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Register a new userStochastic filters based on hybrid approximations of multiscale stochastic reaction networks
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Zhou Fang
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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We consider the problem of estimating the dynamic latent states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. We first prove that accurate solutions to the filtering problem can be constructed by solving the filtering problem for a reduced model that represents the dynamics as a hybrid process. The model reduction is based on exploiting the time-scale separations in the original network, and it can greatly reduce the computational effort required to simulate the dynamics. This enables us to develop efficient particle filters to solve the filtering problem for the original model by applying particle filters to the reduced model. We illustrate the accuracy and the computational efficiency of our approach using a numerical example.
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In the past few decades, the development of fluorescent technologies and microscopic techniques has greatly improved scientists ability to observe real-time single-cell activities. In this paper, we consider the filtering problem associate with these advanced technologies, i.e., how to estimate latent dynamic states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. A good solution to this problem can further improve scientists ability to extract information about intracellular systems from time-course experiments. A straightforward approach to this filtering problem is to use a particle filter where particles are generated by simulation of the full model and weighted according to observations. However, the exact simulation of the full dynamic model usually takes an impractical amount of computational time and prevents this type of particle filters from being used for real-time applications, such as transcription regulation networks. Inspired by the recent development of hybrid approximations to multiscale chemical reaction networks, we approach the filtering problem in an alternative way. We first prove that accurate solutions to the filtering problem can be constructed by solving the filtering problem for a reduced model that represents the dynamics as a hybrid process. The model reduction is based on exploiting the time-scale separations in the original network and, therefore, can greatly reduce the computational effort required to simulate the dynamics. As a result, we are able to develop efficient particle filters to solve the filtering problem for the original model by applying particle filters to the reduced model. We illustrate the accuracy and the computational efficiency of our approach using several numerical examples.
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases these simulations can take an impractical amount of computational time. Therefore many methods have been developed that approximate the Stochastic Process underlying the Chemical Master Equation. Prominent strategies are Hybrid Models that regard the firing of some reaction channels as being continuous and applying the quasi-stationary assumption to approximate the dynamics of fast subnetworks. However as the dynamics of a Stochastic Reaction Network changes with time these approximations might have to be adapted during the simulation. We develop a method that approximates the solution of a CME by automatically partitioning the reaction dynamics into discrete/continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from Systems Biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time.
This study concerns online inference (i.e., filtering) on the state of reaction networks, conditioned on noisy and partial measurements. The difficulty in deriving the equation that the conditional probability distribution of the state satisfies stems from the fact that the master equation, which governs the evolution of the reaction networks, is analytically intractable. The linear noise approximation (LNA) technique, which is widely used in the analysis of reaction networks, has recently been applied to develop approximate inference. Here, we apply the projection method to derive approximate filters, and compare them to a filter based on the LNA numerically in their filtering performance. We also contrast the projection method with moment-closure techniques in terms of approximating the evolution of stochastic reaction networks.
Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible stochastic approximations on the timescale of interest. One of the rigorous and popular approaches is the multiscale approximation method for continuous time Markov processes. In this approach, by scaling species abundances and reaction rates, a family of processes parameterized by a scaling parameter is defined. The limiting process of this family is then used to approximate the original process. However, we find that such approximations become inaccurate when combinations of species with disparate abundances either constitute conservation laws or form virtual slow auxiliary species. To obtain more accurate approximation in such cases, we propose here an appropriate modification of the original method.
Leaping methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue using the partitioned leaping algorithm (PLA) [L.A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a recently-introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks. The networks that we consider are simple enough so as to be accessible to our intuition but sufficiently complex so as to be generally representative of real biological systems. We demonstrate how the PLA allows us to quantify subtle effects of stochasticity in these systems that would be difficult to ascertain otherwise as well as not-so-subtle behaviors that would strain commonly-used exact stochastic methods. We also illustrate bottlenecks that can hinder the approach and exemplify and discuss possible strategies for overcoming them. Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while at the same time elucidating obstacles that are often encountered in practice.
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