Global parameter identification of stochastic reaction networks from single trajectories

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell--cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation, and efficient exact stochastic simulation algorithms that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems Biology

Mathematical Modeling of the Role of Mitochondrial Fusion and Fission in Mitochondrial DNA Maintenance

10.1371/journal.pone.0076230PLOS ONE8101-1

Accelerated maximum likelihood parameter estimation for stochastic biochemical systems

<p>Abstract</p> <p>Background</p> <p>A prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems; methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs). MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence.</p> <p>Results</p> <p>We have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM²): an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM) algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM² substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods.</p> <p>Conclusions</p> <p>This work provides a novel, accelerated version of a likelihood-based parameter estimation method that can be readily applied to stochastic biochemical systems. In addition, our results suggest opportunities for added efficiency improvements that will further enhance our ability to mechanistically simulate biological processes.</p

Stochastic S-system modeling of gene regulatory network

Microarray gene expression data can provide insights into biological processes at a system-wide level and is commonly used for reverse engineering gene regulatory networks (GRN). Due to the amalgamation of noise from different sources, microarray expression profiles become inherently noisy leading to significant impact on the GRN reconstruction process. Microarray replicates (both biological and technical), generated to increase the reliability of data obtained under noisy conditions, have limited influence in enhancing the accuracy of reconstruction. Therefore, instead of the conventional GRN modeling approaches which are deterministic, stochastic techniques are becoming increasingly necessary for inferring GRN from noisy microarray data. In this paper, we propose a new stochastic GRN model by investigating incorporation of various standard noise measurements in the deterministic S-system model. Experimental evaluations performed for varying sizes of synthetic network, representing different stochastic processes, demonstrate the effect of noise on the accuracy of genetic network modeling and the significance of stochastic modeling for GRN reconstruction. The proposed stochastic model is subsequently applied to infer the regulations among genes in two real life networks: (1) the well-studied IRMA network, a real-life in-vivo synthetic network constructed within the Saccharomycescerevisiae yeast, and (2) the SOS DNA repair network in Escherichiacoli. © 2015, Springer Science+Business Media Dordrecht

Towards human cell simulation

none14siThe faithful reproduction and accurate prediction of the phe-notypes and emergent behaviors of complex cellular systems are among the most challenging goals in Systems Biology. Although mathematical models that describe the interactions among all biochemical processes in a cell are theoretically feasible, their simulation is generally hard because of a variety of reasons. For instance, many quantitative data (e.g., kinetic rates) are usually not available, a problem that hinders the execution of simulation algorithms as long as some parameter estimation methods are used. Though, even with a candidate parameterization, the simulation of mechanistic models could be challenging due to the extreme computational effort required. In this context, model reduction techniques and High-Performance Computing infrastructures could be leveraged to mitigate these issues. In addition, as cellular processes are characterized by multiple scales of temporal and spatial organization, novel hybrid simulators able to harmonize different modeling approaches (e.g., logic-based, constraint-based, continuous deterministic, discrete stochastic, spatial) should be designed. This chapter describes a putative unified approach to tackle these challenging tasks, hopefully paving the way to the definition of large-scale comprehensive models that aim at the comprehension of the cell behavior by means of computational tools.noneSpolaor, Simone; Gribaudo, Marco; Iacono, Mauro; Kadavy, Tomas; Oplatková, Zuzana Komínková; Mauri, Giancarlo; Pllana, Sabri; Senkerik, Roman; Stojanovic, Natalija; Turunen, Esko; Viktorin, Adam; Vitabile, Salvatore; Zamuda, Aleš; Nobile, Marco S.Spolaor, Simone; Gribaudo, Marco; Iacono, Mauro; Kadavy, Tomas; Oplatková, Zuzana Komínková; Mauri, Giancarlo; Pllana, Sabri; Senkerik, Roman; Stojanovic, Natalija; Turunen, Esko; Viktorin, Adam; Vitabile, Salvatore; Zamuda, Aleš; Nobile, Marco S

Towards human cell simulation

The faithful reproduction and accurate prediction of the phenotypes and emergent behaviors of complex cellular systems are among the most challenging goals in Systems Biology. Although mathematical models that describe the interactions among all biochemical processes in a cell are theoretically feasible, their simulation is generally hard because of a variety of reasons. For instance, many quantitative data (e.g., kinetic rates) are usually not available, a problem that hinders the execution of simulation algorithms as long as some parameter estimation methods are used. Though, even with a candidate parameterization, the simulation of mechanistic models could be challenging due to the extreme computational effort required. In this context, model reduction techniques and High-Performance Computing infrastructures could be leveraged to mitigate these issues. In addition, as cellular processes are characterized by multiple scales of temporal and spatial organization, novel hybrid simulators able to harmonize different modeling approaches (e.g., logic-based, constraint-based, continuous deterministic, discrete stochastic, spatial) should be designed. This chapter describes a putative unified approach to tackle these challenging tasks, hopefully paving the way to the definition of large-scale comprehensive models that aim at the comprehension of the cell behavior by means of computational tools

Towards human cell simulation

The faithful reproduction and accurate prediction of the phe-notypes and emergent behaviors of complex cellular systems are among the most challenging goals in Systems Biology. Although mathematical models that describe the interactions among all biochemical processes in a cell are theoretically feasible, their simulation is generally hard because of a variety of reasons. For instance, many quantitative data (e.g., kinetic rates) are usually not available, a problem that hinders the execution of simulation algorithms as long as some parameter estimation methods are used. Though, even with a candidate parameterization, the simulation of mechanistic models could be challenging due to the extreme computational effort required. In this context, model reduction techniques and High-Performance Computing infrastructures could be leveraged to mitigate these issues. In addition, as cellular processes are characterized by multiple scales of temporal and spatial organization, novel hybrid simulators able to harmonize different modeling approaches (e.g., logic-based, constraint-based, continuous deterministic, discrete stochastic, spatial) should be designed. This chapter describes a putative unified approach to tackle these challenging tasks, hopefully paving the way to the definition of large-scale comprehensive models that aim at the comprehension of the cell behavior by means of computational tools