3. The method of claim 1, wherein, The obtaining of the hidden Markov model parameters using the EM algorithm comprises setting an iterative initial value of each of the state transition probability distribution and the observation probability distribution, which is limited within 2 orders of magnitude of a reference value of the target biomolecule.

4. The method of claim 1, wherein, The EM algorithm uses a maximum expectation algorithm of a variational Bayesian estimation.

5. The method of claim 4, wherein, The EM algorithm uses a forward algorithm, a backward algorithm or a forward-backward algorithm to reduce the computational time complexity. 6.The method according to any one of claims 1 to 5, further comprising the following steps: after obtaining the target sequence, obtaining fast kinetic information of the target biomolecule according to a plurality of the single-molecule fluorescence lifetimes and corresponding macro-times in the target sequence, comprising: labeling a state in which the target biomolecule is located according to a fluorescence lifetime corresponding to each observation; performing frequency distribution statistics on a residence time distribution of the target biomolecule in each state; fitting the obtained frequency distribution statistics into a single-exponential decay distribution and obtaining a reaction rate constant according to a decay rate, wherein the reaction rate constant is used to calculate a free energy of a conformational change of the biomolecule.

7. The method of claim 6, wherein, performing single-exponential fitting on the obtained frequency distribution according to a least square method to obtain the reaction rate constant.

8. The method of claim 1, wherein, The structure of the observation probability distribution that needs to be iterated in the EM algorithm is defined as: wherein, is the instrument response function, x is the observed value, is the observed probability value, is the ideal observed probability distribution, is a noise constant associated with the instrument.

9. The method of claim 1, wherein, The donor is selected such that the target biomolecule has only a single fluorescence lifetime peak; and The diffusion rate of the target biomolecule is defined such that the time the donor is free to diffuse through the laser focus volume and reside therein is at least 3 times the residence time of the target biomolecule conformational state change in the state to be determined.

10. A single-molecule state analysis apparatus based on a photon-by-photon approach, comprising a fluorescence lifetime microscope unit and a computing unit, wherein the fluorescence lifetime microscope unit comprises: a picosecond pulsed laser for exciting a donor into an excited state; a single-photon detector limited to receive only a single photon within one observation period; a time-correlated single-photon counter for recording the microscopic and macroscopic time associated with the single photon; and the computing unit is configured to implement the single-molecule state analysis method of one of claims 1 to 9 based on the microscopic and macroscopic time associated with the single photon recorded by the fluorescence lifetime microscope unit.

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