When the optimal is not the best: parameter estimation in complex biological models

DataXflow: Synergizing data-driven modeling with best parameter fit and optimal control - An efficient data analysis for cancer research

Building data-driven models is an effective strategy for information extraction from empirical data. Adapting model parameters specifically to data with a best fitting approach encodes the relevant information into a mathematical model. Subsequently, an optimal control framework extracts the most efficient targets to steer the model into desired changes via external stimuli. The DataXflow software framework integrates three software pipelines, D2D for model fitting, a framework solving optimal control problems including external stimuli and JimenaE providing graphical user interfaces to employ the other frameworks lowering the barriers for the need of programming skills, and simultaneously automating reoccurring modeling tasks. Such tasks include equation generation from a graph and script generation allowing also to approach systems with many agents, like complex gene regulatory networks. A desired state of the model is defined, and therapeutic interventions are modeled as external stimuli. The optimal control framework purposefully exploits the model-encoded information by providing those external stimuli that effect the desired changes most efficiently. The implementation of DataXflow is available under https://github.com/MarvelousHopefull/DataXflow. We showcase its application by detecting specific drug targets for a therapy of lung cancer from measurement data to lower proliferation and increase apoptosis. By an iterative modeling process refining the topology of the model, the regulatory network of the tumor is generated from the data. An application of the optimal control framework in our example reveals the inhibition of AURKA and the activation of CDH1 as the most efficient drug target combination. DataXflow paves the way to an agile interplay between data generation and its analysis potentially accelerating cancer research by an efficient drug target identification, even in complex networks.

Single shot detection of alterations across multiple ionic currents from assimilation of cell membrane dynamics

The dysfunction of ion channels is a causative factor in a variety of neurological diseases, thereby defining the implicated channels as key drug targets. The detection of functional changes in multiple specific ionic currents currently presents a challenge, particularly when the neurological causes are either a priori unknown, or are unexpected. Traditional patch clamp electrophysiology is a powerful tool in this regard but is low throughput. Here, we introduce a single-shot method for detecting alterations amongst a range of ion channel types from subtle changes in membrane voltage in response to a short chaotically driven current clamp protocol. We used data assimilation to estimate the parameters of individual ion channels and from these we reconstructed ionic currents which exhibit significantly lower error than the parameter estimates. Such reconstructed currents thereby become sensitive predictors of functional alterations in biological ion channels. The technique correctly predicted which ionic current was altered, and by approximately how much, following pharmacological blockade of BK, SK, A-type K+ and HCN channels in hippocampal CA1 neurons. We anticipate this assay technique could aid in the detection of functional changes in specific ionic currents during drug screening, as well as in research targeting ion channel dysfunction.

Analysis of sloppiness in model simulations: Unveiling parameter uncertainty when mathematical models are fitted to data

This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.

Analysis of cellular kinetic models suggest that physiologically based model parameters may be inherently, practically unidentifiable

Physiologically-based pharmacokinetic and cellular kinetic models are used extensively to predict concentration profiles of drugs or adoptively transferred cells in patients and laboratory animals. Models are fit to data by the numerical optimisation of appropriate parameter values. When quantities such as the area under the curve are all that is desired, only a close qualitative fit to data is required. When the biological interpretation of the model that produced the fit is important, an assessment of uncertainties is often also warranted. Often, a goal of fitting PBPK models to data is to estimate parameter values, which can then be used to assess characteristics of the fit system or applied to inform new modelling efforts and extrapolation, to inform a prediction under new conditions. However, the parameters that yield a particular model output may not necessarily be unique, in which case the parameters are said to be unidentifiable. We show that the parameters in three published physiologically-based pharmacokinetic models are practically (deterministically) unidentifiable and that it is challenging to assess the associated parameter uncertainty with simple curve fitting techniques. This result could affect many physiologically-based pharmacokinetic models, and we advocate more widespread use of thorough techniques and analyses to address these issues, such as established Markov Chain Monte Carlo and Bayesian methodologies. Greater handling and reporting of uncertainty and identifiability of fit parameters would directly and positively impact interpretation and translation for physiologically-based model applications, enhancing their capacity to inform new model development efforts and extrapolation in support of future clinical decision-making.

Advances in systems biology modeling: 10 years of crowdsourcing DREAM challenges

Computational and mathematical models are key to obtain a system-level understanding of biological processes, but their limitations have to be clearly defined to allow their proper application and interpretation. Crowdsourced benchmarks in the form of challenges provide an unbiased assessment of methods, and for the past decade, the Dialogue for Reverse Engineering Assessment and Methods (DREAM) organized more than 15 systems biology challenges. From transcription factor binding to dynamical network models, from signaling networks to gene regulation, from whole-cell models to cell-lineage reconstruction, and from single-cell positioning in a tissue to drug combinations and cell survival, the breadth is broad. To celebrate the 5-year anniversary of Cell Systems, we review the genesis of these systems biology challenges and discuss how interlocking the forward- and reverse-modeling paradigms allows to push the rim of systems biology. This approach will persist for systems levels approaches in biology and medicine.

A Global Minimization Toolkit for Batch-Fitting and χ2 Cluster Analysis of CW-EPR Spectra

Electron paramagnetic resonance spectroscopy (EPR) is a uniquely powerful technique for characterizing conformational dynamics at specific sites within a broad range of molecular species in water. Computational tools for fitting EPR spectra have enabled dynamics parameters to be determined quantitatively. These tools have dramatically broadened the capabilities of EPR dynamics analysis, however, their implementation can easily lead to overfitting or problems with self-consistency. As a result, dynamics parameters and associated properties become difficult to reliably determine, particularly in the slow-motion regime. Here, we present an EPR analysis strategy and the corresponding computational tool for batch-fitting EPR spectra and cluster analysis of the χ2 landscape in Linux. We call this tool CSCA (Chi-Squared Cluster Analysis). The CSCA tool allows us to determine self-consistent rotational diffusion rates and enables calculations of activation energies of diffusion from Arrhenius plots. We demonstrate CSCA using a model system designed for EPR analysis: a self-assembled nanoribbon with radical electron spin labels positioned at known distances off the surface. We anticipate that the CSCA tool will increase the reproducibility of EPR fitting for the characterization of dynamics in biomolecules and soft matter.

Parameter estimation for functional-structural plant models when data are scarce: using multiple patterns for rejecting unsuitable parameter sets

BACKGROUND AND AIMS

Functional-structural plant (FSP) models provide insights into the complex interactions between plant architecture and underlying developmental mechanisms. However, parameter estimation of FSP models remains challenging. We therefore used pattern-oriented modelling (POM) to test whether parameterization of FSP models can be made more efficient, systematic and powerful. With POM, a set of weak patterns is used to determine uncertain parameter values, instead of measuring them in experiments or observations, which often is infeasible.

METHODS

We used an existing FSP model of avocado (Persea americana 'Hass') and tested whether POM parameterization would converge to an existing manual parameterization. The model was run for 10 000 parameter sets and model outputs were compared with verification patterns. Each verification pattern served as a filter for rejecting unrealistic parameter sets. The model was then validated by running it with the surviving parameter sets that passed all filters and then comparing their pooled model outputs with additional validation patterns that were not used for parameterization.

KEY RESULTS

POM calibration led to 22 surviving parameter sets. Within these sets, most individual parameters varied over a large range. One of the resulting sets was similar to the manually parameterized set. Using the entire suite of surviving parameter sets, the model successfully predicted all validation patterns. However, two of the surviving parameter sets could not make the model predict all validation patterns.

CONCLUSIONS

Our findings suggest strong interactions among model parameters and their corresponding processes, respectively. Using all surviving parameter sets takes these interactions into account fully, thereby improving model performance regarding validation and model output uncertainty. We conclude that POM calibration allows FSP models to be developed in a timely manner without having to rely on field or laboratory experiments, or on cumbersome manual parameterization. POM also increases the predictive power of FSP models.

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

The key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their non-linear dynamics. The model dynamics are crucially dependent on the parameter values which are often estimated from observations. Over the past decade, the interest in parameter and state estimation in models of (bio-) chemical reaction networks (BRNs) grew considerably. The related inference problems are also encountered in many other tasks including model calibration, discrimination, identifiability, and checking, and optimum experiment design, sensitivity analysis, and bifurcation analysis. The aim of this review paper is to examine the developments in literature to understand what BRN models are commonly used, and for what inference tasks and inference methods. The initial collection of about 700 documents concerning estimation problems in BRNs excluding books and textbooks in computational biology and chemistry were screened to select over 270 research papers and 20 graduate research theses. The paper selection was facilitated by text mining scripts to automate the search for relevant keywords and terms. The outcomes are presented in tables revealing the levels of interest in different inference tasks and methods for given models in the literature as well as the research trends are uncovered. Our findings indicate that many combinations of models, tasks and methods are still relatively unexplored, and there are many new research opportunities to explore combinations that have not been considered-perhaps for good reasons. The most common models of BRNs in literature involve differential equations, Markov processes, mass action kinetics, and state space representations whereas the most common tasks are the parameter inference and model identification. The most common methods in literature are Bayesian analysis, Monte Carlo sampling strategies, and model fitting to data using evolutionary algorithms. The new research problems which cannot be directly deduced from the text mining data are also discussed.

Evaluation of Parallel Tempering to Accelerate Bayesian Parameter Estimation in Systems Biology

Models of biological systems often have many unknown parameters that must be determined in order for model behavior to match experimental observations. Commonly-used methods for parameter estimation that return point estimates of the best-fit parameters are insufficient when models are high dimensional and under-constrained. As a result, Bayesian methods, which treat model parameters as random variables and attempt to estimate their probability distributions given data, have become popular in systems biology. Bayesian parameter estimation often relies on Markov Chain Monte Carlo (MCMC) methods to sample model parameter distributions, but the slow convergence of MCMC sampling can be a major bottleneck. One approach to improving performance is parallel tempering (PT), a physics-based method that uses swapping between multiple Markov chains run in parallel at different temperatures to accelerate sampling. The temperature of a Markov chain determines the probability of accepting an unfavorable move, so swapping with higher temperatures chains enables the sampling chain to escape from local minima. In this work we compared the MCMC performance of PT and the commonly-used Metropolis-Hastings (MH) algorithm on six biological models of varying complexity. We found that for simpler models PT accelerated convergence and sampling, and that for more complex models, PT often converged in cases MH became trapped in non-optimal local minima. We also developed a freely-available MATLAB package for Bayesian parameter estimation called PTEMPEST (http://github.com/RuleWorld/ptempest), which is closely integrated with the popular BioNetGen software for rule-based modeling of biological systems.

Simulating biological processes: stochastic physics from whole cells to colonies

The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a 'minimal cell'. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.

An improved hybrid of particle swarm optimization and the gravitational search algorithm to produce a kinetic parameter estimation of aspartate biochemical pathways

Mathematical modelling is fundamental to understand the dynamic behavior and regulation of the biochemical metabolisms and pathways that are found in biological systems. Pathways are used to describe complex processes that involve many parameters. It is important to have an accurate and complete set of parameters that describe the characteristics of a given model. However, measuring these parameters is typically difficult and even impossible in some cases. Furthermore, the experimental data are often incomplete and also suffer from experimental noise. These shortcomings make it challenging to identify the best-fit parameters that can represent the actual biological processes involved in biological systems. Computational approaches are required to estimate these parameters. The estimation is converted into multimodal optimization problems that require a global optimization algorithm that can avoid local solutions. These local solutions can lead to a bad fit when calibrating with a model. Although the model itself can potentially match a set of experimental data, a high-performance estimation algorithm is required to improve the quality of the solutions. This paper describes an improved hybrid of particle swarm optimization and the gravitational search algorithm (IPSOGSA) to improve the efficiency of a global optimum (the best set of kinetic parameter values) search. The findings suggest that the proposed algorithm is capable of narrowing down the search space by exploiting the feasible solution areas. Hence, the proposed algorithm is able to achieve a near-optimal set of parameters at a fast convergence speed. The proposed algorithm was tested and evaluated based on two aspartate pathways that were obtained from the BioModels Database. The results show that the proposed algorithm outperformed other standard optimization algorithms in terms of accuracy and near-optimal kinetic parameter estimation. Nevertheless, the proposed algorithm is only expected to work well in small scale systems. In addition, the results of this study can be used to estimate kinetic parameter values in the stage of model selection for different experimental conditions.

Optimisation of an exemplar oculomotor model using multi-objective genetic algorithms executed on a GPU-CPU combination

BACKGROUND

Parameter optimisation is a critical step in the construction of computational biology models. In eye movement research, computational models are increasingly important to understanding the mechanistic basis of normal and abnormal behaviour. In this study, we considered an existing neurobiological model of fast eye movements (saccades), capable of generating realistic simulations of: (i) normal horizontal saccades; and (ii) infantile nystagmus - pathological ocular oscillations that can be subdivided into different waveform classes. By developing appropriate fitness functions, we optimised the model to existing experimental saccade and nystagmus data, using a well-established multi-objective genetic algorithm. This algorithm required the model to be numerically integrated for very large numbers of parameter combinations. To address this computational bottleneck, we implemented a master-slave parallelisation, in which the model integrations were distributed across the compute units of a GPU, under the control of a CPU.

RESULTS

While previous nystagmus fitting has been based on reproducing qualitative waveform characteristics, our optimisation protocol enabled us to perform the first direct fits of a model to experimental recordings. The fits to normal eye movements showed that although saccades of different amplitudes can be accurately simulated by individual parameter sets, a single set capable of fitting all amplitudes simultaneously cannot be determined. The fits to nystagmus oscillations systematically identified the parameter regimes in which the model can reproduce a number of canonical nystagmus waveforms to a high accuracy, whilst also identifying some waveforms that the model cannot simulate. Using a GPU to perform the model integrations yielded a speedup of around 20 compared to a high-end CPU.

CONCLUSIONS

The results of both optimisation problems enabled us to quantify the predictive capacity of the model, suggesting specific modifications that could expand its repertoire of simulated behaviours. In addition, the optimal parameter distributions we obtained were consistent with previous computational studies that had proposed the saccadic braking signal to be the origin of the instability preceding the development of infantile nystagmus oscillations. Finally, the master-slave parallelisation method we developed to accelerate the optimisation process can be readily adapted to fit other highly parametrised computational biology models to experimental data.

Inferring catalysis in biological systems

In systems biology, one is often interested in the communication patterns between several species, such as genes, enzymes or proteins. These patterns become more recognisable when temporal experiments are performed. This temporal communication can be structured by reaction networks such as gene regulatory networks or signalling pathways. Mathematical modelling of data arising from such networks can reveal important details, thus helping to understand the studied system. In many cases, however, corresponding models still deviate from the observed data. This may be due to unknown but present catalytic reactions. From a modelling perspective, the question of whether a certain reaction is catalysed leads to a large increase of model candidates. For large networks the calibration of all possible models becomes computationally infeasible. We propose a method which determines a substantially reduced set of appropriate model candidates and identifies the catalyst of each reaction at the same time. This is incorporated in a multiple-step procedure which first extends the network by additional latent variables and subsequently identifies catalyst candidates using similarity analysis methods. Results from synthetic data examples suggest a good performance even for non-informative data with few observations. Applied on CD95 apoptotic pathway our method provides new insights into apoptosis regulation.

A Neutrophil Phenotype Model for Extracorporeal Treatment of Sepsis

Neutrophils play a central role in eliminating bacterial pathogens, but may also contribute to end-organ damage in sepsis. Interleukin-8 (IL-8), a key modulator of neutrophil function, signals through neutrophil specific surface receptors CXCR-1 and CXCR-2. In this study a mechanistic computational model was used to evaluate and deploy an extracorporeal sepsis treatment which modulates CXCR-1/2 levels. First, a simplified mechanistic computational model of IL-8 mediated activation of CXCR-1/2 receptors was developed, containing 16 ODEs and 43 parameters. Receptor level dynamics and systemic parameters were coupled with multiple neutrophil phenotypes to generate dynamic populations of activated neutrophils which reduce pathogen load, and/or primed neutrophils which cause adverse tissue damage when misdirected. The mathematical model was calibrated using experimental data from baboons administered a two-hour infusion of E coli and followed for a maximum of 28 days. Ensembles of parameters were generated using a Bayesian parallel tempering approach to produce model fits that could recreate experimental outcomes. Stepwise logistic regression identified seven model parameters as key determinants of mortality. Sensitivity analysis showed that parameters controlling the level of killer cell neutrophils affected the overall systemic damage of individuals. To evaluate rescue strategies and provide probabilistic predictions of their impact on mortality, time of onset, duration, and capture efficacy of an extracorporeal device that modulated neutrophil phenotype were explored. Our findings suggest that interventions aiming to modulate phenotypic composition are time sensitive. When introduced between 3–6 hours of infection for a 72 hour duration, the survivor population increased from 31% to 40–80%. Treatment efficacy quickly diminishes if not introduced within 15 hours of infection. Significant harm is possible with treatment durations ranging from 5–24 hours, which may reduce survival to 13%. In severe sepsis, an extracorporeal treatment which modulates CXCR-1/2 levels has therapeutic potential, but also potential for harm. Further development of the computational model will help guide optimal device development and determine which patient populations should be targeted by treatment.

Sepsis occurs when a patient develops a whole body immune response due to infection. In this condition, white blood cells called neutrophils circulate in an active state, seeking and eliminating invading bacteria. However, when neutrophils are activated, healthy tissue is inadvertently targeted, leading to organ damage and potentially death. Even though sepsis kills millions worldwide, there are still no specific treatments approved in the United States. This may be due to the complexity and diversity of the body’s immune response, which can be managed well using computational modeling. We have developed a computational model to predict how different levels of neutrophil activation impact survival in an overactive inflammatory conditions. The model was utilized to assess the effectiveness of a simulated experimental sepsis treatment which modulates neutrophil populations and activity. This evaluation determined that treatment timing plays a critical role in therapeutic effectiveness. When utilized properly the treatment drastically improves survival, but there is also risk of causing patient harm when introduced at the wrong time. We intend for this computational model to support and guide further development of sepsis treatments and help translate these preliminary results from bench to bedside.

Elucidating the genotype-phenotype map by automatic enumeration and analysis of the phenotypic repertoire

Background:

The gap between genotype and phenotype is filled by complex biochemical systems most of which are poorly understood. Because these systems are complex, it is widely appreciated that quantitative understanding can only be achieved with the aid of mathematical models. However, formulating models and measuring or estimating their numerous rate constants and binding constants is daunting. Here we present a strategy for automating difficult aspects of the process.

Methods:

The strategy, based on a system design space methodology, is applied to a class of 16 designs for a synthetic gene oscillator that includes seven designs previously formulated on the basis of experimentally measured and estimated parameters.

Results:

Our strategy provides four important innovations by automating: (1) enumeration of the repertoire of qualitatively distinct phenotypes for a system; (2) generation of parameter values for any particular phenotype; (3) simultaneous realization of parameter values for several phenotypes to aid visualization of transitions from one phenotype to another, in critical cases from functional to dysfunctional; and (4) identification of ensembles of phenotypes whose expression can be phased to achieve a specific sequence of functions for rationally engineering synthetic constructs. Our strategy, applied to the 16 designs, reproduced previous results and identified two additional designs capable of sustained oscillations that were previously missed.

Conclusions:

Starting with a system’s relatively fixed aspects, its architectural features, our method enables automated analysis of nonlinear biochemical systems from a global perspective, without first specifying parameter values. The examples presented demonstrate the efficiency and power of this automated strategy.

Causal drift, robust signaling, and complex disease

The phenotype of many regulatory circuits in which mutations can cause complex, polygenic diseases is to some extent robust to DNA mutations that affect circuit components. Here I demonstrate how such mutational robustness can prevent the discovery of genetic disease determinants. To make my case, I use a mathematical model of the insulin signaling pathway implicated in type 2 diabetes, whose signaling output is governed by 15 genetically determined parameters. Using multiple complementary measures of a parameter's importance for this phenotype, I show that any one disease determinant that is crucial in one genetic background will be virtually irrelevant in other backgrounds. In an evolving population that drifts through the parameter space of this or other robust circuits through DNA mutations, the genetic changes that can cause disease will vary randomly over time. I call this phenomenon causal drift. It means that mutations causing disease in one (human or non-human) population may have no effect in another population, and vice versa. Causal drift casts doubt on our ability to infer the molecular mechanisms of complex diseases from non-human model organisms.

Mammalian cell culture process for monoclonal antibody production: nonlinear modelling and parameter estimation

Monoclonal antibodies (mAbs) are at present one of the fastest growing products of pharmaceutical industry, with widespread applications in biochemistry, biology, and medicine. The operation of mAbs production processes is predominantly based on empirical knowledge, the improvements being achieved by using trial-and-error experiments and precedent practices. The nonlinearity of these processes and the absence of suitable instrumentation require an enhanced modelling effort and modern kinetic parameter estimation strategies. The present work is dedicated to nonlinear dynamic modelling and parameter estimation for a mammalian cell culture process used for mAb production. By using a dynamical model of such kind of processes, an optimization-based technique for estimation of kinetic parameters in the model of mammalian cell culture process is developed. The estimation is achieved as a result of minimizing an error function by a particle swarm optimization (PSO) algorithm. The proposed estimation approach is analyzed in this work by using a particular model of mammalian cell culture, as a case study, but is generic for this class of bioprocesses. The presented case study shows that the proposed parameter estimation technique provides a more accurate simulation of the experimentally observed process behaviour than reported in previous studies.

A Bayesian active learning strategy for sequential experimental design in systems biology

BackgroundDynamical models used in systems biology involve unknown kinetic parameters. Setting these parameters is a bottleneck in many modeling projects. This motivates the estimation of these parameters from empirical data. However, this estimation problem has its own difficulties, the most important one being strong ill-conditionedness. In this context, optimizing experiments to be conducted in order to better estimate a system¿s parameters provides a promising direction to alleviate the difficulty of the task.ResultsBorrowing ideas from Bayesian experimental design and active learning, we propose a new strategy for optimal experimental design in the context of kinetic parameter estimation in systems biology. We describe algorithmic choices that allow to implement this method in a computationally tractable way and make it fully automatic. Based on simulation, we show that it outperforms alternative baseline strategies, and demonstrate the benefit to consider multiple posterior modes of the likelihood landscape, as opposed to traditional schemes based on local and Gaussian approximations.ConclusionThis analysis demonstrates that our new, fully automatic Bayesian optimal experimental design strategy has the potential to support the design of experiments for kinetic parameter estimation in systems biology.

Membrane related dynamics and the formation of actin in cells growing on micro-topographies: a spatial computational model

Background

Intra-cellular processes of cells at the interface to an implant surface are influenced significantly by their extra-cellular surrounding. Specifically, when growing osteoblasts on titanium surfaces with regular micro-ranged geometry, filaments are shorter, less aligned and they concentrate at the top of the geometric structures. Changes to the cytoskeleton network, i. e., its localization, alignment, orientation, and lengths of the filaments, as well as the overall concentration and distribution of key-actors are induced. For example, integrin is distributed homogeneously, whereas integrin in activated state and vinculin, both components of focal adhesions, have been found clustered on the micro-ranged geometries. Also, the concentration of Rho, an intracellular signaling protein related to focal adhesion regulation, was significantly lower.

Results

To explore whether regulations associated with the focal adhesion complex can be responsible for the changed actin filament patterns, a spatial computational model has been developed using ML-Space, a rule-based model description language, and its associated Brownian-motion-based simulator. The focus has been on the deactivation of cofilin in the vicinity of the focal adhesion complex. The results underline the importance of sensing mechanisms to support a clustering of actin filament nucleations on the micro-ranged geometries, and of intracellular diffusion processes, which lead to spatially heterogeneous distributions of active (dephosphorylated) cofilin, which in turn influences the organization of the actin network. We find, for example, that the spatial heterogeneity of key molecular actors can explain the difference in filament lengths in cells on different micro-geometries partly, but to explain the full extent, further model assumptions need to be added and experimentally validated. In particular, our findings and hypothesis referring to the role, distribution, and amount of active cofilin have still to be verified in wet-lab experiments.

Conclusion

Letting cells grow on surface structures is a possibility to shed new light on the intricate mechanisms that relate membrane and actin related dynamics in the cell. Our results demonstrate the need for declarative expressive spatial modeling approaches that allow probing different hypotheses, and the central role of the focal adhesion complex not only for nucleating actin filaments, but also for regulating possible severing agents locally.

In silico model-based inference: a contemporary approach for hypothesis testing in network biology

Inductive inference plays a central role in the study of biological systems where one aims to increase their understanding of the system by reasoning backwards from uncertain observations to identify causal relationships among components of the system. These causal relationships are postulated from prior knowledge as a hypothesis or simply a model. Experiments are designed to test the model. Inferential statistics are used to establish a level of confidence in how well our postulated model explains the acquired data. This iterative process, commonly referred to as the scientific method, either improves our confidence in a model or suggests that we revisit our prior knowledge to develop a new model. Advances in technology impact how we use prior knowledge and data to formulate models of biological networks and how we observe cellular behavior. However, the approach for model-based inference has remained largely unchanged since Fisher, Neyman and Pearson developed the ideas in the early 1900s that gave rise to what is now known as classical statistical hypothesis (model) testing. Here, I will summarize conventional methods for model-based inference and suggest a contemporary approach to aid in our quest to discover how cells dynamically interpret and transmit information for therapeutic aims that integrates ideas drawn from high performance computing, Bayesian statistics, and chemical kinetics.

Bayesian model comparison and parameter inference in systems biology using nested sampling

Inferring parameters for models of biological processes is a current challenge in systems biology, as is the related problem of comparing competing models that explain the data. In this work we apply Skilling's nested sampling to address both of these problems. Nested sampling is a Bayesian method for exploring parameter space that transforms a multi-dimensional integral to a 1D integration over likelihood space. This approach focuses on the computation of the marginal likelihood or evidence. The ratio of evidences of different models leads to the Bayes factor, which can be used for model comparison. We demonstrate how nested sampling can be used to reverse-engineer a system's behaviour whilst accounting for the uncertainty in the results. The effect of missing initial conditions of the variables as well as unknown parameters is investigated. We show how the evidence and the model ranking can change as a function of the available data. Furthermore, the addition of data from extra variables of the system can deliver more information for model comparison than increasing the data from one variable, thus providing a basis for experimental design.

Network topology and parameter estimation: from experimental design methods to gene regulatory network kinetics using a community based approach

Background

Accurate estimation of parameters of biochemical models is required to characterize the dynamics of molecular processes. This problem is intimately linked to identifying the most informative experiments for accomplishing such tasks. While significant progress has been made, effective experimental strategies for parameter identification and for distinguishing among alternative network topologies remain unclear. We approached these questions in an unbiased manner using a unique community-based approach in the context of the DREAM initiative (Dialogue for Reverse Engineering Assessment of Methods). We created an in silico test framework under which participants could probe a network with hidden parameters by requesting a range of experimental assays; results of these experiments were simulated according to a model of network dynamics only partially revealed to participants.

Results

We proposed two challenges; in the first, participants were given the topology and underlying biochemical structure of a 9-gene regulatory network and were asked to determine its parameter values. In the second challenge, participants were given an incomplete topology with 11 genes and asked to find three missing links in the model. In both challenges, a budget was provided to buy experimental data generated in silico with the model and mimicking the features of different common experimental techniques, such as microarrays and fluorescence microscopy. Data could be bought at any stage, allowing participants to implement an iterative loop of experiments and computation.

Conclusions

A total of 19 teams participated in this competition. The results suggest that the combination of state-of-the-art parameter estimation and a varied set of experimental methods using a few datasets, mostly fluorescence imaging data, can accurately determine parameters of biochemical models of gene regulation. However, the task is considerably more difficult if the gene network topology is not completely defined, as in challenge 2. Importantly, we found that aggregating independent parameter predictions and network topology across submissions creates a solution that can be better than the one from the best-performing submission.

An improved swarm optimization for parameter estimation and biological model selection

One of the key aspects of computational systems biology is the investigation on the dynamic biological processes within cells. Computational models are often required to elucidate the mechanisms and principles driving the processes because of the nonlinearity and complexity. The models usually incorporate a set of parameters that signify the physical properties of the actual biological systems. In most cases, these parameters are estimated by fitting the model outputs with the corresponding experimental data. However, this is a challenging task because the available experimental data are frequently noisy and incomplete. In this paper, a new hybrid optimization method is proposed to estimate these parameters from the noisy and incomplete experimental data. The proposed method, called Swarm-based Chemical Reaction Optimization, integrates the evolutionary searching strategy employed by the Chemical Reaction Optimization, into the neighbouring searching strategy of the Firefly Algorithm method. The effectiveness of the method was evaluated using a simulated nonlinear model and two biological models: synthetic transcriptional oscillators, and extracellular protease production models. The results showed that the accuracy and computational speed of the proposed method were better than the existing Differential Evolution, Firefly Algorithm and Chemical Reaction Optimization methods. The reliability of the estimated parameters was statistically validated, which suggests that the model outputs produced by these parameters were valid even when noisy and incomplete experimental data were used. Additionally, Akaike Information Criterion was employed to evaluate the model selection, which highlighted the capability of the proposed method in choosing a plausible model based on the experimental data. In conclusion, this paper presents the effectiveness of the proposed method for parameter estimation and model selection problems using noisy and incomplete experimental data. This study is hoped to provide a new insight in developing more accurate and reliable biological models based on limited and low quality experimental data.

An evolutionary firefly algorithm for the estimation of nonlinear biological model parameters

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.

When the lowest energy does not induce native structures: parallel minimization of multi-energy values by hybridizing searching intelligences

Background

Protein structure prediction (PSP), which is usually modeled as a computational optimization problem, remains one of the biggest challenges in computational biology. PSP encounters two difficult obstacles: the inaccurate energy function problem and the searching problem. Even if the lowest energy has been luckily found by the searching procedure, the correct protein structures are not guaranteed to obtain.

Results

A general parallel metaheuristic approach is presented to tackle the above two problems. Multi-energy functions are employed to simultaneously guide the parallel searching threads. Searching trajectories are in fact controlled by the parameters of heuristic algorithms. The parallel approach allows the parameters to be perturbed during the searching threads are running in parallel, while each thread is searching the lowest energy value determined by an individual energy function. By hybridizing the intelligences of parallel ant colonies and Monte Carlo Metropolis search, this paper demonstrates an implementation of our parallel approach for PSP. 16 classical instances were tested to show that the parallel approach is competitive for solving PSP problem.

Conclusions

This parallel approach combines various sources of both searching intelligences and energy functions, and thus predicts protein conformations with good quality jointly determined by all the parallel searching threads and energy functions. It provides a framework to combine different searching intelligence embedded in heuristic algorithms. It also constructs a container to hybridize different not-so-accurate objective functions which are usually derived from the domain expertise.

Mathematical modelling of the MAP kinase pathway using proteomic datasets

The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.

Optimal experiment selection for parameter estimation in biological differential equation models

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.

Thermodynamically consistent model calibration in chemical kinetics

Background

The dynamics of biochemical reaction systems are constrained by the fundamental laws of thermodynamics, which impose well-defined relationships among the reaction rate constants characterizing these systems. Constructing biochemical reaction systems from experimental observations often leads to parameter values that do not satisfy the necessary thermodynamic constraints. This can result in models that are not physically realizable and may lead to inaccurate, or even erroneous, descriptions of cellular function.

Results

We introduce a thermodynamically consistent model calibration (TCMC) method that can be effectively used to provide thermodynamically feasible values for the parameters of an open biochemical reaction system. The proposed method formulates the model calibration problem as a constrained optimization problem that takes thermodynamic constraints (and, if desired, additional non-thermodynamic constraints) into account. By calculating thermodynamically feasible values for the kinetic parameters of a well-known model of the EGF/ERK signaling cascade, we demonstrate the qualitative and quantitative significance of imposing thermodynamic constraints on these parameters and the effectiveness of our method for accomplishing this important task. MATLAB software, using the Systems Biology Toolbox 2.1, can be accessed from http://www.cis.jhu.edu/~goutsias/CSS lab/software.html. An SBML file containing the thermodynamically feasible EGF/ERK signaling cascade model can be found in the BioModels database.

Conclusions

TCMC is a simple and flexible method for obtaining physically plausible values for the kinetic parameters of open biochemical reaction systems. It can be effectively used to recalculate a thermodynamically consistent set of parameter values for existing thermodynamically infeasible biochemical reaction models of cellular function as well as to estimate thermodynamically feasible values for the parameters of new models. Furthermore, TCMC can provide dimensionality reduction, better estimation performance, and lower computational complexity, and can help to alleviate the problem of data overfitting.

Workflow for generating competing hypothesis from models with parameter uncertainty

Mathematical models are increasingly used in life sciences. However, contrary to other disciplines, biological models are typically over-parametrized and loosely constrained by scarce experimental data and prior knowledge. Recent efforts on analysis of complex models have focused on isolated aspects without considering an integrated approach-ranging from model building to derivation of predictive experiments and refutation or validation of robust model behaviours. Here, we develop such an integrative workflow, a sequence of actions expanding upon current efforts with the purpose of setting the stage for a methodology facilitating an extraction of core behaviours and competing mechanistic hypothesis residing within underdetermined models. To this end, we make use of optimization search algorithms, statistical (machine-learning) classification techniques and cluster-based analysis of the state variables' dynamics and their corresponding parameter sets. We apply the workflow to a mathematical model of fat accumulation in the arterial wall (atherogenesis), a complex phenomena with limited quantitative understanding, thus leading to a model plagued with inherent uncertainty. We find that the mathematical atherogenesis model can still be understood in terms of a few key behaviours despite the large number of parameters. This result enabled us to derive distinct mechanistic predictions from the model despite the lack of confidence in the model parameters. We conclude that building integrative workflows enable investigators to embrace modelling of complex biological processes despite uncertainty in parameters.