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BiGpairSEQ SIMULATOR

CONTENTS

  1. ABOUT
  2. THEORY
  3. THE BiGpairSEQ ALGORITHM
  4. USAGE
  5. PERFORMANCE
  6. TODO
  7. CITATIONS
  8. ACKNOWLEDGEMENTS
  9. AUTHOR

ABOUT

This program simulates BiGpairSEQ (Bipartite Graph pairSEQ), a graph theory-based adaptation of the pairSEQ algorithm (Howie, et al. 2015) for pairing T cell receptor sequences.

THEORY

T cell receptors (TCRs) are encoded by pairs of sequences, alpha sequences (TCRAs) and beta sequences (TCRBs). These sequences are extremely diverse; to the first approximation, this pair of sequences uniquely identifies a line of T cell (of which there may be many clones).

As described in the original 2015 paper, pairSEQ pairs TCRAs and TCRBs by distributing a sample of T cells across a 96-well sample plate, then sequencing the contents of each well. It then calculates p-values for every TCRA/TCRB sequence overlap and compares that against a null distribution, to find the most statistically probable pairings.

BiGpairSEQ uses the same fundamental idea of using occupancy overlap to pair TCR sequences, but unlike pairSEQ it does not require performing any statistical calculations at all. Instead, BiGpairSEQ uses graph theory methods which produce provably optimal solutions.

BiGpairSEQ creates a weighted bipartite graph representing the sample plate. The distinct TCRA and TCRB sequences form the two sets of vertices. Every TCRA/TCRB pair that share a well on the sample plate are connected by an edge in the graph, with the edge weight set to the number of wells in which both sequences appear. The vertices themselves are labeled with the occupancy data for the individual sequences they represent, which is useful for pre-filtering before finding a maximum weight matching. Such a graph fully encodes the distribution data from the sample plate.

The problem of pairing TCRA/TCRB sequences thus reduces to the assignment problem of finding a maximum weight matching (MWM) on a bipartite graph--the subset of vertex-disjoint edges whose weights sum to the maximum possible value.

This is a well-studied combinatorial optimization problem, with many known algorithms that produce provably-optimal solutions. The most theoretically efficient algorithm known to the author for maximum weight matching of a bipartite graph with strictly integral weights is from Duan and Su (2012). For a graph with m edges, n vertices per side, and maximum integer edge weight N, their algorithm runs in O(m sqrt(n) log(N)) time. As the graph representation of a pairSEQ experiment is bipartite with integer weights, this algorithm is ideal for BiGpairSEQ. Unfortunately, it's a fairly new algorithm, and not yet implemented by the graph theory library used in this simulator (JGraphT), nor has the author had time to implement it himself.

There have been some studies which show that auction algorithms for the assignment problem can have superior performance in real-world implementations, due to their simplicity, than more complex algorithms with better theoretical asymptotic performance. But, again, there is no such algorithms implemented by JGraphT, nor has the author yet had time to implement one.

So this program instead uses the Fibonacci heap based algorithm of Fredman and Tarjan (1987) (essentially the Hungarian algorithm augmented with a more efficeint priority queue) which has a worst-case runtime of O(n (n log(n) + m)). The algorithm is implemented as described in Melhorn and Näher (1999). (The simulator allows the substitution of a pairing heap for a Fibonacci heap, though the relative performance difference of the two has not yet been thoroughly tested.)

One possible advantage of this less efficient algorithm is that Hungarian algorithm and its variations work with both the balanced and the unbalanced assignment problem (that is, cases where both sides of the bipartite graph have the same number of vertices and those in which they don't.) Many other MWM algorithms only work for the balanced assignment problem. While pairSEQ-style experiments should theoretically be balanced assignment problems, in practice sequence dropout can cause them to be unbalanced. The unbalanced case can be reduced to the balanced case, but doing so involves doubling the graph. Since the current implementation uses only the Hungarian algorithm, graph doubling--which could be challenging with the computational resources available to the author-- has not yet been necessary.

The relative time/space efficiencies of BiGpairSEQ when backed by different MWM algorithms remains an open problem

THE BiGpairSEQ ALGORITHM

  • Sequence a sample plate of T cells as in pairSEQ.
  • Pre-filter the sequence data to minimize the size of the necessary graph.
    • Saturating sequence filter: remove any sequences present in all of the wells on the sample plate, as there is no signal in the occupancy data of saturating sequences.
    • Non-existent sequence filter: sequencing misreads can pollute the data from the sample plate with non-existent sequences. These can be identified by the discrepancy between their occupancy and their total read count. If a sequence is read correctly at least half the time, then the total read count of a sequence (R) should be at least half the well occupancy of that sequence (O) times the read depth of the sequencing run (D). Remove any sequences for which C < (O * D) / 2.
    • Misidentified sequence filter: sequencing misreads can cause one real sequence to be misidentified as a different real sequence. This should be fairly infrequent, but is a problem if it causes a sequence to seem to be in a well where it is not, in fact, present. This can be detected by looking at discrepancies in a sequence's per-well read count. On average, the read count for a sequence in an individual well (r) should be equal to its total read count (R) divided by its total well occupancy (O). Remove from the list of wells occupied by a sequence any wells for which r < R / (2 * O).
  • Encode the occupancy data from the sample plate as a weighted bipartite graph, where one set of vertices represent the distinct TCRAs and the other set represents distinct TCRBs. Between any TCRA and TCRB that share a well, draw an edge. Assign that edge a weight equal to the total number of wells shared by both sequences.
  • Find a maximum weight matching of the bipartite graph, using any MWM algorithm that produces a provably optimal result.
    • If desired, restrict the matching to a subset of the graph. (Example: restricting matching attempts to cases where the occupancy overlap is 3 or more wells--that is, edges with weight >= 3.0.)
  • The resultant matching represents the likeliest TCRA/TCRB sequence pairs based on the occupancy pattern of the sample plate.

USAGE

RUNNING THE PROGRAM

Download the current version of BiGpairSEQ_Sim.

BiGpairSEQ_Sim is an executable .jar file. Requires Java 14 or higher. OpenJDK 17 recommended.

Run with the command:

java -jar BiGpairSEQ_Sim.jar

Processing sample plates with tens of thousands of sequences may require large amounts of RAM. It is often desirable to increase the JVM maximum heap allocation with the -Xmx flag. For example, to run the program with 32 gigabytes of memory, use the command:

java -Xmx32G -jar BiGpairSEQ_Sim.jar

There are a number of command line options, to allow the program to be used in shell scripts. For a full list, use the -help flag:

java -jar BiGpairSEQ_Sim.jar -help

If no command line arguments are given, BiGpairSEQ_Sim will launch with an interactive, menu-driven CLI for generating files and simulating TCR pairing. The main menu looks like this:

--------BiGPairSEQ SIMULATOR--------
ALPHA/BETA T CELL RECEPTOR MATCHING
  USING WEIGHTED BIPARTITE GRAPHS  
------------------------------------
Please select an option:
1) Generate a population of distinct cells
2) Generate a sample plate of T cells
3) Generate CDR3 alpha/beta occupancy data and overlap graph
4) Simulate bipartite graph CDR3 alpha/beta matching (BiGpairSEQ)
8) Options
9) About/Acknowledgments
0) Exit

By default, the Options menu looks like this:

--------------OPTIONS---------------
1) Turn on cell sample file caching
2) Turn on plate file caching
3) Turn on graph/data file caching
4) Turn off serialized binary graph output
5) Turn on GraphML graph output
6) Maximum weight matching algorithm options
0) Return to main menu

INPUT/OUTPUT

To run the simulation, the program reads and writes 4 kinds of files:

  • Cell Sample files in CSV format
  • Sample Plate files in CSV format
  • Graph/Data files in binary object serialization format
  • Matching Results files in CSV format

These files are often generated in sequence. When entering filenames, it is not necessary to include the file extension (.csv or .ser). When reading or writing files, the program will automatically add the correct extension to any filename without one.

To save file I/O time when using the interactive interface, the most recent instance of each of these four files either generated or read from disk can be cached in program memory. When caching is active, subsequent uses of the same data file won't need to be read in again until another file of that type is used or generated, or caching is turned off for that file type. The program checks whether it needs to update its cached data by comparing filenames as entered by the user. On encountering a new filename, the program flushes its cache and reads in the new file.

(Note that cached Graph/Data files must be transformed back into their original state after a matching experiment, which may take some time. Whether file I/O or graph transformation takes longer for graph/data files is likely to be device-specific.)

The program's caching behavior can be controlled in the Options menu. By default, all caching is OFF.

The program can optionally output Graph/Data files in GraphML format (.graphml) for data portability. This can be turned on in the Options menu. By default, GraphML output is OFF.

Cell Sample Files

Cell Sample files consist of any number of distinct "T cells." Every cell contains four sequences: Alpha CDR3, Beta CDR3, Alpha CDR1, Beta CDR1. The sequences are represented by random integers. CDR3 Alpha and Beta sequences are all unique within a given Cell Sample file. CDR1 Alpha and Beta sequences are not necessarily unique; the relative diversity of CRD1s with respect to CDR3s can be set when making the file.

(Note: though cells still have CDR1 sequences, matching of CDR1s is currently awaiting re-implementation.)

Options when making a Cell Sample file:

  • Number of T cells to generate
  • Factor by which CDR3s are more diverse than CDR1s

Files are in CSV format. Rows are distinct T cells, columns are sequences within the cells. Comments are preceded by #

Structure:

# Sample contains 1 unique CDR1 for every 4 unique CDR3s.
Alpha CDR3 Beta CDR3 Alpha CDR1 Beta CDR1
unique number unique number number number

Sample Plate Files

Sample Plate files consist of any number of "wells" containing any number of T cells (as described above). The wells are filled randomly from a Cell Sample file, according to a selected frequency distribution. Additionally, every individual sequence within each cell may, with some given dropout probability, be omitted from the file; this simulates the effect of amplification errors prior to sequencing. Plates can also be partitioned into any number of sections, each of which can have a different concentration of T cells per well.

Options when making a Sample Plate file:

  • Cell Sample file to use
  • Statistical distribution to apply to Cell Sample file
    • Poisson
    • Gaussian
      • Standard deviation size
    • Exponential
      • Lambda value
        • (Based on the slope of the graph in Figure 4C of the pairSEQ paper, the distribution of the original experiment was approximately exponential with a lambda ~0.6. (Howie, et al. 2015))
  • Total number of wells on the plate
  • Well populations random or fixed
    • If random, minimum and maximum population sizes
    • If fixed
      • Number of sections on plate
      • Number of T cells per well
        • per section, if more than one section
  • Sequence dropout rate

Files are in CSV format. There are no header labels. Every row represents a well. Every value represents an individual cell, containing four sequences, depicted as an array string: [CDR3A, CDR3B, CDR1A, CDR1B]. So a representative cell might look like this:

[525902, 791533, -1, 866282]

Notice that the CDR1 Alpha is missing in the cell above--sequence dropout from simulated amplification error. Dropout sequences are replaced with the value -1. Comments are preceded by #

Structure:

# Cell source file name:
# Each row represents one well on the plate
# Plate size:
# Concentrations:
# Lambda -or- StdDev:
Well 1, cell 1 Well 1, cell 2 Well 1, cell 3 ...
Well 2, cell 1 Well 2, cell 2 Well 2, cell 3 ...
Well 3, cell 1 Well 3, cell 2 Well 3, cell 3 ...
... ... ... ...

Graph/Data Files

Graph/Data files are serialized binaries of a Java object containing the weigthed bipartite graph representation of a Sample Plate, along with the necessary metadata for matching and results output. Making them requires a Cell Sample file (to construct a list of correct sequence pairs for checking the accuracy of BiGpairSEQ simulations) and a Sample Plate file (to construct the associated occupancy graph).

These files can be several gigabytes in size. Writing them to a file lets us generate a graph and its metadata once, then use it for multiple different BiGpairSEQ simulations.

Options for creating a Graph/Data file:

  • The Cell Sample file to use
  • The Sample Plate file to use. (This must have been generated from the selected Cell Sample file.)
  • Whether to simulate sequence read depth. If simulated:
    • The read depth (number of times each sequence is read)
    • The read error rate (probability a sequence is misread)
    • The error collision rate (probability two misreads produce the same spurious sequence)
    • The real sequence collision rate (probability that a misread will produce a different, real sequence from the sample plate. Only applies to new misreads; once an error of this type has occurred, it's likelihood of ocurring again is dominated by the error collision probability.)

These files do not have a human-readable structure, and are not portable to other programs.

Optional GraphML output

For portability of graph data to other software, turn on GraphML output in the Options menu in interactive mode, or use the -graphmlcommand line argument. This will produce a .graphml file for the weighted graph, with vertex attributes for sequence, type, total occupancy, total read count, and the read count for every individual occupied well. This graph contains all the data necessary for the BiGpairSEQ matching algorithm. It does not include the data to measure pairing accuracy; for that, compare the matching results to the original Cell Sample .csv file.

Matching Results Files

Matching results files consist of the results of a BiGpairSEQ matching simulation. Making them requires a serialized binary Graph/Data file (.ser). (Because .graphML files are larger than .ser files, BiGpairSEQ_Sim supports .graphML output only. Graph/data input must use a serialized binary.)

Matching results files are in CSV format. Rows are sequence pairings with extra relevant data. Columns are pairing-specific details. Metadata about the matching simulation is included as comments. Comments are preceded by #.

Options when running a BiGpairSEQ simulation of CDR3 alpha/beta matching:

  • The minimum number of alpha/beta overlap wells to attempt to match
    • (must be >= 1)
  • The maximum number of alpha/beta overlap wells to attempt to match
    • (must be <= the number of wells on the plate - 1)
  • The maximum difference in alpha/beta occupancy to attempt to match
    • (Optional. To skip using this filter, enter a value >= the number of wells on the plate)
  • The minimum overlap percentage--the percentage of a sequence's occupied wells shared by another sequence--to attempt to match. Given as value in range 0 - 100.
    • (Optional. To skip using this filter, enter 0)

Example output:

# Source Sample Plate file: 4MilCellsPlate.csv
# Source Graph and Data file: 4MilCellsPlateGraph.ser
# T cell counts in sample plate wells: 30000
# Total alphas found: 11813
# Total betas found: 11808
# High overlap threshold: 94
# Low overlap threshold: 3
# Minimum overlap percent: 0
# Maximum occupancy difference: 96
# Pairing attempt rate: 0.438
# Correct pairings: 5151
# Incorrect pairings: 18
# Pairing error rate: 0.00348
# Simulation time: 862 seconds
Alpha Alpha well count Beta Beta well count Overlap count Matched Correctly? P-value
5242972 17 1571520 18 17 true 1.41E-18
5161027 18 2072219 18 18 true 7.31E-20
4145198 33 1064455 30 29 true 2.65E-21
7700582 18 112748 18 18 true 7.31E-20
... ... ... ... ... ... ...

NOTE: The p-values in the output are not used for matching—they aren't part of the BiGpairSEQ algorithm at all. P-values are calculated after BiGpairSEQ matching is completed, for purposes of comparison only, using the (2021 corrected) formula from the original pairSEQ paper. (Howie, et al. 2015)

PERFORMANCE (old results; need updating to reflect current, improved simulator performance)

On a home computer with a Ryzen 5600X CPU, 64GB of 3200MHz DDR4 RAM (half of which was allocated to the Java Virtual Machine), and a PCIe 3.0 SSD, running Linux Mint 20.3 Edge (5.13 kernel), the author ran a BiGpairSEQ simulation of a 96-well sample plate with 30,000 T cells/well comprising ~11,800 alphas and betas, taken from a sample of 4,000,000 distinct cells with an exponential frequency distribution (lambda 0.6).

With min/max occupancy threshold of 3 and 94 wells for matching, and no other pre-filtering, BiGpairSEQ identified 5,151 correct pairings and 18 incorrect pairings, for an accuracy of 99.652%.

The total simulation time was 14'22". If intermediate results were held in memory, this would be equivalent to the total elapsed time.

Since this implementation of BiGpairSEQ writes intermediate results to disk (to improve the efficiency of repeated simulations with different filtering options), the actual elapsed time was greater. File I/O time was not measured, but took slightly less time than the simulation itself. Real elapsed time from start to finish was under 30 minutes.

As mentioned in the theory section, performance could be improved by implementing a more efficient algorithm for finding the maximum weight matching.

BEHAVIOR WITH RANDOMIZED WELL POPULATIONS

A series of BiGpairSEQ simulations were conducted using a cell sample file of 3.5 million unique T cells. From these cells, 10 sample plate files were created. All of these sample plates had 96 wells, used an exponential distribution with a lambda of 0.6, and had a sequence dropout rate of 10%.

The well populations of the plates were:

  • One sample plate with 1000 T cells/well
  • One sample plate with 2000 T cells/well
  • One sample plate with 3000 T cells/well
  • One sample plate with 4000 T cells/well
  • One sample plate with 5000 T cells/well
  • Five sample plates with each individual well's population randomized, from 1000 to 5000 T cells. (Average population ~3000 T cells/well.)

All BiGpairSEQ simulations were run with a low overlap threshold of 3 and a high overlap threshold of 94. No optional filters were used, so pairing was attempted for all sequences with overlaps within the threshold values.

Constant well population plate results:

1000 Cell/Well Plate 2000 Cell/Well Plate 3000 Cell/Well Plate 4000 Cell/Well Plate 5000 Cell/Well Plate
Total Alphas Found 6407 7330 7936 8278 8553
Total Betas Found 6405 7333 7968 8269 8582
Pairing Attempt Rate 0.661 0.653 0.600 0.579 0.559
Correct Pairing Count 4231 4749 4723 4761 4750
Incorrect Pairing Count 3 34 40 26 29
Pairing Error Rate 0.000709 0.00711 0.00840 0.00543 0.00607
Simulation Time (Seconds) 500 643 700 589 598

Randomized well population plate results:

Random Plate 1 Random Plate 2 Random Plate 3 Random Plate 4 Random Plate 5 Average
Total Alphas Found 7853 7904 7964 7898 7917 7907
Total Betas Found 7851 7891 7920 7910 7894 7893
Pairing Attempt Rate 0.607 0.610 0.601 0.605 0.603 0.605
Correct Pairing Count 4718 4782 4721 4755 4731 4741
Incorrect Pairing Count 51 35 42 27 29 37
Pairing Error Rate 0.0107 0.00727 0.00882 0.00565 0.00609 0.00771
Simulation Time (Seconds) 590 677 730 618 615 646

The average results for the randomized plates are closest to the constant plate with 3000 T cells/well. This and several other tests indicate that BiGpairSEQ treats a sample plate with a highly variable number of T cells/well roughly as though it had a constant well population equal to the plate's average well population.

TODO

  • Try invoking GC at end of workloads to reduce paging to disk DONE
  • Hold graph data in memory until another graph is read-in? ABANDONED UNABANDONED DONE
    • No, this won't work, because BiGpairSEQ simulations alter the underlying graph based on filtering constraints. Changes would cascade with multiple experiments.
    • Might have figured out a way to do it, by taking edges out and then putting them back into the graph. This may actually be possible.
    • It is possible, though the modifications to the graph incur their own performance penalties. Need testing to see which option is best. It may be computer-specific.
  • Test whether pairing heap (currently used) or Fibonacci heap is more efficient for priority queue in current matching algorithm DONE
    • in theory Fibonacci heap should be more efficient, but complexity overhead may eliminate theoretical advantage
    • Add controllable heap-type parameter?
      • Parameter implemented. Fibonacci heap the current default.
  • Implement sample plates with random numbers of T cells per well. DONE
    • Possible BiGpairSEQ advantage over pairSEQ: BiGpairSEQ is resilient to variations in well population sizes on a sample plate; pairSEQ is not due to nature of probability calculations.
      • preliminary data suggests that BiGpairSEQ behaves roughly as though the whole plate had whatever the average well concentration is, but that's still speculative.
  • See if there's a reasonable way to reformat Sample Plate files so that wells are columns instead of rows.
    • Problem is variable number of cells in a well
    • Apache Commons CSV library writes entries a row at a time
      • Got this working, but at the cost of a profoundly strange bug in graph occupancy filtering. Have reverted the repo until I can figure out what caused that. Given how easily Thingiverse transposes CSV matrices in R, might not even be worth fixing.
  • Enable GraphML output in addition to serialized object binaries, for data portability DONE
    • Have a branch where this is implemented, but there's a bug that broke matching. Don't currently have time to fix.
  • Re-implement command line arguments, to enable scripting and statistical simulation studies DONE
  • Implement custom Vertex class to simplify code and make it easier to implement different MWM algorithms DONE
    • Advantage: would eliminate the need to use maps to associate vertices with sequences, which would make the code easier to understand.
    • This also seems to be faster when using the same algorithm than the version with lots of maps, which is a nice bonus!
  • Implement simulation of read depth, and of read errors. Pre-filter graph for difference in read count to eliminate spurious sequences. DONE
    • Pre-filtering based on comparing (read depth) * (occupancy) to (read count) for each sequence works extremely well
  • Add read depth simulation options to CLI DONE
  • Update graphml output to reflect current Vertex class attributes DONE
    • Individual well data from the SequenceRecords could be included, if there's ever a reason for it
  • Implement simulation of sequences being misread as other real sequence DONE
  • Update matching metadata output options in CLI
  • Update performance data in this readme
  • Add section to ReadMe describing data filtering methods.
  • Re-implement CDR1 matching method
  • Refactor simulator code to collect all needed data in a single scan of the plate
    • Currently it scans once for the vertices and then again for the edge weights. This made simulating read depth awkward, and incompatible with caching of plate files.
    • This would be a fairly major rewrite of the simulator code, but could make things faster, and would definitely make them cleaner.
  • Implement Duan and Su's maximum weight matching algorithm
    • Add controllable algorithm-type parameter?
    • This would be fun and valuable, but probably take more time than I have for a hobby project.
  • Implement an auction algorithm for maximum weight matching
  • Implement an algorithm for approximating a maximum weight matching
    • Some of these run in linear or near-linear time
    • given that the underlying biological samples have many, many sources of error, this would probably be the most useful option in practice. It seems less mathematically elegant, though, and so less fun for me.
  • Implement Vose's alias method for arbitrary statistical distributions of cells
    • Should probably refactor to use apache commons rng for this
  • Use commons JCS for caching
  • Parameterize pre-filtering. Currently, sequences present in all wells are filtered out before constructing the graph, which massively reduces graph size. But, ideally, no pre-filtering would be necessary.

CITATIONS

EXTERNAL LIBRARIES USED

  • JGraphT -- Graph theory data structures and algorithms
  • JHeaps -- For pairing heap priority queue used in maximum weight matching algorithm
  • Apache Commons CSV -- For CSV file output
  • Apache Commons CLI -- To enable command line arguments for scripting.

ACKNOWLEDGEMENTS

BiGpairSEQ was conceived in collaboration with Dr. Alice MacQueen, who brought the original pairSEQ paper to the author's attention and explained all the biology terms he didn't know.

AUTHOR

BiGpairSEQ algorithm and simulation by Eugene Fischer, 2021. Improvements and documentation, 2022.