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Stochastic simulation algorithms for Interacting Particle Systems.

ABSTRACT: Interacting Particle Systems (IPSs) are used to model spatio-temporal stochastic systems in many disparate areas of science. We design an algorithmic framework that reduces IPS simulation to simulation of well-mixed Chemical Reaction Networks (CRNs). This framework minimizes the number of associated reaction channels and decouples the computational cost of the simulations from the size of the lattice. Decoupling allows our software to make use of a wide class of techniques typically reserved for well-mixed CRNs. We implement the direct stochastic simulation algorithm in the open source programming language Julia. We also apply our algorithms to several complex spatial stochastic phenomena. including a rock-paper-scissors game, cancer growth in response to immunotherapy, and lipid oxidation dynamics. Our approach aids in standardizing mathematical models and in generating hypotheses based on concrete mechanistic behavior across a wide range of observed spatial phenomena.

SUBMITTER: Stutz TC

PROVIDER: S-EPMC7924777 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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Stochastic simulation algorithms for Interacting Particle Systems.

Stutz Timothy C TC Landeros Alfonso A Xu Jason J Sinsheimer Janet S JS Sehl Mary M Lange Kenneth K

PloS one 20210302 3

Interacting Particle Systems (IPSs) are used to model spatio-temporal stochastic systems in many disparate areas of science. We design an algorithmic framework that reduces IPS simulation to simulation of well-mixed Chemical Reaction Networks (CRNs). This framework minimizes the number of associated reaction channels and decouples the computational cost of the simulations from the size of the lattice. Decoupling allows our software to make use of a wide class of techniques typically reserved for ...[more]

PMID: 33651796

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Project description:BackgroundThe wet-lab synthesis of the simplest forms of life (minimal cells) is a challenging aspect in modern synthetic biology. Quasi-cellular systems able to produce proteins directly from DNA can be obtained by encapsulating the cell-free transcription/translation system PURESYSTEM(PS) in liposomes. It is possible to detect the intra-vesicle protein production using DNA encoding for GFP and monitoring the fluorescence emission over time. The entrapment of solutes in small-volume liposomes is a fundamental open problem. Stochastic simulation is a valuable tool in the study of biochemical reaction at nanoscale range. QDC (Quick Direct-Method Controlled), a stochastic simulation software based on the well-known Gillespie's SSA algorithm, was used. A suitable model formally describing the PS reactions network was developed, to predict, from inner species concentrations (very difficult to measure in small-volumes), the resulting fluorescence signal (experimentally observable).ResultsThanks to suitable features specific of QDC, we successfully formalized the dynamical coupling between the transcription and translation processes that occurs in the real PS, thus bypassing the concurrent-only environment of Gillespie's algorithm. Simulations were firstly performed for large liposomes (2.67µm of diameter) entrapping the PS to synthetize GFP. By varying the initial concentrations of the three main classes of molecules involved in the PS (DNA, enzymes, consumables), we were able to stochastically simulate the time-course of GFP-production. The sigmoid fit of the GFP-production curves allowed us to extract three quantitative parameters which are significantly dependent on the various initial states. Then we extended this study for small-volume liposomes (575 nm of diameter), where it is more complex to infer the intra-vesicle composition, due to the expected anomalous entrapment phenomena. We identified almost two extreme states that are forecasted to give rise to significantly different experimental observables.ConclusionsThe present work is the first one describing in the detail the stochastic behavior of the PS. Thanks to our results, an experimental approach is now possible, aimed at recording the GFP production kinetics in very small micro-emulsion droplets or liposomes, and inferring, by using the simulation as a reverse-engineering procedure, the internal solutes distribution, and shed light on the still unknown forces driving the entrapment phenomenon.

Project description:Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This "network-free" approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of "partial network expansion" into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.

Project description:A stochastic, individual animal systems simulation model describing U.S. beef cow-calf production was developed and parameterized to match typical U.S. Angus genetics under cow-calf production conditions in the Kansas Flint Hills. Model simulation results were compared to available actual, multivariate U.S. cow-calf production data reported according to beef cow-calf standardized performance analysis (SPA) methodology through North Dakota State University's CHAPS program to assess model validity. Individual animal nutrition, reproduction, growth, and health characteristics, as well as production state are determined on a daily time step. Any number of days can be simulated. These capabilities allow for decision analysis and assessment of long-run outcomes of various genetic, management, and economic scenarios regarding multiple metrics simultaneously. Parameterizing the model to match Kansas Flint Hills production conditions for the years 1995 through 2018, 32 different genetic combinations for mature cow weight and peak lactation potential were simulated with 100 iterations each. Sire mature cow weight genetics ranged from 454 to 771 kg in 45 to 46 kg increments. Sire peak lactation genetics were considered at 6.8, 9, 11.3, and 13.6 kg/d for all eight mature cow weights. Utilizing model results for the years 2000 to 2018, raw model results were assessed against actual historical cow-calf production data. Exploratory factor analysis was applied to interpret the underlying factor scores of model output relative to actual cow-calf production data. Comparing modeled herd output with CHAPS herd data, median average calf weaning age, average cow age, percent pregnant per cow exposed, and percent calf mortality per calf born of model output was 3.4 d greater, 0.2 yr greater, 1 percentage point less, and 1.7 percentage points greater, respectively. Subtracting the median CHAPS pre-weaning average daily gain from the median modeled pre-weaning average daily gain for each of the eight respective mature cow weight genetics categories, and then calculating the median of the eight values, the median difference was -0.21 kg/d. Performing the same calculation for birth weight and adjusted 205 d weaning weight, the modeled data was 4.9 and 48.6 kg lighter than the CHAPS data, respectively. Management and genetic details underlying the CHAPS data were unknown.

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Stochastic simulation algorithms for Interacting Particle Systems.

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Stochastic simulation algorithms for Interacting Particle Systems.

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