WO2015154137A1

WO2015154137A1 - A method and a system for identifying molecules

Info

Publication number: WO2015154137A1
Application number: PCT/AU2015/000216
Authority: WO
Inventors: Philip Russell NICOVICH; Katharina Gaus
Original assignee: NewSouth Innovations Pty Ltd
Current assignee: NewSouth Innovations Pty Ltd
Priority date: 2014-04-11
Filing date: 2015-04-10
Publication date: 2015-10-15
Anticipated expiration: 2016-10-11

Abstract

A method and an apparatus for counting fluorescent molecules in a sample are disclosed in this specification. The disclosed method and apparatus allows counting fluorescent molecules and derive molecules trajectories based on spatial and temporal information. Spatial and temporal information are processed using mathematical models and variable thresholds to extract a reliable number of fluorescent molecules and their trajectories in a cluster in a regime where the activation rate is not constant in time. The system and methods disclosed herein are non-destructive for the sample as they are based on the acquisition of a sequence of optical images. They may be used to identify the presence and number of target molecules in situ, within a cell for example.

Description

A METHOD AND A SYSTEM FOR IDENTIFYING MOLECULES

FIELD OF THE INVENTION

The present invention relates to microscopy methods and systems for identifying molecules, and particularly, but not exclusively to a system and a method for locating and counting molecules.

BACKGROUND OF THE INVENTION

Microscopy techniques are generally used to investigate macromolecular structures at intermediate and high

resolution. For example, electron microscopy (EM), cryo-EM and crystallography are used to examine the molecular structure of proteins, but these techniques often involve elaborate sample preparation or require isolating the protein complexes from their natural environment.

Optical microscopy techniques with fluorescent molecules are used as a less invasive alternative. However, the resolution of conventional light microscopy is limited by the diffraction limit of light to approximately 250 nm. This is generally larger than the size of protein

complexes .

Photo-activated localization microscopy (PALM) and related techniques aim to enable imaging and counting fluorescent molecules spatially closer than the diffraction limit. However, errors related to the fluorescent blinking, photo-physics and photo-bleaching behaviour make this technique unreliable when quantitative data are required. There is a need for improved microscopy techniques for imaging and counting fluorescent molecules.

SUMMARY OF THE INVENTION

In accordance with the first aspect, the present invention provides a method for counting fluorescent molecules in a sample comprising the steps of:

obtaining detection data from a plurality of image frames of a sample, the detection data regarding timing and location of fluorescent events;

dividing detection data into spatial regions of interest based on location of fluorescent events;

linking detection data in a plurality of detection paths in a region of interest based on location and timing of fluorescent events in the region of interest;

analysing the detection paths to determine whether each detection path is related to a new fluorescent molecule or a new fluorescent event of an existing

fluorescent molecule. In an embodiment, the method further comprises the step of associating detection paths corresponding to fluorescent events of existing fluorescent molecules into detection trajectories; each trajectory representing an exclusive association of detection events of a single fluorescent molecule.

In an embodiment, the step of dividing detection data into spatial regions of interest comprises calculating a spatial distance between two fluorescent events and comparing the calculated distance with a predetermined distance. A modified version of a DBSCAN algorithm may be used to perform the step of dividing detection data into spatial regions of interest. In embodiments, a plurality of spatial distances are calculated to compose at least one region of interest comprising at least a portion of the sample surface.

In embodiments, the step of linking detection data in a plurality of detection paths further comprises the step of setting a variable metric to measure a distance between fluorescent events occurring in different frames. The variable metric may be a mathematical function of the Hellinger Distance. The variable metric may also be a probabilistic metric related to one or more probabilistic distributions of the fluorescent events. Further, the different frames may be consecutive frames. Each of the one or more probabilistic distributions may be used to define a position and a localisation precision of a fluorescent event.

In some embodiments, the method further comprises the step of comparing the metric to a score threshold to define if two fluorescent events are linked. The score threshold may vary for different samples and may be related to dye photo-physical kinetics.

In an embodiment, the method further comprises the step of organising linked fluorescent events in short tracks of fluorescent events. In an embodiment, the method comprises the step of

calculating a histogram of the number of short tracks for each frame. In an embodiment, the method further comprises the step of calculating a number of new particles born in each frame based on the histogram of the frame.

In an embodiment, the method further comprises the step of calculating the probability that a new fluorescent

molecule would stochastically be born in an area proximal to an existing fluorescent molecule.

In an embodiment, the method further comprises the step of calculating a likelihood of a short track being the result of a new molecule arising at a given time in a given location .

In embodiments, the method further comprises the step of calculating a likelihood of a short track being the result of the same molecule. The likelihood may be calculated simultaneously for all the short tracks in a given region of interest. A Munkres algorithm may be used to associate short tracks to existing molecules of new molecules arising at a given time in a given location.

In an embodiment, the method further comprises the step of calculating a plurality of trajectories related to a plurality of fluorescent molecules by pairing short tracks. In an embodiment, the method further comprises the step of simulating a kinetic behaviour of a molecular cluster compatible with the detection data extracted from at least a portion of the acquired frames and comparing the

calculated plurality of trajectories with the simulated kinetic behaviour of a molecular cluster to correct errors .

In an embodiment, the method further comprises the step of calculating a kinetic behaviour of a molecular cluster compatible with the detection data extracted from at least a portion of the acquired frames based on a theoretical model and comparing the calculated plurality of

trajectories with the calculated kinetic behaviour of a molecular cluster to correct errors.

In accordance with the second aspect, the present

invention provides a data processing apparatus comprising a plurality of operating modules arranged for carrying out a method in accordance with the first aspect.

In accordance with the third aspect, the present invention provides a computer program, comprising instructions for controlling a computer to perform a method in accordance with the first aspect.

In accordance with the fourth aspect, the present

invention provides a computer readable medium, providing the computer program of the third aspect. In accordance with the fifth aspect, the present invention provides a data signal, providing a computer program in accordance with the third aspect. In accordance with the sixth aspect, the present invention provides an apparatus for counting fluorescent molecules in a sample, from fluorescence detection data regarding timing and location of fluorescent events obtained from a plurality of image frames of the sample, the apparatus comprising;

a splitting module for dividing the detection data into spatial regions of interest based on location of fluorescent events;

a linking module for linking the split detection data in a plurality of detection paths in a region of interest based on location and timing of fluorescent events in the region of interest;

a processing module for analysing the detection paths and determine whether each detection path is related to a new fluorescent molecule or a new fluorescent event of an existing fluorescent molecule.

In an embodiment, the apparatus further comprises an associator for associating detection paths corresponding to fluorescent events of existing fluorescent molecules into detection trajectories; each trajectory representing an exclusive association of detection events of a single fluorescent molecule. In an embodiment, the apparatus further comprises a microscopy unit arranged to acquire image frames of a biological sample and an analyser unit arranged to extract detection data related to timing and location of

fluorescent events. In accordance with the seventh aspect, the present

invention provides a method for counting fluorescent molecules in a sample comprising the steps of:

acquiring images of the sample showing the

fluorescent molecules;

obtaining from images of the sample showing the fluorescent molecules, detection data regarding timing of fluorescence and location of fluorescence;

comparing the timing detection data with the location detection data to identify a number and location of the fluorescent molecules.

In accordance with the eighth aspect, the present

invention provides an apparatus for counting fluorescent molecules in a biological sample, the apparatus

comprising:

a microscopy unit arranged to acquire image frames of a biological sample;

an image analyser unit arranged to extract detection data related to timing and location of fluorescent events; a comparator arranged to compare the timing detection data with the location detection data to identify a number and location of the fluorescent molecules.

Advantageous embodiments provide microscopy methods and systems for counting molecules based on spatial and temporal information. Spatial and temporal information are processed using mathematical models and variable thresholds to extract a reliable number of fluorophores and their trajectories in a cluster in a regime where the activation rate of the clusters is not constant in time.

Advantageous embodiments may be used to identify the presence and number of target molecules in situ, within a cell for example. The system and methods disclosed herein are non-destructive for the sample as they are based on the acquisition of a sequence of optical images.

BRIEF DESCRIPTION OF THE DRAWINGS In order to fully understand the present invention, embodiments of the present invention will now be

described, by way of example only, with reference to the accompanying drawings, in which:

Figure 1 shows a common photo-conversion scheme of photo- activatable fluorescent proteins;

Figures 2 and 3 shows flow-charts with steps for counting fluorescent molecules in a sample in accordance with embodiments ;

Figure 4 schematically illustrates the linking of short tracks into trajectories in accordance with embodiments;

Figures 5 to 7 show maps of a simulated data set, a calculated data set and a comparison of true and

calculated cluster stoichiometry respectively in

accordance with embodiments; Figure 8 shows a fit of the calculated cluster data to a probability distribution and the variance of cluster data as a function of sampling fraction in accordance with embodiments ;

Figure 9 shows a plot with experimental data and simulated data in accordance with embodiments; Figure 10 is a schematic illustration of a computer system suitable to implement a method in accordance with

embodiments .

DETAILED DESCRIPTION OF EMBODIMENTS

Embodiments of the present invention relate to microscopy methods and systems for counting molecules. Some

embodiments provide techniques to utilize fluorophore photophysics and the spatiotemporal localization to quantify cluster numbers in a serial localization

microscopy domain. The approach used allows tracking and deriving

trajectories of fluorescent molecule using spatial and temporal information extracted from high resolution images of samples. The process is based and operates on detection data of fluorescent events extracted from the high

resolution images. The process does not operate on image data as such.

Referring now to figure 1, there is shown a common photo- conversion scheme 100 of photo-activatable fluorescent proteins, such as mEos. The photo-activatable fluorescent proteins may be in a ^xpre-activation' state 102, an ^xactive' state 104, a ^xbleached state' 106 or two

different dark states, Mark 1' 108 and Mark 2' 110. The transitions from pre-activation 102 to active 104, and active 104 to bleached 106 are considered to be

irreversible and have respective transition rates k_a and k_b. The transitions from active 104 to dark 1 108 or dark 2 110 are considered to be reversible and have respective transition rates k_d and ak_d. a is a scaling factor which biases the transition probability towards one dark state over the other. The transition rates from dark 1 108 and dark 2 110 to active 104 are instead different and defined respectively as k_rl and k_r2.

In embodiments, values of k_b, k_d, a, k_ri and k_r2 estimated by measurements of a known sample of monomeric fluorophores are used. The measurements are performed in the same conditions as per the molecule counting process. In particular, the same incident laser intensity is used.

Referring now to figure 2, there is shown a flow-chart 200 with steps for counting fluorescent molecules in a sample in accordance with embodiments. At step 205 a plurality of image frames of a sample are acquired using an image acquisition system, such as a fluorescence optical

microscope with an objective lens of high numerical aperture and a camera detector.

The data are processed at step 210 to extract information related to timing and spatial location of fluorescent events. In some embodiments these information are

collected in a data file which can be processed by a computing system.

The detection data are then divided into spatial regions of interest at step 220 based on the location of fluorescent events. The splitting of the data in regions of interest (ROIs) is performed to optimise the analysis of the data using performing fitting algorithms and ultimately improve molecule detection. The splitting process allows reducing the number of detection events that must be considered simultaneously. In advantageous embodiments the division is performed using a recursive approach .

Starting from the first detection event in the data file, other detection events within a given distance from the first detection event location are added to a list of localizations for a given detection region. The survey region is then expanded to that given distance from the new additions to the detection region list, capturing more detection events. The process is repeated until there are no detection events within the given distance to add to the list in an iteration. The ROI created is stored and the related detection events are removed from the data file. The process restarts from the new first detection event in the data file to create another ROI.

After the detection data are divided into spatial ROIs at step 220, each ROI is considered to be exclusive from all other regions of interest and events from one region cannot be linked to events in another region. Once the ROIs are identified, the detection events in each ROI are linked in a plurality of detection paths in a ROI at step 225. The detection events are linked based on both their location and timing. The data related to detection paths obtained by linking detection events in each ROI are analysed at step 230 to determine whether each detection path is related to a new fluorescent molecule or a new fluorescent event of an existing fluorescent molecule. The number of molecules in each ROI is added to obtain the number of molecules in the sample .

Referring now to figure 3, there is shown a flow-chart 300 listing method steps to perform the counting algorithm in accordance with embodiments. The flow-chart 300 is based on the chart 200 of figure 2 and adds further details.

Calibration data 305 is collected by analysis of data acquired in a similar manner as the image data from a sample of known form of isolated molecules. Analysis of the signal intermittency and total length for individual molecules the kinetics constants k_b, k_d, k_rl, k_r2, and a are determined .

After the detection data are divided into spatial ROIs at step 220, as explained above with reference to figure 2, the detection events in each ROI are first linked into short tracks of events occurring in consecutive frames at step 310. Starting with the earliest detection event in a region, at step 310, the algorithm monitors detection events occurring in the next frame. In case an event is found, Gaussian distributions related to the two detection events are calculated together with a mathematical

distance 315 which separates the two distributions. The position of each detection event is the mean of the respective Gaussian distribution and the localization precision is the covariance of the distributions. The distance metric at 315 is compared against a score

threshold (ST) 320 which defines a threshold for detection events in consecutive frames to be linked. The value of ST may be varied in accordance with the requirements in specific experiments. In advantageous embodiments the value of ST is based on the dye kinetics yields.

The kinetics-based value of ST is given by the probability that a molecule transition away from an active state in a single frame.

In the equation t_f is the time between consecutive frames. If the distance metric exceeds the ST value, the two detection events are linked into a short track. In the case where more than one detection event may occur in either the current or next frame then the distance metric and score threshold values are concatenated into an appropriate matrix and a global minimization assignment algorithm executed to pair current detection events with either future detection events or the ST. Those

assignments paired with future detection events are associated together as a part of the respective short track; those assignments paired with the ST are taken as terminal events in the track and not associated with later events . The status of new active molecule or part of a short track is assigned to each detection event in the consecutive frame, then the algorithm moves to the next frame and the process is repeated until all detection events in a given region are assigned to short tracks or as a track end. In advantageous embodiments, the distance metric 315 is the square root of 1 minus the Hellinger Distance ((1- D_H)^1/2) and can be calculated according to the equation below based on the multivariate Bhattacharyya Coefficient.

Once all the short tracks are calculated for each ROI, detection events within a single short track are

aggregated into a single detection event. The new

positions of the new aggregated events and their accuracy are calculated by weighted averages accounting for the number of photons detected for each short track and the number of events in the short track.

^' V - ..„^ ^* V

In the equations x and y± are the positions of the detection events and N± the number of photons detected for each event i in the short track. The spatial uncertainty of the localisation is given by σ. σ± and N_Events correspond to the uncertainty of localization i in the short track and the number of events in the track, respectively. The overall uncertainty, σ, is taken as the greater of σ_χ and Oy (equivalent to σ_χ given above) . The greater of the two uncertainties is carried forward. After a list of short tracks, each with a start frame, end frame, position, and uncertainty has been collected at 310, 315, 320, a histogram of the number of short tracks starting from each frame is generated. The bin width is specified as an algorithm input. For example, a bin width of 1000-2000 frames may be appropriate for a dataset of 25000 frames. Scaling this histogram provides a smoothed approximation of the number of new particles born in a given frame, 330. This approximation may be a slight over- estimate of the actual probability as some of the tracks in some frames are continuations of other short tracks rather than true new molecules. The accuracy of the estimate is related to the kinetics of the fluorophores , namely the number of occurrences of a molecule returning from a dark state 108 or 110 to an on state 104 before transitioning to a bleach state 106.

The probability of a new molecule arriving in a given position in a given frame (P_Wew) is the product of the probability of a new molecule arising in that frame and the fraction of the total experimental area under

consideration (PSF_Area) .

The fractional area for randomly-distributed molecules is taken as the area occupied by a circle with a radius equal to the sum of the objective PSFs of the two molecules that could be linked, divided by the area of the entire

experimental field of view. For non-randomly-distributed molecules the fractional area is taken as a fraction of the intensity of the image generated from the sum of all frames in the data set that is present within a given distance from the detection event. In advantageous embodiments this distance is a circle with the radius of one objective PSF.

The product of the area fraction PSF_Area and P_New yields a score S_New which is a measure of the likelihood of a short track being the result of a new molecule arising at a given time in a given location.

The complementary score S_Li_nk is a measure of the likelihood of a short track being related to the same molecule and is calculated at 335. S_Li_nk is the product of three values: the overlap score between short track positions, {1-D_H)^1/2 , the off time score S_off, and the dark state probability, P_dar_k-

S_0ff is proportional to the probability that a molecule in the dark state will return to the active state after a dark state dwell time of At. S_0ff is calculated in

accordance with the equations below. The values for k_rl, k_r2r and a are obtained from the results of calibration experiments with the same fluorescent molecule as

described previously.

J

The dark state probability, Pdar_kr is the probability that molecule in the active state will transition to a dark state rather than to the bleach state. Pdar_k is calculated according to the following equation. The values for k^, and are obtained from the results of calibration experiments with the same fluorescent molecule as described previously. The product of (1-D_H)^{1 2}, S_0ff and Pdar_k generated at 335 is compared in an inequality with the product of PSF_Area and P_Neu of 330 to ascertain whether a short track originating in the spatial and temporal proximity of the end of another short track is more likely due to a molecule returning from a dark state to the active state or from the activation of a new molecule. In practice there may be many molecules in a single region activating, blinking, and bleaching simultaneously. This problem may be addressed by considering all short tracks built from detection events in a single ROI . A matrix of S_Lin_k values is determined for each possible pairings between a short track and all other tracks sharing as origination frame subsequent to the final frame the short track .

Referring now to figure 4 there is shown a line diagram 400 that schematically illustrates the linking of short tracks (solid lines) into trajectories by bridging off gaps between valid short track termini pairs (dashed and dotted lines) . Scores for each valid gap are assembled into a matrix to be passed to an optimal assignment algorithm. Those associations found to be valid are used to assemble trajectories from short tracks and gaps, here shown as dashed lines. The structure of a possible score matrix is provided below. Tuck J

Scores are indicated by S±,_j and are generated for all valid parings (or where a short track start is followed by a short track end) taking into account spatial and

temporal information. For each track a score S_New is also calculated as a metric for that track not linking to a prior track. This matrix is entered into an optimal assignment algorithm and the resulting assignments used to create trajectories from short tracks. The associations of figure 4 show termini of short tracks (solid lines) in which a short track start comes

subsequent to another short track end. These are indicated as valid potential associations by a dashed or dotted line. The S_Link values for each of these potential

associations is used to generate the matrix.

S_New values are considered for the later short tracks in a further matrix appended to the matrix of S_Li_nk values. In embodiments, the optimal assignment is determined via Munkres algorithm which enforces the constraint that each short track origination can be paired with either a single short track end or the null S_New option, and each short track end can be paired with at most a single short track start .

In the matrix shown above, the elements indicated by S±_fj designate a valid potential pairing between the end of short track i and the start of short track j (this element will have the value of S∑ink for this pairing) . The elements indicated by S_NeH/j designate the value of S_New for that particular short track. The trajectories of each molecule are determined at 340 by pairing short tracks.

In embodiments, the kinetic behaviour of the analysed individual molecule trajectory data from at least a portion of the acquired frames and at least a portion of the analysed trajectories are compared to the calculated kinetic behaviour of a similar molecular cluster based on a theoretical model, in a manner similar to the isolated fluorophore calibration data. Those trajectories whose kinetic behaviours are found to lead to the greatest deviations from the theoretical model are then re^¬ evaluated to result in a smaller deviation from the model. This process is repeated recursively until a satisfactory agreement or convergence is reached.

In other embodiments, individual molecule trajectories are used for simulating a kinetic behaviour of a molecular cluster compatible with the detection data extracted from at least a portion of the acquired frames. The simulated data are then compared to the analysed detection paths with the simulated kinetic behaviour of a molecular cluster to correct errors in the analysed detection paths.

This comparative step may lead to detection of counting errors due to over-joining of very short tracks,

especially those of a single frame in length, or under- joining. In some embodiments, performing calibration routines on known molecular systems enables optimising detection thresholds for investigating unknown molecular systems, for which calibrated data may not be available of may have a poor accuracy. A Euclidean distance may be imposed between molecules for consideration as a multimer molecule and the stoichiometry of molecular clusters may be determined. Other techniques such as DBSCAN, may be used to segment the trajectories into clusters. Determining the overall underlying stoichiometry in a sample is a difficult task for expected clusters of only a few molecules. It is typical for a significant portion of the molecules to go undetected during the course of an experiment; this portion is unknown, increases during the course of an experiment, and extremely cumbersome to control. Here we contrast the underlying stoichiometry, or the true stoichiometry of the sample of interest, against the apparent stoichiometry, or the stoichiometry of the sample as has been measured in an experiment. The complexity of using the mean value to determine stoichiometry of molecules in clusters and complexes increases linearly as more molecules are detected. In advantageous embodiments the standard deviation (or variance) of the detected stoichiometry distribution is used.

If for example a perfectly labelled sample is considered, where all fluorophores are correctly detected. The

molecules represent all potential binding sites (of number N) and can be assembled into M clusters based on spatial criteria as described above. In each step of the analysis a subset of N_sub molecules is randomly chosen from the master list of molecules. The N_sub molecules are assembled into M_sub clusters as before and the distribution of apparent stoichiometries in those M_sub clusters determined and the variance of this distribution is given as V (N_sub) . The behaviour of V (N_sub) as N_sub is incremented from 1 to N is characteristic of the underlying stoichiometry of the sample. The position and amplitude of a peak in this function may be used to determine the underlying

stoichiometry of the sample as well as the number of potential binding sites within that sample.

For example, for a sample of dimers, the maximum amplitude of V(N_sub) = 0,25 at a position of N_peak/N = 2/3 . With increasing underlying stoichiometry the peak amplitude increases and N_peak/N moves towards 0.5.

Samples with mixed cluster stoichiometry may also have characteristic V (N_sub) curves. However, these distributions can be very similar to the curves of a different number of binding sites of a stoichiometry between the two in the mixed sample. In these situations the variance may not be sufficient to adequately describe the clustering

distribution behaviour.

In embodiments, a third order moment (the skew) is used as a further indicator of underlying stoichiometry. The distributions consisting of a single stoichiometry

generally have a skew function S_k (N_sub) that decreases with a sharply decrease in slope as N_sub → N. In a mixed

stoichiometry distribution S_k(N_sub) generally does not show this sharp decrease or may increase, depending on the nature of the stoichiometry. With this additional

information it is sometimes possible to separate, for example, a mixture of dimers and tetramers from that of a sample of trimers . Referring now to figure 5 there is shown a map 500 of a molecular data set simulated in accordance with

theoretical molecular models. The data set shows the simulated positions and stoichiometry of clusters of molecules across the area of a sample. Although the simulated data set in this figure is of dimers a

significant portion of the fluorophores will not be activated during the course of the experiment and as such the apparent stoichiometry of the resulting clusters will vary according a zero-truncated binomial distribution with variables of underlying stoichiometry and detection fraction (N_sub above) . In figure 5 the crosses represent clusters where both fluorophores were activated in the simulation while circles represent clusters in which only one of the two fluorophores was activated in the

simulation. The analysis method facilitates taking the simulated detection event output of the simulation and reassembles those events into trajectories with the same number of apparent fluorophores in each corresponding cluster as shown in figure 5. Figure 6 shows a map 600 similar to map 500 calculated in accordance with an embodiment of the method described above for the same data set as for map 500. The calculated position and number of clusters generated by the method can be related to the simulated data 500 for optimisation of calculation parameters. Figure 6 shows the output of an embodiment of the method obtained with an input similar to the input used for the simulation of figure 5. Figure 6 shows the apparent stoichiometry of each cluster in the data set. Here circles represent clusters in which one fluorophore trajectory was assigned, crosses where two trajectories were assigned, squares where three clusters assigned, and diamonds where four clusters were assigned.

Referring now to figure 7, there is shown a comparison map 700 of simulated data and calculated cluster

stoichiometry. Markers show under-counting and overcounting errors. Map 700 is comparison of the ground truth shown in figure 5 and the output of the embodiment of the method shown in figure 6. Circles indicate clusters where the assignment of trajectories is correct and the apparent cluster stoichiometry in figure 5 matches that of

corresponding cluster in figure 6. Diamonds and squares in figure 7 indicate undercounting and overcounting errors, respectively. An undercounting error corresponds to a cluster where the number of assigned trajectories in a cluster is less than the true apparent cluster

stoichiometry; an overcounting error corresponds to a cluster in which the number of assigned trajectories is greater than the true apparent cluster stoichiometry. Referring now to figure 8 (a) , there is shown a histogram 800 generated from the true 802 and calculated 804 apparent cluster stoichiometries for the data

corresponding to figures 5 and 6. In addition a linear fit (black line and circles) of the calculated

stoichiometry to a zero-truncated binomial distribution with a set stoichiometry of dimers is shown. This figure shows that the assigned cluster stoichiometries follow well the distribution as expected for dimers and with a fraction of detected molecules close to that as produced by the simulation.

Figure 8 (b) is a plot 850 showing the standard deviation of cluster data as a function of sampling fraction. Plot 850 shows the curves of the standard deviation of the apparent cluster stoichiometry distribution (which follows the zero-truncated binomial distribution) as a function of sampling (detection) fraction for underlying cluster stoichiometries of monomers through to decamers (10-mers). The curve for monomers is a straight line at a value of 0, with increasing values at a given sampling fraction for increasing underlying cluster stoichiometry. These curves do not intersect at points greater than 0 and less than 1, exclusive, and are independent of the number of clusters or molecules. As such a curve generated from experimental data as described above is expected to fall along one of these curves which can be used for visualization and identification of the underlying cluster stoichiometry at a range of sampling fractions and when the sampling fraction is unknown a priori.

In some embodiments, a combination of multiple

distributions can be used to fit to the experimental data. Figure 9 shows a plot 900 with experimental data (solid lines) and fits (dashed lines) for simulated data

generated in the same manner as for figures 5 to 7 but with underlying cluster stoichiometries of monomers (902), dimers (904), trimers (906) and tetramers (908). Results from three data sets at each condition are shown. Here the fit is taken to be a combination of two standard deviation vs sampling fraction curves. In each of the curves the data points related to a given stoichiometry condition are very close to one another and separated from the other curves, providing a manner in which to identify the underlying cluster stoichiometry in a rapid and accurate manner. As the number of molecules detected is significantly smaller than the underlying number of molecules the experimental curves stop at a position characteristic of a sampling fraction of approximately 2/3. This information can furthermore be used to

calculate the number of underlying molecules, even though a significant portion is not detected during the

experiment.

Embodiments of the methods disclosed herein can be carried out on a computer system. In advantageous embodiments the computer system may be interconnected with a high

resolution microscopy unit. An example of computer system which may be used to implement the methods is schematised in figure 10. The computer system 901 may be a high performance machine, a desktop workstation or a personal computer, or may be a portable computer such as a laptop or a notebook or may be a distributed computing array or a computer cluster or a networked cluster of computers.

The computer system 901 also comprises a suitable

operating system and appropriate software for

implementation of embodiments of the present invention. The computer system 901 comprises one or more data

processing units (CPUs) 902; memory 904, which may include volatile or non volatile memory, such as various types of RAM memories, magnetic discs, optical disks and solid state memories; a user interface 906, which may comprise a monitor, keyboard, mouse and/or touch-screen display; a network or other communication interface 908 for

communicating with other computers as well as other devices; and one or more communication busses 910 for interconnecting the different parts of the system 901. Memory 904 comprises program code to execute computer programs in accordance with embodiments of the methods described herein.

The computer system 901 may also be connected directly to microscope 912 to download data. The computer system 901 may also access data stored in a remote database 914 via network interface 908. Remote database 914 may be a distributed database.

A computer system for implementing embodiments of the invention is not limited to the computer system described in the preceding paragraphs. Any computer system

architecture may be utilised, such as standalone

computers, networked computers, dedicated computing devices, handheld devices or any device capable of receiving processing information in accordance with embodiments of the present invention. The architecture may comprise client/server architecture, or any other architecture. The software for implementing embodiments of the invention may be processed by "cloud" computing architecture .

The method, system and apparatus described herein are not limited to the detection of fluorophores in a luminescence experiment, but may be used in any circumstance where individual members of a population can be assembled into a list of clusters for sub-sampling.

It is to be understood that, if any prior art publication is referred to herein, such reference does not constitute an admission that the publication forms a part of the common general knowledge in art, in Australia or any other country .

In the claims which follow and in the preceding

description of the invention, except where the context requires otherwise due to express language or necessary implication the word "comprise" or variations such as "comprises" or "comprising" is used in an inclusive sense i.e. to specify the presence of the stated features but not to preclude the presence or addition of further features in various embodiments of the invention.

It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. The present embodiments are,

therefore, to be considered in all respects as

illustrative and not restrictive.

Claims

THE CLAIMS:

1. A method for counting fluorescent molecules in a sample comprising the steps of:

fluorescent molecule.

2. The method of claim 1 further comprising the step of associating detection paths corresponding to fluorescent events of existing fluorescent molecules into detection trajectories; each trajectory representing an exclusive association of detection events of a single fluorescent molecule .

3. The method of claim 1 or claim 2 wherein the step of dividing detection data into spatial regions of interest comprises calculating a spatial distance between two fluorescent events and comparing the calculated distance with a predetermined distance.

4. The method of claim 3 further comprising the step of using a modified version of a DBSCAN algorithm is used to perform the step of dividing detection data into spatial regions of interest.

5. The method of claim 3 or claim 4 wherein a plurality of spatial distances are calculated to compose at least one region of interest comprising at least a portion of the sample surface.

6. The method of any one of the preceding claims wherein the step of linking detection data in a plurality of detection paths further comprises the step of setting a variable metric to measure a distance between fluorescent events occurring in different frames.

7. The method of claim 6 wherein the variable metric is a mathematical function of the Hellinger Distance.

8. The method of claim 6 or 7 wherein the different frames are consecutive frames.

9. The method of any one of claims 6 to 8 wherein the variable metric is a probabilistic metric and is related to one or more probabilistic distributions of the

fluorescent events.

10. The method of claim 9 wherein each of the one or more probabilistic distributions defines a position and a localisation precision of a fluorescent event. - so

il. The method of any one of claims 6 to 10 further comprising the step of comparing the metric to a score threshold to define if two fluorescent events are linked.

12. The method of claim 11 wherein the score threshold varies for different samples and is related to dye photo- physical kinetics.

13. The method of claim 11 or claim 12 further comprising the step of organising linked fluorescent events in short tracks of fluorescent events.

14. The method of claim 13 further comprising the step of calculating a histogram of the number of short tracks for each frame.

15. The method of claim 14 further comprising the step of calculating a number of new particles born in each frame based on the histogram of the frame.

16. The method of any one of claims 13 to 15 further comprising the step of calculating the probability that a new fluorescent molecule would stochastically be born in an area proximal to an existing fluorescent molecule.

17. The method of any one claims 13 to 16 further

comprising the step of calculating a likelihood of a short track being the result of a new molecule arising at a given time in a given location.

18. The method of any one claims 13 to 16 further

comprising the step of calculating a likelihood of a short track being the result of the same molecule.

19. The method of claim 18 wherein the likelihood is calculated simultaneously for all the short tracks in a given region of interest.

20. The method of any one of claims 17 to 19 wherein a Munkres algorithm is used to associate short tracks to existing molecules of new molecules arising at a given time in a given location.

21. The method of any one of claims 17 to 20 further comprising the step of calculating a plurality of

trajectories related to a plurality of fluorescent

molecules by pairing short tracks.

22. The method of claim 21 further comprising the step of simulating a kinetic behaviour of a molecular cluster; the molecular cluster being compatible with the detection data extracted from at least a portion of the acquired frames; and

comparing the calculated plurality of trajectories with the simulated kinetic behaviour of a molecular cluster to correct errors.

23. The method of claim 21 further comprising the step of calculating a kinetic behaviour of a molecular cluster based on a theoretical model; the molecular cluster being compatible with the detection data extracted from at least a portion of the acquired frames; and comparing the calculated plurality of trajectories with the calculated kinetic behaviour of a molecular cluster to correct errors.

24. A data processing apparatus comprising a plurality of operating modules arranged for carrying out the method of any one of claims 1 to 23.

25. A computer program, comprising instructions for controlling a computer to perform the method of any one of claims 1 to 23.

26. A computer readable medium, providing the computer program of claim 25.

27. A data signal, providing a computer program in accordance with claim 25.

28. An apparatus for counting fluorescent molecules in a sample, from fluorescence detection data regarding timing and location of fluorescent events obtained from a

plurality of image frames of the sample, the apparatus comprising;

29. The apparatus of claim 28 further comprising an associator for associating detection paths corresponding to fluorescent events of existing fluorescent molecules into detection trajectories; each trajectory representing an exclusive association of detection events of a single fluorescent molecule.

30. The apparatus of claim 29 further comprising a microscopy unit arranged to acquire image frames of a biological sample and an analyser unit arranged to extract detection data related to timing and location of

fluorescent events.

31. A method for counting fluorescent molecules in a sample comprising the steps of:

acquiring images of the sample showing the

fluorescent molecules;

32. An apparatus for counting fluorescent molecules in a biological sample, the apparatus comprising:

a microscopy unit arranged to acquire image frames of a biological sample;