Parameter Identification for Markov Models of Biochemical Reactions

We consider the problem of synthesising rate parameters for stochastic biochemical networks so that a given time-bounded CSL property is guaranteed to hold, or, in the case of quantitative properties, the probability of satisfying the property is maximised or minimised. Our method is based on extending CSL model checking and standard uniformisation to parametric models, in order to compute safe bounds on the satisfaction probability of the property. We develop synthesis algorithms that yield answers that are precise to within an arbitrarily small tolerance value. The algorithms combine the computation of probability bounds with the refinement and sampling of the parameter space. Our methods are precise and efficient, and improve on existing approximate techniques that employ discretisation and refinement. We evaluate the usefulness of the methods by synthesising rates for three biologically motivated case studies: infection control for a SIR epidemic model; reliability

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“…This implies that termination is achieved with = 2 and, according to Eq. 72, in a number of steps equal to: k = log 2 2 · (m + c + c ⊥ ) · w(P) .…”

Section: Propositionmentioning

confidence: 99%

“…Inference of parameter values in probabilistic models from time-series measurements is a well studied area of research [2,10], but different from the problem we consider.…”

Section: Related Workmentioning

confidence: 99%

Precise parameter synthesis for stochastic biochemical systems

et al. 2016

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“…Problem (10) written with the data of the model has 19 variables and 11 constraints. All variables are (implicitly) bounded to be positive apart from the ones labeled as free at the bottom of the formulation.…”

Section: Toy Lpmentioning

confidence: 99%

“…Further, depending on the field, researchers use different models to represent uncertainty. Maximum likelihood models are often used, for example, to estimate chemical reaction parameters [10]. To increase modeling expressiveness, we introduce the model of Convex-MDP (CMDP), i.e., an MDP whose state transition probabilities are only known to lie within convex uncertainty sets.…”

Section: Introductionmentioning

confidence: 99%

Polynomial-Time Verification of PCTL Properties of MDPs with Convex Uncertainties

Puggelli

Sangiovanni-Vincentelli

et al. 2013

Lecture Notes in Computer Science

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Abstract. We address the problem of verifying Probabilistic Computation Tree Logic (PCTL) properties of Markov Decision Processes (MDPs) whose state transition probabilities are only known to lie within uncertainty sets. We first introduce the model of Convex-MDPs (CMDPs), i.e., MDPs with convex uncertainty sets. CMDPs generalize Interval-MDPs (IMDPs) by allowing also more expressive (convex) descriptions of uncertainty. Using results on strong duality for convex programs, we then present a PCTL verification algorithm for CMDPs, and prove that it runs in time polynomial in the size of a CMDP for a rich subclass of convex uncertainty models. This result allows us to lower the previously known algorithmic complexity upper bound for IMDPs from co-NP to PTIME. Using the proposed approach, we verify a consensus protocol and a dynamic configuration protocol for IPv4 addresses.

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“…These systems are generally high dimensional. To address this problem a state space truncation can be used [10] or moment-closure methods, which are an approximation focusing on a finite number of moments of the probability distribution [11,12]. [13,14] use an adaptive Galerkin method for the solution of the CME.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation for Stochastic Models of Biochemical Reactions

Zimmer¹

2013

J Comput Sci Syst Biol

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Parameter estimation is central for the analysis of models in Systems Biology. Stochastic models are of increasing importance. However, parameter estimation for stochastic models is still in the early phase of development and there is need for efficient methods to estimate model parameters from time course data which is intrinsically stochastic, only partially observed and has measurement noise.The thesis investigates methods for parameter estimation for stochastic models presenting one efficient method based on integration of ordinary differential equations (ODE) which allows parameter estimation even for models which have qualitatively different behavior in stochastic modeling compared to modeling with ODEs. Further methods proposed in the thesis are based on stochastic simulations. One of the methods uses the stochastic simulations for an estimation of the transition probabilities in the likelihood function. This method is suggested as an addition to the ODE-based method and should be used in systems with few reactions and small state spaces. The resulting stochastic optimization problem can be solved with a Particle Swarm algorithm. To this goal a stopping criterion suited to the stochasticity is proposed. Another approach is a transformation to a deterministic optimization problem. Therefore the polynomial chaos expansion is extended to stochastic functions in this thesis and then used for the transformation.The ODE-based method is motivated from a fast and efficient method for parameter estimation for systems of ODEs. A multiple shooting procedure is used in which the continuity constraints are omitted to allow for stochasticity. Unobserved states are treated by enlarging the optimization vector or using resulting values from the forward integration. To see how well the method covers the stochastic dynamics some test functions will be suggested. It is demonstrated that the method works well even in systems which have qualitatively different behavior in stochastic modeling than in modeling with ODEs. From a computational point of view, this method allows to tackle systems as large as those tackled in deterministic modeling. Zusammenfassung

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Parameter Identification for Markov Models of Biochemical Reactions

Cited by 36 publications

References 20 publications

Precise parameter synthesis for stochastic biochemical systems

Precise parameter synthesis for stochastic biochemical systems

Polynomial-Time Verification of PCTL Properties of MDPs with Convex Uncertainties

Parameter Estimation for Stochastic Models of Biochemical Reactions

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