TRACKING MULTIPLE PARTICLES IN BIOLOGICAL SYSTEMS
A method of tracking a plurality of tagged molecules in a cell in two or three dimensions may include receiving a plurality of unambiguous track segments, where each of the plurality of unambiguous track segments may include a plurality of time-valued observations of individual tagged molecules. The method may also include separating the plurality of unambiguous track segments into a plurality of time windows. The method may additionally include, for each of the plurality of unambiguous track segments, deriving one or more data sets representing features of the unambiguous track segment. The method may further include associating a first unambiguous track segment from a first time window with a second unambiguous track segment from a second time window using the one or more data sets.
1 . A method of tracking a plurality of tagged molecules in a cell in two or three dimensions, the method comprising:
receiving, using a computer system, a plurality of unambiguous track segments, wherein each of the plurality of unambiguous track segments comprises a plurality of time-valued observations of individual tagged molecules;
separating the plurality of unambiguous track segments into a plurality of time windows;
for each of the plurality of unambiguous track segments, deriving one or more data sets representing features of the unambiguous track segment; and
associating a first unambiguous track segment from a first time window with a second unambiguous track segment from a second time window using the one or more data sets.
2 . The method of claim 1 wherein the one or more data sets comprise a data set representing a velocity of an associated tagged molecule as a function of time or spatial location.
3 . The method of claim 1 wherein the one or more data sets comprise a data set representing a matrix of effective force vectors acting on an associated tagged molecule as a function of time or spatial location.
4 . The method of claim 1 wherein the one or more data sets comprise a data set representing a diffusion coefficient for an associated tagged molecule as a function of time or spatial location.
5 . The method of claim 1 wherein the one or more data sets comprise a data set representing an effective measurement noise magnitude for an associated tagged molecule as a function of time or spatial location.
6 . The method of claim 1 wherein associating the first unambiguous track segment from the first time window with the second unambiguous track segment from the second time window using the features comprises:
formulating an association problem using the one or more data sets representing features; and
solving the association problem.
7 . The method of claim 1 wherein associating the first unambiguous track segment from the first time window with the second unambiguous track segment from the second time window using the one or more data sets comprises:
creating a semi-parametric model using a Linear Mixed Effect (LME) formulation and the plurality of unambiguous track segments;
computing a Maximum Likelihood Estimate (MLE) for the LME; and
efficiently computing a set of Expected Best Linear Unbiased Parameters (EBLUPs) for each of the unambiguous track segments.
8 . The method of claim 7 wherein the first unambiguous track segment from the first time window is associated with the second unambiguous track segment from the second time window using the EBLUPs.
9 . The method of claim 8 wherein each of the EBLUPs is associated with kinetic parameters that describes an interaction between the molecule and the environment inside the cell.
10 . The method of claim 1 further comprising combining the first unambiguous track segment with the second unambiguous track segment to form a single track segment representing a path of an associated tagged molecule.
11 . The method of claim 1 wherein each of the plurality of tagged molecules is tagged such that the molecule, over time, emits a gradually changing fluorescent signature.
12 . A computer-readable memory comprising a sequence of instructions which, when executed by one or more processors, causes the one or more processors to track a plurality of tagged molecules in a cell in two or three dimensions by:
receiving a plurality of unambiguous track segments, wherein each of the plurality of unambiguous track segments comprises a plurality of time-valued observations of individual tagged molecules;
separating the plurality of unambiguous track segments into a plurality of time windows;
for each of the plurality of unambiguous track segments, deriving one or more data sets representing features of the unambiguous track segment; and
associating a first unambiguous track segment from a first time window with a second unambiguous track segment from a second time window using the one or more data sets.
13 . The computer-readable memory according to claim 12 wherein associating the first unambiguous track segment from the first time window with the second unambiguous track segment from the second time window using the features comprises:
formulating an association problem using the one or more data sets representing features; and
solving the association problem.
14 . The computer-readable memory according to claim 12 wherein associating the first unambiguous track segment from the first time window with the second unambiguous track segment from the second time window using the one or more data sets comprises:
creating a semi-parametric model using a Linear Mixed Effect (LME) formulation and the plurality of unambiguous track segments;
computing a Maximum Likelihood Estimate (MLE) for the LME; and
efficiently computing a set of Expected Best Linear Unbiased Parameters (EBLUPs) for each of the unambiguous track segments.
15 . The computer-readable memory according to claim 14 wherein the first unambiguous track segment from the first time window is associated with the second unambiguous track segment from the second time window using the EBLUPs.
16 . The computer-readable memory according to claim 15 wherein each of the EBLUPs is associated with kinetic parameters that describes an interaction between the molecule and the environment inside the cell.
17 . A system comprising:
one or more processors; and
a memory communicatively coupled with and readable by the one or more processors and comprising a sequence of instructions which, when executed by the one or more processors, cause the one or more processors to track a plurality of tagged molecules in a cell in two or three dimensions by:
receiving a plurality of unambiguous track segments, wherein each of the plurality of unambiguous track segments comprises a plurality of time-valued observations of individual tagged molecules;
separating the plurality of unambiguous track segments into a plurality of time windows;
for each of the plurality of unambiguous track segments, deriving one or more data sets representing features of the unambiguous track segment; and
associating a first unambiguous track segment from a first time window with a second unambiguous track segment from a second time window using the one or more data sets.
18 . The system of claim 17 wherein the instructions further cause the one or more processors to track the plurality of tagged molecules in the cell in two or three dimensions by combining the first unambiguous track segment with the second unambiguous track segment to form a single track segment representing a path of an associated tagged molecule.
19 . The system of claim 17 wherein associating the first unambiguous track segment from the first time window with the second unambiguous track segment from the second time window using the one or more data sets comprises:
creating a semi-parametric model using a Linear Mixed Effect (LME) formulation and the plurality of unambiguous track segments;
computing a Maximum Likelihood Estimate (MLE) for the LME; and
efficiently computing a set of Expected Best Linear Unbiased Parameters (EBLUPs) for each of the unambiguous track segments.
20 . The system of claim 17 wherein one or more data sets comprise a data set representing a matrix of effective force vectors acting on an associated tagged molecule as a function of time or spatial location.