Conformal prediction for uncertainty quantification in dynamic biological systems

Uncertainty quantification (UQ) is the process of systematically determining and characterizing the degree of confidence in computational model predictions. In systems biology, and particularly with dynamic models, UQ is critical due to the nonlinearities and parameter sensitivities that influence the behavior of complex biological systems. Addressing these issues through robust UQ enables a deeper understanding of system dynamics and more reliable extrapolation beyond observed conditions. Many state-of-the-art UQ approaches in this field are grounded in Bayesian statistical methods. While these frameworks naturally incorporate uncertainty quantification, they often require the specification of parameter distributions as priors and may impose parametric assumptions that do not always reflect biological reality. Additionally, Bayesian methods can be computationally expensive, posing significant challenges when dealing with large-scale models and seeking rapid, reliable uncertainty calibration. As an alternative, we propose using conformal predictions methods and introduce two novel algorithms designed for dynamic biological systems. These approaches can provide non-asymptotic guarantees, improving robustness and scalability across various applications, even when the predictive models are misspecified. Through several illustrative scenarios, we demonstrate that these conformal algorithms can serve as powerful complements-or even alternatives-to conventional Bayesian methods, delivering effective uncertainty quantification for predictive tasks in systems biology.

Deciphering the topological landscape of glioma using a network theory framework

Glioma stem cells have been recognized as key players in glioma recurrence and therapeutic resistance, presenting a promising target for novel treatments. However, the limited understanding of the role glioma stem cells play in the glioma hierarchy has drawn controversy and hindered research translation into therapies. Despite significant advances in our understanding of gene regulatory networks, the dynamics of these networks and their implications for glioma remain elusive. This study employs a systemic theoretical perspective to integrate experimental knowledge into a core endogenous network model for glioma, thereby elucidating its energy landscape through network dynamics computation. The model identifies two stable states corresponding to astrocytic-like and oligodendrocytic-like tumor cells, connected by a transition state with the feature of high stemness, which serves as one of the energy barriers between astrocytic-like and oligodendrocytic-like states, indicating the instability of glioma stem cells in vivo. We also obtained various stable states further supporting glioma's multicellular origins and uncovered a group of transition states that could potentially induce tumor heterogeneity and therapeutic resistance. This research proposes that the transition states linking both glioma stable states are central to glioma heterogeneity and therapy resistance. Our approach may contribute to the advancement of glioma therapy by offering a novel perspective on the complex landscape of glioma biology.

From Cognitive Agents to Cognitive Systems: Theoretical, Methodological, and Empirical Developments of van Gelder's (1998) "Dynamical Hypothesis"

Over two decades have passed since the publication of van Gelder's (1998) "dynamical hypothesis." In that paper, van Gelder proposed that cognitive agents were not digital computers-per the representational computational approach-but dynamical systems. The evolution of the dynamical hypothesis was driven by parallel advances in three areas. Theoretically, a deeper understanding of genetics, biology, neuroscience, and cognitive science inspired questions about how systems within each domain dynamically interact and extend their effects across spatiotemporal scales. Methodologically, more sophisticated and domain-general tools allowed researchers to discover, model, and quantify system dynamics, structure, and patterns across multiple scales to generate a more comprehensive system-level understanding of behaviors. Empirically, we can analyze a system's behavior while preserving its natural dynamics, revealing evidence that the reductionist approach leads to an incomplete understanding of the components and the overall system. Researchers have traditionally reduced a complex system into its component processes and assumed that the parts can be recombined to explain the whole. These three advances fundamentally altered our understanding of a "cognitive agent:" How their behaviors are driven by long-range coordination across multiple processes, how the interdependent and nested structure of interacting variables produces behaviors that are greater than the sum of its parts, and how environmental constraints shape adaptive yet stable behavioral patterns.

Repeated Decision Stumping Distils Simple Rules from Single-Cell Data

Single-cell data afford unprecedented insights into molecular processes. But the complexity and size of these data sets have proved challenging and given rise to a large armory of statistical and machine learning approaches. The majority of approaches focuses on either describing features of these data, or making predictions and classifying unlabeled samples. In this study, we introduce repeated decision stumping (ReDX) as a method to distill simple models from single-cell data. We develop decision trees of depth one-hence "stumps"-to identify in an inductive manner, gene products involved in driving cell fate transitions, and in applications to published data we are able to discover the key players involved in these processes in an unbiased manner without prior knowledge. Our algorithm is deliberately targeting the simplest possible candidate hypotheses that can be extracted from complex high-dimensional data. There are three reasons for this: (1) the predictions become straightforwardly testable hypotheses; (2) the identified candidates form the basis for further mechanistic model development, for example, for engineering and synthetic biology interventions; and (3) this approach complements existing descriptive modeling approaches and frameworks. The approach is computationally efficient, has remarkable predictive power, including in simulation studies where the ground truth is known, and yields robust and statistically stable predictors; the same set of candidates is generated by applying the algorithm to different subsamples of experimental data.

Julia for biologists

Major computational challenges exist in relation to the collection, curation, processing and analysis of large genomic and imaging datasets, as well as the simulation of larger and more realistic models in systems biology. Here we discuss how a relative newcomer among programming languages-Julia-is poised to meet the current and emerging demands in the computational biosciences and beyond. Speed, flexibility, a thriving package ecosystem and readability are major factors that make high-performance computing and data analysis available to an unprecedented degree. We highlight how Julia's design is already enabling new ways of analyzing biological data and systems, and we provide a list of resources that can facilitate the transition into Julian computing.

Surveying membrane landscapes: a new look at the bacterial cell surface

Recent studies applying advanced imaging techniques are changing the way we understand bacterial cell surfaces, bringing new knowledge on everything from single-cell heterogeneity in bacterial populations to their drug sensitivity and mechanisms of antimicrobial resistance. In both Gram-positive and Gram-negative bacteria, the outermost surface of the bacterial cell is being imaged at nanoscale; as a result, topographical maps of bacterial cell surfaces can be constructed, revealing distinct zones and specific features that might uniquely identify each cell in a population. Functionally defined assembly precincts for protein insertion into the membrane have been mapped at nanoscale, and equivalent lipid-assembly precincts are suggested from discrete lipopolysaccharide patches. As we review here, particularly for Gram-negative bacteria, the applications of various modalities of nanoscale imaging are reawakening our curiosity about what is conceptually a 3D cell surface landscape: what it looks like, how it is made and how it provides resilience to respond to environmental impacts.

NetAct: a computational platform to construct core transcription factor regulatory networks using gene activity

A major question in systems biology is how to identify the core gene regulatory circuit that governs the decision-making of a biological process. Here, we develop a computational platform, named NetAct, for constructing core transcription factor regulatory networks using both transcriptomics data and literature-based transcription factor-target databases. NetAct robustly infers regulators' activity using target expression, constructs networks based on transcriptional activity, and integrates mathematical modeling for validation. Our in silico benchmark test shows that NetAct outperforms existing algorithms in inferring transcriptional activity and gene networks. We illustrate the application of NetAct to model networks driving TGF-β-induced epithelial-mesenchymal transition and macrophage polarization.

Open problems in mathematical biology

Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.

Improving dynamic predictions with ensembles of observable models

MOTIVATION

Dynamic mechanistic modelling in systems biology has been hampered by the complexity and variability associated with the underlying interactions, and by uncertain and sparse experimental measurements. Ensemble modelling, a concept initially developed in statistical mechanics, has been introduced in biological applications with the aim of mitigating those issues. Ensemble modelling uses a collection of different models compatible with the observed data to describe the phenomena of interest. However, since systems biology models often suffer from a lack of identifiability and observability, ensembles of models are particularly unreliable when predicting non-observable states.

RESULTS

We present a strategy to assess and improve the reliability of a class of model ensembles. In particular, we consider kinetic models described using ordinary differential equations with a fixed structure. Our approach builds an ensemble with a selection of the parameter vectors found when performing parameter estimation with a global optimization metaheuristic. This technique enforces diversity during the sampling of parameter space and it can quantify the uncertainty in the predictions of state trajectories. We couple this strategy with structural identifiability and observability analysis, and when these tests detect possible prediction issues we obtain model reparameterizations that surmount them. The end result is an ensemble of models with the ability to predict the internal dynamics of a biological process. We demonstrate our approach with models of glucose regulation, cell division, circadian oscillations and the JAK-STAT signalling pathway.

AVAILABILITY AND IMPLEMENTATION

The code that implements the methodology and reproduces the results is available at https://doi.org/10.5281/zenodo.6782638.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A dynamically structured matrix population model for insect life histories observed under variable environmental conditions

Various environmental drivers influence life processes of insect vectors that transmit human disease. Life histories observed under experimental conditions can reveal such complex links; however, designing informative experiments for insects is challenging. Furthermore, inferences obtained under controlled conditions often extrapolate poorly to field conditions. Here, we introduce a pseudo-stage-structured population dynamics model to describe insect development as a renewal process with variable rates. The model permits representing realistic life stage durations under constant and variable environmental conditions. Using the model, we demonstrate how random environmental variations result in fluctuating development rates and affect stage duration. We apply the model to infer environmental dependencies from the life history observations of two common disease vectors, the southern (Culex quinquefasciatus) and northern (Culex pipiens) house mosquito. We identify photoperiod, in addition to temperature, as pivotal in regulating larva stage duration, and find that carefully timed life history observations under semi-field conditions accurately predict insect development throughout the year. The approach we describe augments existing methods of life table design and analysis, and contributes to the development of large-scale climate- and environment-driven population dynamics models for important disease vectors.

OUP accepted manuscript

Motivation

Inferring the parameters of models describing biological systems is an important problem in the reverse engineering of the mechanisms underlying these systems. Much work has focused on parameter inference of stochastic and ordinary differential equation models using Approximate Bayesian Computation (ABC). While there is some recent work on inference in spatial models, this remains an open problem. Simultaneously, advances in topological data analysis (TDA), a field of computational mathematics, have enabled spatial patterns in data to be characterized.

Results

Here, we focus on recent work using TDA to study different regimes of parameter space for a well-studied model of angiogenesis. We propose a method for combining TDA with ABC to infer parameters in the Anderson–Chaplain model of angiogenesis. We demonstrate that this topological approach outperforms ABC approaches that use simpler statistics based on spatial features of the data. This is a first step toward a general framework of spatial parameter inference for biological systems, for which there may be a variety of filtrations, vectorizations and summary statistics to be considered.

Availability and implementation

All code used to produce our results is available as a Snakemake workflow from github.com/tt104/tabc_angio.

Turing pattern design principles and their robustness

Turing patterns have morphed from mathematical curiosities into highly desirable targets for synthetic biology. For a long time, their biological significance was sometimes disputed but there is now ample evidence for their involvement in processes ranging from skin pigmentation to digit and limb formation. While their role in developmental biology is now firmly established, their synthetic design has so far proved challenging. Here, we review recent large-scale mathematical analyses that have attempted to narrow down potential design principles. We consider different aspects of robustness of these models and outline why this perspective will be helpful in the search for synthetic Turing-patterning systems. We conclude by considering robustness in the context of developmental modelling more generally. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Bayesian uncertainty quantification for data-driven equation learning

Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with relatively small amounts of noise, the relationship between observation noise and uncertainty in the learned differential equation models remains unexplored. We demonstrate that for noisy datasets there exists great variation in both the structure of the learned differential equation models and their parameter values. We explore how to exploit multiple datasets to quantify uncertainty in the learned models, and at the same time draw mechanistic conclusions about the target differential equations. We showcase our results using simulation data from a relatively straightforward agent-based model (ABM) which has a well-characterized partial differential equation description that provides highly accurate predictions of averaged ABM behaviours in relevant regions of parameter space. Our approach combines equation learning methods with Bayesian inference approaches so that a quantification of uncertainty can be given by the posterior parameter distribution of the learned model.

Collocation based training of neural ordinary differential equations

The predictive power of machine learning models often exceeds that of mechanistic modeling approaches. However, the interpretability of purely data-driven models, without any mechanistic basis is often complicated, and predictive power by itself can be a poor metric by which we might want to judge different methods. In this work, we focus on the relatively new modeling techniques of neural ordinary differential equations. We discuss how they relate to machine learning and mechanistic models, with the potential to narrow the gulf between these two frameworks: they constitute a class of hybrid model that integrates ideas from data-driven and dynamical systems approaches. Training neural ODEs as representations of dynamical systems data has its own specific demands, and we here propose a collocation scheme as a fast and efficient training strategy. This alleviates the need for costly ODE solvers. We illustrate the advantages that collocation approaches offer, as well as their robustness to qualitative features of a dynamical system, and the quantity and quality of observational data. We focus on systems that exemplify some of the hallmarks of complex dynamical systems encountered in systems biology, and we map out how these methods can be used in the analysis of mathematical models of cellular and physiological processes.

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.

In silico health effect prioritization of environmental chemicals through transcriptomics data exploration from a chemo-centric view

With the explosive growth of synthetic compounds, the health effects caused by exogenous chemical exposure have attracted more and more public attention. The prediction of health effect is a never-ending story. Collective resource of transcriptomics data offers an opportunity to understand and identify the multiple health effects of small molecule. Inspired by the fact that environmental chemicals of high health risk frequently share both similar gene expression profile and common structural feature of certain drugs, we here propose a novel computational effect prioritization method for environmental chemicals through transcriptomics data exploration from a chemo-centric view. Specifically, non-negative matrix factorization (NMF) method has been adopted to get the association network linking structural features with transcriptomics characteristics of drugs with specific effects. The model yields 13 pivotal types of effects, so-called components, that represent drug categories with common chemo- and geno- type features. Moreover, the established model effectively prioritizes potential toxic effects for the external chemicals from the endocrine disruptor screening program (EDSP) for their potential estrogenicity and other verified risks. Even if only the highest priority is set for the estrogenic effect, the precision and recall can reach 0.76 and 0.77 respectively for these chemicals. Our effort provides a successful endeavor as to profile potential toxic effects simultaneously for environmental chemicals using both chemical and omics data.

Addressing uncertainty in genome-scale metabolic model reconstruction and analysis

The reconstruction and analysis of genome-scale metabolic models constitutes a powerful systems biology approach, with applications ranging from basic understanding of genotype-phenotype mapping to solving biomedical and environmental problems. However, the biological insight obtained from these models is limited by multiple heterogeneous sources of uncertainty, which are often difficult to quantify. Here we review the major sources of uncertainty and survey existing approaches developed for representing and addressing them. A unified formal characterization of these uncertainties through probabilistic approaches and ensemble modeling will facilitate convergence towards consistent reconstruction pipelines, improved data integration algorithms, and more accurate assessment of predictive capacity.

Tools for time-course simulation in systems biology: a brief overview

Dynamic modeling of biological systems is essential for understanding all properties of a given organism as it allows us to look not only at the static picture of an organism but also at its behavior under various conditions. With the increasing amount of experimental data, the number of tools that enable dynamic analysis also grows. However, various tools are based on different approaches, use different types of data and offer different functions for analyses; so it can be difficult to choose the most suitable tool for a selected type of model. Here, we bring a brief overview containing descriptions of 50 tools for the reconstruction of biological models, their time-course simulation and dynamic analysis. We examined each tool using test data and divided them based on the qualitative and quantitative nature of the mathematical apparatus they use.

Guidelines for the use and interpretation of assays for monitoring autophagy (4th edition)1

In 2008, we published the first set of guidelines for standardizing research in autophagy. Since then, this topic has received increasing attention, and many scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Thus, it is important to formulate on a regular basis updated guidelines for monitoring autophagy in different organisms. Despite numerous reviews, there continues to be confusion regarding acceptable methods to evaluate autophagy, especially in multicellular eukaryotes. Here, we present a set of guidelines for investigators to select and interpret methods to examine autophagy and related processes, and for reviewers to provide realistic and reasonable critiques of reports that are focused on these processes. These guidelines are not meant to be a dogmatic set of rules, because the appropriateness of any assay largely depends on the question being asked and the system being used. Moreover, no individual assay is perfect for every situation, calling for the use of multiple techniques to properly monitor autophagy in each experimental setting. Finally, several core components of the autophagy machinery have been implicated in distinct autophagic processes (canonical and noncanonical autophagy), implying that genetic approaches to block autophagy should rely on targeting two or more autophagy-related genes that ideally participate in distinct steps of the pathway. Along similar lines, because multiple proteins involved in autophagy also regulate other cellular pathways including apoptosis, not all of them can be used as a specific marker for bona fide autophagic responses. Here, we critically discuss current methods of assessing autophagy and the information they can, or cannot, provide. Our ultimate goal is to encourage intellectual and technical innovation in the field.

Multi-model and network inference based on ensemble estimates: avoiding the madness of crowds

Recent progress in theoretical systems biology, applied mathematics and computational statistics allows us to compare the performance of different candidate models at describing a particular biological system quantitatively. Model selection has been applied with great success to problems where a small number-typically less than 10-of models are compared, but recent studies have started to consider thousands and even millions of candidate models. Often, however, we are left with sets of models that are compatible with the data, and then we can use ensembles of models to make predictions. These ensembles can have very desirable characteristics, but as I show here are not guaranteed to improve on individual estimators or predictors. I will show in the cases of model selection and network inference when we can trust ensembles, and when we should be cautious. The analyses suggest that the careful construction of an ensemble-choosing good predictors-is of paramount importance, more than had perhaps been realized before: merely adding different methods does not suffice. The success of ensemble network inference methods is also shown to rest on their ability to suppress false-positive results. A Jupyter notebook which allows carrying out an assessment of ensemble estimators is provided.

Heat shock response regulates stimulus-specificity and sensitivity of the pro-inflammatory NF-κB signalling

BACKGROUND

Ability to adapt to temperature changes trough the Heat Shock Response (HSR) pathways is one of the most fundamental and clinically relevant cellular response systems. Heat Shock (HS) affects the signalling and gene expression responses of the Nuclear Factor κB (NF-κB) transcription factor, a critical regulator of proliferation and inflammation, however, our quantitative understanding of how cells sense and adapt to temperature changes is limited.

METHODS

We used live-cell time-lapse microscopy and mathematical modelling to understand the signalling of the NF-κB system in the human MCF7 breast adenocarcinoma cells in response to pro-inflammatory Interleukin 1β (IL1β) and Tumour Necrosis Factor α (TNFα) cytokines, following exposure to a 37-43 °C range of physiological and clinical temperatures.

RESULTS

We show that exposure to 43 °C 1 h HS inhibits the immediate NF-κB signalling response to TNFα and IL1β stimulation although uptake of cytokines is not impaired. Within 4 h after HS treatment IL1β-induced NF-κB responses return to normal levels, but the recovery of the TNFα-induced responses is still affected. Using siRNA knock-down of Heat Shock Factor 1 (HSF1) we show that this stimulus-specificity is conferred via the Inhibitory κB kinase (IKK) signalosome where HSF1-dependent feedback regulates TNFα, but not IL1β-mediated IKK recovery post HS. Furthermore, we demonstrate that through the temperature-dependent denaturation and recovery of IKK, TNFα and IL1β-mediated signalling exhibit different temperature sensitivity and adaptation to repeated HS when exposed to a 37-43 °C temperature range. Specifically, IL1β-mediated NF-κB responses are more robust to temperature changes in comparison to those induced by TNFα treatment.

CONCLUSIONS

We demonstrate that the kinetics of the NF-κB system following temperature stress is cytokine specific and exhibit differential adaptation to temperature changes. We propose that this differential temperature sensitivity is mediated via the IKK signalosome, which acts as a bona fide temperature sensor trough the HSR cross-talk. This novel quantitative understanding of NF-κB and HSR interactions is fundamentally important for the potential optimization of therapeutic hyperthermia protocols. Video Abstract.

Model Averaging in Viral Dynamic Models

The paucity of experimental data makes both inference and prediction particularly challenging in viral dynamic models. In the presence of several candidate models, a common strategy is model selection (MS), in which models are fitted to the data but only results obtained with the "best model" are presented. However, this approach ignores model uncertainty, which may lead to inaccurate predictions. When several models provide a good fit to the data, another approach is model averaging (MA) that weights the predictions of each model according to its consistency to the data. Here, we evaluated by simulations in a nonlinear mixed-effect model framework the performances of MS and MA in two realistic cases of acute viral infection, i.e., (1) inference in the presence of poorly identifiable parameters, namely, initial viral inoculum and eclipse phase duration, (2) uncertainty on the mechanisms of action of the immune response. MS was associated in some scenarios with a large rate of false selection. This led to a coverage rate lower than the nominal coverage rate of 0.95 in the majority of cases and below 0.50 in some scenarios. In contrast, MA provided better estimation of parameter uncertainty, with coverage rates ranging from 0.72 to 0.98 and mostly comprised within the nominal coverage rate. Finally, MA provided similar predictions than those obtained with MS. In conclusion, parameter estimates obtained with MS should be taken with caution, especially when several models well describe the data. In this situation, MA has better performances and could be performed to account for model uncertainty.

TopoFilter: a MATLAB package for mechanistic model identification in systems biology

Background

To develop mechanistic dynamic models in systems biology, one often needs to identify all (or minimal) representations of the biological processes that are consistent with experimental data, out of a potentially large set of hypothetical mechanisms. However, a simple enumeration of all alternatives becomes quickly intractable when the number of model parameters grows. Selecting appropriate dynamic models out of a large ensemble of models, taking the uncertainty in our biological knowledge and in the experimental data into account, is therefore a key current problem in systems biology.

Results

The TopoFilter package addresses this problem in a heuristic and automated fashion by implementing the previously described topological filtering method for Bayesian model selection. It includes a core heuristic for searching the space of submodels of a parametrized model, coupled with a sampling-based exploration of the parameter space. Recent developments of the method allow to balance exhaustiveness and speed of the model space search, to efficiently re-sample parameters, to parallelize the search, and to use custom scoring functions. We use a theoretical example to motivate these features and then demonstrate TopoFilter’s applicability for a yeast signaling network with more than 250’000 possible model structures.

Conclusions

TopoFilter is a flexible software framework that makes Bayesian model selection and reduction efficient and scalable to network models of a complexity that represents contemporary problems in, for example, cell signaling. TopoFilter is open-source, available under the GPL-3.0 license at https://gitlab.com/csb.ethz/TopoFilter. It includes installation instructions, a quickstart guide, a description of all package options, and multiple examples.

Parameter inference in dynamical systems with co-dimension 1 bifurcations

Dynamical systems with intricate behaviour are all-pervasive in biology. Many of the most interesting biological processes indicate the presence of bifurcations, i.e. phenomena where a small change in a system parameter causes qualitatively different behaviour. Bifurcation theory has become a rich field of research in its own right and evaluating the bifurcation behaviour of a given dynamical system can be challenging. An even greater challenge, however, is to learn the bifurcation structure of dynamical systems from data, where the precise model structure is not known. Here, we study one aspects of this problem: the practical implications that the presence of bifurcations has on our ability to infer model parameters and initial conditions from empirical data; we focus on the canonical co-dimension 1 bifurcations and provide a comprehensive analysis of how dynamics, and our ability to infer kinetic parameters are linked. The picture thus emerging is surprisingly nuanced and suggests that identification of the qualitative dynamics-the bifurcation diagram-should precede any attempt at inferring kinetic parameters.

Simulation of live-cell imaging system reveals hidden uncertainties in cooperative binding measurements

We propose a computational method to quantitatively evaluate the systematic uncertainties that arise from undetectable sources in biological measurements using live-cell imaging techniques. We then demonstrate this method in measuring the biological cooperativity of molecular binding networks, in particular, ligand molecules binding to cell-surface receptor proteins. Our results show how the nonstatistical uncertainties lead to invalid identifications of the measured cooperativity. Through this computational scheme, the biological interpretation can be more objectively evaluated and understood under a specific experimental configuration of interest.

Reversible jump MCMC for multi-model inference in Metabolic Flux Analysis

Motivation

The validity of model based inference, as used in systems biology, depends on the underlying model formulation. Often, a vast number of competing models is available, that are built on different assumptions, all consistent with the existing knowledge about the studied biological phenomenon. As a remedy for this, Bayesian Model Averaging (BMA) facilitates parameter and structural inferences based on multiple models simultaneously. However, in fields where a vast number of alternative, high-dimensional and non-linear models are involved, the BMA-based inference task is computationally very challenging.

Results

Here we use BMA in the complex setting of Metabolic Flux Analysis (MFA) to infer whether potentially reversible reactions proceed uni- or bidirectionally, using 13C labeling data and metabolic networks. BMA is applied on a large set of candidate models with differing directionality settings, using a tailored multi-model Markov Chain Monte Carlo (MCMC) approach. The applicability of our algorithm is shown by inferring the in vivo probability of reaction bidirectionalities in a realistic network setup, thereby extending the scope of 13C MFA from parameter to structural inference.

Supplementary information

Supplementary data are available at Bioinformatics online.

Tension and Resolution: Dynamic, Evolving Populations of Organelle Genomes within Plant Cells

Mitochondria and plastids form dynamic, evolving populations physically embedded in the fluctuating environment of the plant cell. Their evolutionary heritage has shaped how the cell controls the genetic structure and the physical behavior of its organelle populations. While the specific genes involved in these processes are gradually being revealed, the governing principles underlying this controlled behavior remain poorly understood. As the genetic and physical dynamics of these organelles are central to bioenergetic performance and plant physiology, this challenges both fundamental biology and strategies to engineer better-performing plants. This article reviews current knowledge of the physical and genetic behavior of mitochondria and chloroplasts in plant cells. An overarching hypothesis is proposed whereby organelles face a tension between genetic robustness and individual control and responsiveness, and different species resolve this tension in different ways. As plants are immobile and thus subject to fluctuating environments, their organelles are proposed to favor individual responsiveness, sacrificing genetic robustness. Several notable features of plant organelles, including large genomes, mtDNA recombination, fragmented organelles, and plastid/mitochondrial differences may potentially be explained by this hypothesis. Finally, the ways that quantitative and systems biology can help shed light on the plethora of open questions in this field are highlighted.

Functionalized Nanomaterial Assembling and Biosynthesis Using the Extremophile Deinococcus radiodurans for Multifunctional Applications

The development of functionalized nanomaterial biosynthesis processes is important to expand many cutting-edge nanomaterial application areas. However, unclear synthesis mechanisms and low synthesis efficiency under various chemical stresses have limited the use of these biomaterials. Deinococcus radiodurans is an extreme bacterium well known for its exceptional resistance to radiation oxidants and electrophilic agents. This extremophile, which possesses a spontaneous self-assembled surface-layer (S-layer), has been an optimal model organism to study microbial nanomaterial biotemplates and biosynthesis under various stresses. This review summarizes the S-layers from D. radiodurans as an excellent biotemplate for various pre-synthesized nanomaterials and multiple applications, and highlights recent progresses about the biosynthesis of functionalized gold nanoparticles (AuNPs), silver nanoparticles (AgNPs), as well as gold and silver bimetallic nanoparticles using D. radiodurans. Their formation mechanisms, properties, and applications are discussed and summarized to provide significant insights into the design or modification of functionalized nanomaterials via natural materials. Grand challenges and future directions to realize the multifunctional applications of these nanomaterials are highlighted for a better understanding of their biosynthesis mechanisms and functionalized modifications.

Quantitative Mechanistic Modeling in Support of Pharmacological Therapeutics Development in Immuno-Oncology

Following the approval, in recent years, of the first immune checkpoint inhibitor, there has been an explosion in the development of immuno-modulating pharmacological modalities for the treatment of various cancers. From the discovery phase to late-stage clinical testing and regulatory approval, challenges in the development of immuno-oncology (IO) drugs are multi-fold and complex. In the preclinical setting, the multiplicity of potential drug targets around immune checkpoints, the growing list of immuno-modulatory molecular and cellular forces in the tumor microenvironment-with additional opportunities for IO drug targets, the emergence of exploratory biomarkers, and the unleashed potential of modality combinations all have necessitated the development of quantitative, mechanistically-oriented systems models which incorporate key biology and patho-physiology aspects of immuno-oncology and the pharmacokinetics of IO-modulating agents. In the clinical setting, the qualification of surrogate biomarkers predictive of IO treatment efficacy or outcome, and the corresponding optimization of IO trial design have become major challenges. This mini-review focuses on the evolution and state-of-the-art of quantitative systems models describing the tumor vs. immune system interplay, and their merging with quantitative pharmacology models of IO-modulating agents, as companion tools to support the addressing of these challenges.

Investigating sensitivity coefficients characterizing the response of a model of tau protein transport in an axon to model parameters

Evaluating the sensitivity of biological models to various model parameters is a critical step towards advancing our understanding of biological systems. In this paper, we investigated sensitivity coefficients for a model simulating transport of tau protein along the axon. This is an important problem due to the relevance of tau transport and agglomeration to Alzheimer's disease and other tauopathies, such as some forms of parkinsonism. The sensitivity coefficients that we obtained characterize how strongly three observables (the tau concentration, average tau velocity, and the percentage of tau bound to microtubules) depend on model parameters. The fact that the observables strongly depend on a parameter characterizing tau transition from the retrograde to the anterograde kinetic states suggests the importance of motor-driven transport of tau. The observables are sensitive to kinetic constants characterizing tau concentration in the free (cytosolic) state only at small distances from the soma. Cytosolic tau can only be transported by diffusion, suggesting that diffusion-driven transport of tau only plays a role in the proximal axon. Our analysis also shows the location in the axon in which an observable has the greatest sensitivity to a certain parameter. For most parameters, this location is in the proximal axon. This could be useful for designing an experiment aimed at determining the value of this parameter. We also analyzed sensitivity of the average tau velocity, the total tau concentration, and the percentage of microtubule-bound tau to cytosolic diffusivity of tau and diffusivity of bound tau along the MT lattice. The model predicts that at small distances from the soma the effect of these two diffusion processes is comparable.

A Bayesian mixture modelling approach for spatial proteomics

Analysis of the spatial sub-cellular distribution of proteins is of vital importance to fully understand context specific protein function. Some proteins can be found with a single location within a cell, but up to half of proteins may reside in multiple locations, can dynamically re-localise, or reside within an unknown functional compartment. These considerations lead to uncertainty in associating a protein to a single location. Currently, mass spectrometry (MS) based spatial proteomics relies on supervised machine learning algorithms to assign proteins to sub-cellular locations based on common gradient profiles. However, such methods fail to quantify uncertainty associated with sub-cellular class assignment. Here we reformulate the framework on which we perform statistical analysis. We propose a Bayesian generative classifier based on Gaussian mixture models to assign proteins probabilistically to sub-cellular niches, thus proteins have a probability distribution over sub-cellular locations, with Bayesian computation performed using the expectation-maximisation (EM) algorithm, as well as Markov-chain Monte-Carlo (MCMC). Our methodology allows proteome-wide uncertainty quantification, thus adding a further layer to the analysis of spatial proteomics. Our framework is flexible, allowing many different systems to be analysed and reveals new modelling opportunities for spatial proteomics. We find our methods perform competitively with current state-of-the art machine learning methods, whilst simultaneously providing more information. We highlight several examples where classification based on the support vector machine is unable to make any conclusions, while uncertainty quantification using our approach provides biologically intriguing results. To our knowledge this is the first Bayesian model of MS-based spatial proteomics data.

Distribution shapes govern the discovery of predictive models for gene regulation

Systems biology seeks to combine experiments with computation to predict biological behaviors. However, despite tremendous data and knowledge, biological models make less-accurate predictions compared with other fields. By analyzing single-cell, single-molecule measurements of mRNA during yeast stress response, we explore why and how the shapes of experimental distributions control prediction accuracy. We show how asymmetric data distributions with long tails cause standard modeling approaches to yield excellent fits but make meaningless predictions. We show how these biases arise from the violation of fundamental assumptions in standard modeling approaches. We demonstrate how advanced computational tools solve this dilemma and achieve predictive understanding of spatiotemporal mechanisms of transcription control including RNA polymerase initiation and elongation and mRNA accumulation, transport, and decay.

Despite substantial experimental and computational efforts, mechanistic modeling remains more predictive in engineering than in systems biology. The reason for this discrepancy is not fully understood. One might argue that the randomness and complexity of biological systems are the main barriers to predictive understanding, but these issues are not unique to biology. Instead, we hypothesize that the specific shapes of rare single-molecule event distributions produce substantial yet overlooked challenges for biological models. We demonstrate why modern statistical tools to disentangle complexity and stochasticity, which assume normally distributed fluctuations or enormous datasets, do not apply to the discrete, positive, and nonsymmetric distributions that characterize mRNA fluctuations in single cells. As an example, we integrate single-molecule measurements and advanced computational analyses to explore mitogen-activated protein kinase induction of multiple stress response genes. Through systematic analyses of different metrics to compare the same model to the same data, we elucidate why standard modeling approaches yield nonpredictive models for single-cell gene regulation. We further explain how advanced tools recover precise, reproducible, and predictive understanding of transcription regulation mechanisms, including gene activation, polymerase initiation, elongation, mRNA accumulation, spatial transport, and decay.

The three-legged stool of understanding metabolism: integrating metabolomics with biochemical genetics and computational modeling

Traditional biochemical research has resulted in a good understanding of many aspects of metabolism. However, this reductionist approach is time consuming and requires substantial resources, thus raising the question whether modern metabolomics and genomics should take over and replace the targeted experiments of old. We proffer that such a replacement is neither feasible not desirable and propose instead the tight integration of modern, system-wide omics with traditional experimental bench science and dedicated computational approaches. This integration is an important prerequisite toward the optimal acquisition of knowledge regarding metabolism and physiology in health and disease. The commentary describes advantages and drawbacks of current approaches to assessing metabolism and highlights the challenges to be overcome as we strive to achieve a deeper level of metabolic understanding in the future.

MitoCore: a curated constraint-based model for simulating human central metabolism

BACKGROUND

The complexity of metabolic networks can make the origin and impact of changes in central metabolism occurring during diseases difficult to understand. Computer simulations can help unravel this complexity, and progress has advanced in genome-scale metabolic models. However, many models produce unrealistic results when challenged to simulate abnormal metabolism as they include incorrect specification and localisation of reactions and transport steps, incorrect reaction parameters, and confounding of prosthetic groups and free metabolites in reactions. Other common drawbacks are due to their scale, making them difficult to parameterise and simulation results hard to interpret. Therefore, it remains important to develop smaller, manually curated models.

RESULTS

We present MitoCore, a manually curated constraint-based computer model of human metabolism that incorporates the complexity of central metabolism and simulates this metabolism successfully under normal and abnormal physiological conditions, including hypoxia and mitochondrial diseases. MitoCore describes 324 metabolic reactions, 83 transport steps between mitochondrion and cytosol, and 74 metabolite inputs and outputs through the plasma membrane, to produce a model of manageable scale for easy interpretation of results. Its key innovations include a more accurate partitioning of metabolism between cytosol and mitochondrial matrix; better modelling of connecting transport steps; differentiation of prosthetic groups and free co-factors in reactions; and a new representation of the respiratory chain and the proton motive force. MitoCore's default parameters simulate normal cardiomyocyte metabolism, and to improve usability and allow comparison with other models and types of analysis, its reactions and metabolites have extensive annotation, and cross-reference identifiers from Virtual Metabolic Human database and KEGG. These innovations-including over 100 reactions absent or modified from Recon 2-are necessary to model central metabolism more accurately.

CONCLUSION

We anticipate MitoCore as a research tool for scientists, from experimentalists looking to interpret their data and test hypotheses, to experienced modellers predicting the consequences of disease or using computationally intensive methods that are infeasible with larger models, as well as a teaching tool for those new to modelling and needing a small, manageable model on which to learn and experiment.

MAMMOTh: A new database for curated mathematical models of biomolecular systems

MOTIVATION

Living systems have a complex hierarchical organization that can be viewed as a set of dynamically interacting subsystems. Thus, to simulate the internal nature and dynamics of the entire biological system, we should use the iterative way for a model reconstruction, which is a consistent composition and combination of its elementary subsystems. In accordance with this bottom-up approach, we have developed the MAthematical Models of bioMOlecular sysTems (MAMMOTh) tool that consists of the database containing manually curated MAMMOTh fitted to the experimental data and a software tool that provides their further integration.

RESULTS

The MAMMOTh database entries are organized as building blocks in a way that the model parts can be used in different combinations to describe systems with higher organizational level (metabolic pathways and/or transcription regulatory networks). The tool supports export of a single model or their combinations in SBML or Mathematica standards. The database currently contains 110 mathematical sub-models for Escherichia coli elementary subsystems (enzymatic reactions and gene expression regulatory processes) that can be combined in at least 5100 complex/sophisticated models concerning more complex biological processes as de novo nucleotide biosynthesis, aerobic/anaerobic respiration and nitrate/nitrite utilization in E. coli. All models are functionally interconnected and sufficiently complement public model resources.

AVAILABILITY

http://mammoth.biomodelsgroup.ru.

The optimal regulation mode of Bcl-2 apoptotic switch revealed by bistability analysis

In most cell types, apoptosis occurs by the mitochondrial outer membrane permeability (MOMP)-mediated pathway, which is controlled by Bcl-2 family proteins (often referred to as Bcl-2 apoptotic switch). These proteins, which display a range of bioactivities, can be divided into four types: effectors, inhibitors, activators and sensitizers. Although the complex interactions among Bcl-2 family members have been studied intensively, a unifying hypothesis for the mechanism they use to regulate MOMP remains elusive. The bistable behaviors are often used to explain the all-or-none decisions of apoptosis. Here, we attempt to reveal the optimal interaction mode by comparing the bistable performances of three different modes (direct activation, indirect activation, and unified mode) proposed by biologists. Using the method that combines mathematical analysis and numerical simulation, we discover that bistability can only emerge from the unified mode when proteins synthesis and degradation are considered, which is in favor of it as an optimal regulation mode of Bcl-2 apoptotic switch. The parameter sensitivity analysis for the unified mode further consolidates this view. Moreover, two-parameter bifurcation analysis suggests that the sensitizers lower the threshold of activation of Bax, but have a negative influence on the width of the bistability region. Our study may provide mechanistic insights into the heterogeneity of tumor cells and the efficiency of BH3 mimetic-mediated killing of cancer cells, and suggest that a combination treatment might be required to overcome apoptosis resistance in the Bcl-2 family targeted therapies.

Kinetic Analysis of the Multivalent Ligand Binding Interaction between Protein A/G and IgG: A Standard System Setting

Recombinant protein A/G (PAG) has a sequence coding for eight IgG binding sites and has enhanced interspecies affinity. High-frequency sampling of a PAG titration with IgG produces concentration profiles that are sensitive to the kinetic availability of the binding sites. The full kinetic model developed here for IgG binding sequentially to PAG shows only two distinct kinetic processes, describing an initial rapid association of two antibodies to PAG with a rate constant k-fast = (1.86 ± 0.08) × 10⁶ M^-1 s^-1 and a slower antibody binding process to all remaining sites, k-slow = (1.24 ± 0.05) × 10⁴ M^-1 s^-1. At equilibrium (after 1 h), the maximum IgG occupancy of PAG is 2.8 ± 0.5, conflicting with the genetic evidence of eight binding sites and suggesting significant steric hindrance of the neighboring IgG binding sites. The phosphate-buffered saline (PBS) solution defines a standard system setting, and this may be compared with other settings. The mean association rate of PAG-IgG_n in the standard setting is 282 ± 20% higher than when PAG is tethered to a surface. A systems biology approach requires that a model parameter set that defines a system in a standard setting should be transferable to another system. The transfer of parameters between settings may be performed using activity coefficients characterizing an effective concentration of species in a system, a_i = γ_ic_i. The activity correction, γ, for the eight-site occupancy is γ = 0.35 ± 0.06, and mapping from the standard setting to the solution setting suggests γ_PAG-IgG = 0.4 ± 0.03. The role of activity coefficients and transferability of kinetic parameters between system settings is discussed.

Control mechanisms for stochastic biochemical systems via computation of reachable sets

Controlling the behaviour of cells by rationally guiding molecular processes is an overarching aim of much of synthetic biology. Molecular processes, however, are notoriously noisy and frequently nonlinear. We present an approach to studying the impact of control measures on motifs of molecular interactions that addresses the problems faced in many biological systems: stochasticity, parameter uncertainty and nonlinearity. We show that our reachability analysis formalism can describe the potential behaviour of biological (naturally evolved as well as engineered) systems, and provides a set of bounds on their dynamics at the level of population statistics: for example, we can obtain the possible ranges of means and variances of mRNA and protein expression levels, even in the presence of uncertainty about model parameters.

How to deal with parameters for whole-cell modelling

Dynamical systems describing whole cells are on the verge of becoming a reality. But as models of reality, they are only useful if we have realistic parameters for the molecular reaction rates and cell physiological processes. There is currently no suitable framework to reliably estimate hundreds, let alone thousands, of reaction rate parameters. Here, we map out the relative weaknesses and promises of different approaches aimed at redressing this issue. While suitable procedures for estimation or inference of the whole (vast) set of parameters will, in all likelihood, remain elusive, some hope can be drawn from the fact that much of the cellular behaviour may be explained in terms of smaller sets of parameters. Identifying such parameter sets and assessing their behaviour is now becoming possible even for very large systems of equations, and we expect such methods to become central tools in the development and analysis of whole-cell models.

Epithelial/mesenchymal plasticity: how have quantitative mathematical models helped improve our understanding?

Phenotypic plasticity, the ability of cells to reversibly alter their phenotypes in response to signals, presents a significant clinical challenge to treating solid tumors. Tumor cells utilize phenotypic plasticity to evade therapies, metastasize, and colonize distant organs. As a result, phenotypic plasticity can accelerate tumor progression. A well‐studied example of phenotypic plasticity is the bidirectional conversions among epithelial, mesenchymal, and hybrid epithelial/mesenchymal (E/M) phenotype(s). These conversions can alter a repertoire of cellular traits associated with multiple hallmarks of cancer, such as metabolism, immune evasion, invasion, and metastasis. To tackle the complexity and heterogeneity of these transitions, mathematical models have been developed that seek to capture the experimentally verified molecular mechanisms and act as ‘hypothesis‐generating machines’. Here, we discuss how these quantitative mathematical models have helped us explain existing experimental data, guided further experiments, and provided an improved conceptual framework for understanding how multiple intracellular and extracellular signals can drive E/M plasticity at both the single‐cell and population levels. We also discuss the implications of this plasticity in driving multiple aggressive facets of tumor progression.

Dissolution test for risk assessment of nanoparticles: a pilot study

Worldwide efforts are currently trying to produce effective risk assessment models for orally ingested nanoparticles. These tests should provide quantitative information on the bioaccessibility and bioavailability of products of biotransformation, such as dissolved ionic species and/or aggregates. In vitro dissolution tests might be useful for nanoparticle risk assessment, because of their potential to quantitatively monitor the changes of specific properties (e.g., dissolution, agglomeration, etc.), which are critical factors linked to bioaccessibility/bioavailability. Unfortunately, the technological advancement of such tools is currently hampered by the complexity and evolving nature of nanoparticle properties that are strongly influenced by the environment and are often difficult to trace in a standardized manner. Hence, the test's success depends on its ability to quantify such properties using standardized experimental conditions to mimic reality as closely as possible. Here we applied an in vitro dissolution test to quantify the dissolution of silver nanoparticles under dynamic conditions, which likely occur in human digestion, providing a clear description of the bioaccessible ionic species (free and matrix bound ions or soluble silver organic or inorganic complexes) occurring during the different digestion phases. We demonstrated the test feasibility using a multi-technique approach and following pre-standardized operational procedures to allow for a comprehensive description of the process as a whole. Moreover, this can favour data reliability for benchmarking. Finally, we showed how the estimated values of the bioaccessible ionic species relate to absorption and excretion parameters, as measured in vivo. The outcomes presented in this work highlight the potential regulatory role of the dissolution test for orally ingested nanoparticles and, although preliminary, experimentally demonstrate the regulatory oriented "read-across" principle.

Utilization of the bootstrap method for determining confidence intervals of parameters for a model of MAP1B protein transport in axons

This paper develops a model of axonal transport of MAP1B protein. The problem of determining parameter values for the proposed model utilizing limited available experimental data is addressed. We used a global minimum search algorithm to find parameter values that minimize the discrepancy between model predictions and published experimental results. By analyzing the best fit parameter values it was established that some processes can be dropped from the model without losing accuracy, thus a simplified version of the model was formulated. In particular, our analysis suggests that reversals in MAP1B transport are infrequent and can be neglected. The detachment of anterogradely-biased MAP1B from microtubules (MTs) and the attachment of retrogradely-biased MAP1B to MTs can also be neglected. An analytical solution for the simplified model was obtained. Confidence intervals for the determined parameters were found by bootstrapping model residuals. The resultant analysis heavily constrained the values of some parameters while showing that some could vary without significantly impacting model error. For example, our analysis suggests that, above a certain threshold value, the kinetic constant determining the rate of MAP1B transition from the retrograde pausing state to the off-track state has little impact on model error. On the contrary, the kinetic constant describing MAP1B transition from a pausing to a running state has great impact on model error.

Cancer as robust intrinsic state shaped by evolution: a key issues review

Cancer is a complex disease: its pathology cannot be properly understood in terms of independent players-genes, proteins, molecular pathways, or their simple combinations. This is similar to many-body physics of a condensed phase that many important properties are not determined by a single atom or molecule. The rapidly accumulating large 'omics' data also require a new mechanistic and global underpinning to organize for rationalizing cancer complexity. A unifying and quantitative theory was proposed by some of the present authors that cancer is a robust state formed by the endogenous molecular-cellular network, which is evolutionarily built for the developmental processes and physiological functions. Cancer state is not optimized for the whole organism. The discovery of crucial players in cancer, together with their developmental and physiological roles, in turn, suggests the existence of a hierarchical structure within molecular biology systems. Such a structure enables a decision network to be constructed from experimental knowledge. By examining the nonlinear stochastic dynamics of the network, robust states corresponding to normal physiological and abnormal pathological phenotypes, including cancer, emerge naturally. The nonlinear dynamical model of the network leads to a more encompassing understanding than the prevailing linear-additive thinking in cancer research. So far, this theory has been applied to prostate, hepatocellular, gastric cancers and acute promyelocytic leukemia with initial success. It may offer an example of carrying physics inquiring spirit beyond its traditional domain: while quantitative approaches can address individual cases, however there must be general rules/laws to be discovered in biology and medicine.

A Multiscale Description of Biomolecular Active Matter: The Chemistry Underlying Many Life Processes

This Commentary will describe the goal of developing and implementing novel, powerful, and integrated multiscale computer simulation methodology capable of accessing the large length and long time scales inherent in the behavior of biomolecular, multiprotein "active matter" complexes within the context of cellular biology. Examples include those involved in the actin-based cytoskeleton and its mechanochemistry. The primary objective is to connect detailed molecular and chemical properties with the key mesoscopic features manifest at the scales of cellular biology through a transformative theoretical and computer simulation approach, based on real physical and chemical interactions. This multiscale computational work would also make critical contact with rapidly developing experimental techniques such as super-resolution optical imaging, single molecule spectroscopy, and cryo-electron tomography, which are providing remarkable insight into the internal mesoscale self-organization and dynamics of cells.

Modelling the molecular mechanisms of aging

The aging process is driven at the cellular level by random molecular damage that slowly accumulates with age. Although cells possess mechanisms to repair or remove damage, they are not 100% efficient and their efficiency declines with age. There are many molecular mechanisms involved and exogenous factors such as stress also contribute to the aging process. The complexity of the aging process has stimulated the use of computational modelling in order to increase our understanding of the system, test hypotheses and make testable predictions. As many different mechanisms are involved, a wide range of models have been developed. This paper gives an overview of the types of models that have been developed, the range of tools used, modelling standards and discusses many specific examples of models that have been grouped according to the main mechanisms that they address. We conclude by discussing the opportunities and challenges for future modelling in this field.

Parameter estimation in large-scale systems biology models: a parallel and self-adaptive cooperative strategy

Background

The development of large-scale kinetic models is one of the current key issues in computational systems biology and bioinformatics. Here we consider the problem of parameter estimation in nonlinear dynamic models. Global optimization methods can be used to solve this type of problems but the associated computational cost is very large. Moreover, many of these methods need the tuning of a number of adjustable search parameters, requiring a number of initial exploratory runs and therefore further increasing the computation times.

Here we present a novel parallel method, self-adaptive cooperative enhanced scatter search (saCeSS), to accelerate the solution of this class of problems. The method is based on the scatter search optimization metaheuristic and incorporates several key new mechanisms: (i) asynchronous cooperation between parallel processes, (ii) coarse and fine-grained parallelism, and (iii) self-tuning strategies.

Results

The performance and robustness of saCeSS is illustrated by solving a set of challenging parameter estimation problems, including medium and large-scale kinetic models of the bacterium E. coli, bakerés yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network.

The results consistently show that saCeSS is a robust and efficient method, allowing very significant reduction of computation times with respect to several previous state of the art methods (from days to minutes, in several cases) even when only a small number of processors is used.

Conclusions

The new parallel cooperative method presented here allows the solution of medium and large scale parameter estimation problems in reasonable computation times and with small hardware requirements. Further, the method includes self-tuning mechanisms which facilitate its use by non-experts. We believe that this new method can play a key role in the development of large-scale and even whole-cell dynamic models.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1452-4) contains supplementary material, which is available to authorized users.