Accurate Reaction-Diffusion Operator Splitting on Tetrahedral Meshes for Parallel Stochastic Molecular Simulations

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, meaning that the serial limit has already been reached in sub-cellular models. This calls for parallel simulations that can take advantage of the power of modern supercomputers; however exact methods are known to be inherently serial. We introduce an operator splitting implementation for irregular grids with a novel method to improve accuracy, and demonstrate potential for scalable parallel simulations in an initial MPI version. We foresee that this groundwork will enable larger scale, whole-cell stochastic simulations in the near future.Comment: 33 pages, 10 figure

Neural-network solutions to stochastic reaction networks

The stochastic reaction network is widely used to model stochastic processes in physics, chemistry and biology. However, the size of the state space increases exponentially with the number of species, making it challenging to investigate the time evolution of the chemical master equation for the reaction network. Here, we propose a machine-learning approach using the variational autoregressive network to solve the chemical master equation. The approach is based on the reinforcement learning framework and does not require any data simulated in prior by another method. Different from simulating single trajectories, the proposed approach tracks the time evolution of the joint probability distribution in the state space of species counts, and supports direct sampling on configurations and computing their normalized joint probabilities. We apply the approach to various systems in physics and biology, and demonstrate that it accurately generates the probability distribution over time in the genetic toggle switch, the early life self-replicator, the epidemic model and the intracellular signaling cascade. The variational autoregressive network exhibits a plasticity in representing the multi-modal distribution by feedback regulations, cooperates with the conservation law, enables time-dependent reaction rates, and is efficient for high-dimensional reaction networks with allowing a flexible upper count limit. The results suggest a general approach to investigate stochastic reaction networks based on modern machine learning

The thermodynamics of computational copying in biochemical systems

Living cells use readout molecules to record the state of receptor proteins, similar to measurements or copies in typical computational devices. But is this analogy rigorous? Can cells be optimally efficient, and if not, why? We show that, as in computation, a canonical biochemical readout network generates correlations; extracting no work from these correlations sets a lower bound on dissipation. For general input, the biochemical network cannot reach this bound, even with arbitrarily slow reactions or weak thermodynamic driving. It faces an accuracy-dissipation trade-off that is qualitatively distinct from and worse than implied by the bound, and more complex steady-state copy processes cannot perform better. Nonetheless, the cost remains close to the thermodynamic bound unless accuracy is extremely high. Additionally, we show that biomolecular reactions could be used in thermodynamically optimal devices under exogenous manipulation of chemical fuels, suggesting an experimental system for testing computational thermodynamics.Comment: Accepted versio

Kinetic Intersections as a Source of Information on Rate Coefficients

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Dielectrophoretic characterization of particles and erythrocytes

Medical lab work, such as blood testing, will one day be near instantaneous and inexpensive via capabilities enabled by the fast growing world of microtechnology. In this research study, sorting and separation of different ABO blood types have been investigated by applying alternating and direct electric fields using class=SpellE\u3edielectrophoresis in microdevices. Poly(dimethylsiloxane) (PDMS) microdevices, fabricated by standard photolithography techniques have been used. Embedded perpendicular platinum (Pt) electrodes to generate forces in AC dielectrophoresis were used to successfully distinguish positive ABO blood types, with O+ distinguishable from other blood types at \u3e95% confidence. This is an important foundation for exploring DC dielectrophoretic sorting of blood types. The expansion of red blood cell sorting employing direct current insulative class=SpellE\u3edielectrophoresis (DC-iDEP) is novel. Here Pt electrodes were remotely situated in the inlet and outlet ports of the microdevice and an insulating obstacle generates the required dielectrophoretic force. The presence of ABO antigens on the red blood cell were found to affect the class=SpellE\u3edielectrophoretic deflection around the insulating obstacle thus sorting cells by type. To optimize the placement of insulating obstacle in the microchannel, COMSOL Multiphysics® simulations were performed. Microdevice dimensions were optimized by evaluating the behaviors of fluorescent polystyrene particles of three different sizes roughly corresponding to the three main components of blood: platelets (2-4 µm), erythrocytes (6-8 µm) and leukocytes (10-15 µm). This work provided the operating conditions for successfully performing size dependent blood cell insulator based DC dielectrophoresis in PDMS microdevices. In subsequent studies, the optimized microdevice geometry was then used for continuous separation of erythrocytes. The class=SpellE\u3emicrodevice design enabled erythrocyte collection into specific channels based on the cell’s deflection from the high field density region of the obstacle. The channel with the highest concentration of cells is indicative of the ABO blood type of the sample. DC resistance measurement system for quantification of erythrocytes was developed with single PDMS class=SpellE\u3emicrochannel system to be integrated with the DC- class=SpellE\u3eiDEP device developed in this research. This lab-on-a-chip technology application could be applied to emergency situations and naturalcalamities for accurate, fast, and portable blood typing with minimal error

Special Function Methods for Bursty Models of Transcription

We explore a Markov model used in the analysis of gene expression, involving the bursty production of pre-mRNA, its conversion to mature mRNA, and its consequent degradation. We demonstrate that the integration used to compute the solution of the stochastic system can be approximated by the evaluation of special functions. Furthermore, the form of the special function solution generalizes to a broader class of burst distributions. In light of the broader goal of biophysical parameter inference from transcriptomics data, we apply the method to simulated data, demonstrating effective control of precision and runtime. Finally, we suggest a non-Bayesian approach to reducing the computational complexity of parameter inference to linear order in state space size and number of candidate parameters.Comment: Body: 15 pages, 2 figures, 2 tables. Supplement: 10 pages, 1 figur

Special function methods for bursty models of transcription

We explore a Markov model used in the analysis of gene expression, involving the bursty production of pre-mRNA, its conversion to mature mRNA, and its consequent degradation. We demonstrate that the integration used to compute the solution of the stochastic system can be approximated by the evaluation of special functions. Furthermore, the form of the special function solution generalizes to a broader class of burst distributions. In light of the broader goal of biophysical parameter inference from transcriptomics data, we apply the method to simulated data, demonstrating effective control of precision and runtime. Finally, we propose and validate a non-Bayesian approach for parameter estimation based on the characteristic function of the target joint distribution of pre-mRNA and mRNA