A formal language for computational systems biology

The post-genomic era has opened new insights into the complex biochemical reaction systems present in the cell and has generated huge amount of information. The biological systems are highly complex and can overwhelm the numerically computable models. Therefore, models employing symbolical techniques might provide a faster insight. This paper presents some preliminary results and recent trends in the above direction. Specifically, it presents an overview of the main features of some formalisms and techniques from the field of specification languages for concurrency and mobility, which have been proposed to model and simulate the dynamics of the interaction of complex biological systems. The ultimate goal of these symbolic approaches is the modeling, analysis, simulation, and hopefully prediction of the behavior of biological systems (vs. biological components).     

Statistical methods for model comparison in parameter estimation problems for distributed systems

In this note we outline some recent results on the development of a statistical testing methodology for inverse problems involving partial differential equation models. Applications to several problems from biology are presented. The statistical tests, which are in the spirit of analysis of variance (ANOVA), are based on asymptotic distributional results for estimators and residuals in a least squares approach.Research supported in part under grants NSF MCS 8504316, NASA NAG-1-517, and AFOSRF-49620-86-C-0111. Part of this research was carried out while the first author was a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA, which is operated under NASA contracts NASI-18107 and NASI-18605     

The differential evolution entirely parallel method for model adaptation in systems biology

Biophysics - The differential evolution entirely parallel method has been developed to enable the identification of unknown parameters of mathematical models by minimization of the deviation of the...     

Cellware--a multi-algorithmic software for computational systems biology

The intracellular environment of a cell hosts a wide variety of enzymatic reactions, diffusion events, molecular binding, polymerization and metabolic channeling. To transform these biological events into a computational framework, distinct modeling strategies are required. While currently no tool is capable of capturing all these events, progress is being made to create an integrated environment for the modeling community. To address this niche requirement, Cellware has been developed to offer a multi-algorithmic environment for modeling and simulating both deterministic and stochastic events in the cell. AVAILABILITY: The software is available for free and can be downloaded from http://www.bii.a-star.edu.sg/sbg/cellware     

A variational approach to parameter estimation in ordinary differential equations

ABSTRACT: BACKGROUND: Ordinary differential equations are widely-used in the field of systems biology andchemical engineering to model chemical reaction networks. Numerous techniques havebeen developed to estimate parameters like rate constants, initial conditions or steady stateconcentrations from time-resolved data. In contrast to this countable set of parameters, theestimation of entire courses of network components corresponds to an innumerable set ofparameters. RESULTS: The approach presented in this work is able to deal with course estimation for extrinsicsystem inputs or intrinsic reactants, both not being constrained by the reaction networkitself. Our method is based on variational calculus which is carried out analytically toderive an augmented system of differential equations including the unconstrainedcomponents as ordinary state variables. Finally, conventional parameter estimation isapplied to the augmented system resulting in a combined estimation of courses andparameters. CONCLUSIONS: The combined estimation approach takes the uncertainty in input courses correctly intoaccount. This leads to precise parameter estimates and correct confidence intervals. Inparticular this implies that small motifs of large reaction networks can be analysedindependently of the rest. By the use of variational methods, elements from control theoryand statistics are combined allowing for future transfer of methods between the two fields.     

Global parameter estimation methods for stochastic biochemical systems

Background  

The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.     

Bayesian methods in bioinformatics and computational systems biology

Bayesian methods are valuable, inter alia, whenever there is a need to extract information from data that are uncertain or subject to any kind of error or noise (including measurement error and experimental error, as well as noise or random variation intrinsic to the process of interest). Bayesian methods offer a number of advantages over more conventional statistical techniques that make them particularly appropriate for complex data. It is therefore no surprise that Bayesian methods are becoming more widely used in the fields of genetics, genomics, bioinformatics and computational systems biology, where making sense of complex noisy data is the norm. This review provides an introduction to the growing literature in this area, with particular emphasis on recent developments in Bayesian bioinformatics relevant to computational systems biology.     

Agents in bioinformatics, computational and systems biology

The adoption of agent technologies and multi-agent systems constitutes an emerging area in bioinformatics. In this article, we report on the activity of the Working Group on Agents in Bioinformatics (BIOAGENTS) founded during the first AgentLink III Technical Forum meeting on the 2nd of July, 2004, in Rome. The meeting provided an opportunity for seeding collaborations between the agent and bioinformatics communities to develop a different (agent-based) approach of computational frameworks both for data analysis and management in bioinformatics and for systems modelling and simulation in computational and systems biology. The collaborations gave rise to applications and integrated tools that we summarize and discuss in context of the state of the art in this area. We investigate on future challenges and argue that the field should still be explored from many perspectives ranging from bio-conceptual languages for agent-based simulation, to the definition of bio-ontology-based declarative languages to be used by information agents, and to the adoption of agents for computational grids.     

Optimal experiment selection for parameter estimation in biological differential equation models

ABSTRACT: BACKGROUND: Parameter estimation in biological models is a common yet challenging problem. In this work we explore the problem for gene regulatory networks modeled by differential equations with unknown parameters, such as decay rates, reaction rates, Michaelis-Menten constants, and Hill coefficients. We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection. RESULTS: A minimization formulation is used to find the parameter values that best fit the experiment data. When the data is insufficient, the minimization problem often has many local minima that fit the data reasonably well. We show that selecting a new experiment based on the local Fisher Information of one local minimum generates additional data that allows one to successfully discriminate among the many local minima. The parameters can be estimated to high accuracy by iteratively performing minimization and experiment selection. We show that the experiment choices are roughly independent of which local minima is used to calculate the local Fisher Information. CONCLUSIONS: We show that by an appropriate choice of experiments, one can, in principle, efficiently and accurately estimate all the parameters of gene regulatory network. In addition, we demonstrate that appropriate experiment selection can also allow one to restrict model predictions without constraining the parameters using many fewer experiments. We suggest that predicting model behaviors and inferring parameters represent two different approaches to model calibration with different requirements on data and experimental cost.     

系统生物学(Systems Biology)的几大重要问题

近几年来,系统生物学从正式提出到受到普遍关注和研究,对生物学的研究发展起了革命性的变化。主要从系统生物学的发展及其内容进行分析,讨论了生物数据整合,模型建立和模拟分析等几点关键性的问题,并展望了系统生物学的研究。     

Universally sloppy parameter sensitivities in systems biology models

Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring in vivo biochemical parameters is difficult, and collectively fitting them to other experimental data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a “sloppy” spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our model collection are consistent with this suggestion. This difficulty with collective fits may seem to argue for direct parameter measurements, but sloppiness also implies that such measurements must be formidably precise and complete to usefully constrain many model predictions. We confirm this implication in our growth-factor-signaling model. Our results suggest that sloppy sensitivity spectra are universal in systems biology models. The prevalence of sloppiness highlights the power of collective fits and suggests that modelers should focus on predictions rather than on parameters.     

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

Background  

We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness.     

A modified particle swarm optimization algorithm for parameter estimation of a biological system

Background

Mathematical modeling has achieved a broad interest in the field of biology. These models represent the associations among the metabolism of the biological phenomenon with some mathematical equations such that the observed time course profile of the biological data fits the model. However, the estimation of the unknown parameters of the model is a challenging task. Many algorithms have been developed for parameter estimation, but none of them is entirely capable of finding the best solution. The purpose of this paper is to develop a method for precise estimation of parameters of a biological model.

Methods

In this paper, a novel particle swarm optimization algorithm based on a decomposition technique is developed. Then, its root mean square error is compared with simple particle swarm optimization, Iterative Unscented Kalman Filter and Simulated Annealing algorithms for two different simulation scenarios and a real data set related to the metabolism of CAD system.

Results

Our proposed algorithm results in 54.39% and 26.72% average reduction in root mean square error when applied to the simulation and experimental data, respectively.

Conclusion

The results show that the metaheuristic approaches such as the proposed method are very wise choices for finding the solution of nonlinear problems with many unknown parameters.

     

Accelerated maximum likelihood parameter estimation for stochastic biochemical systems

ABSTRACT: BACKGROUND: 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. RESULTS: 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. CONCLUSIONS: 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.     

Regularized EM algorithm for sparse parameter estimation in nonlinear dynamic systems with application to gene regulatory network inference

Parameter estimation in dynamic systems finds applications in various disciplines, including system biology. The well-known expectation-maximization (EM) algorithm is a popular method and has been widely used to solve system identification and parameter estimation problems. However, the conventional EM algorithm cannot exploit the sparsity. On the other hand, in gene regulatory network inference problems, the parameters to be estimated often exhibit sparse structure. In this paper, a regularized expectation-maximization (rEM) algorithm for sparse parameter estimation in nonlinear dynamic systems is proposed that is based on the maximum a posteriori (MAP) estimation and can incorporate the sparse prior. The expectation step involves the forward Gaussian approximation filtering and the backward Gaussian approximation smoothing. The maximization step employs a re-weighted iterative thresholding method. The proposed algorithm is then applied to gene regulatory network inference. Results based on both synthetic and real data show the effectiveness of the proposed algorithm.     

A hybrid parameter estimation algorithm for beta mixtures and applications to methylation state classification

Background

Mixtures of beta distributions are a flexible tool for modeling data with values on the unit interval, such as methylation levels. However, maximum likelihood parameter estimation with beta distributions suffers from problems because of singularities in the log-likelihood function if some observations take the values 0 or 1.

Methods

While ad-hoc corrections have been proposed to mitigate this problem, we propose a different approach to parameter estimation for beta mixtures where such problems do not arise in the first place. Our algorithm combines latent variables with the method of moments instead of maximum likelihood, which has computational advantages over the popular EM algorithm.

Results

As an application, we demonstrate that methylation state classification is more accurate when using adaptive thresholds from beta mixtures than non-adaptive thresholds on observed methylation levels. We also demonstrate that we can accurately infer the number of mixture components.

Conclusions

The hybrid algorithm between likelihood-based component un-mixing and moment-based parameter estimation is a robust and efficient method for beta mixture estimation. We provide an implementation of the method (“betamix”) as open source software under the MIT license.

     

A systems biology approach to the evolution of plant-virus interactions

Omic approaches to the analysis of plant-virus interactions are becoming increasingly popular. These types of data, in combination with models of interaction networks, will aid in revealing not only host components that are important for the virus life cycle, but also general patterns about the way in which different viruses manipulate host regulation of gene expression for their own benefit and possible mechanisms by which viruses evade host defenses. Here, we review studies identifying host genes regulated by viruses and discuss how these genes integrate in host regulatory and interaction networks, with a particular focus on the physical properties of these networks.