How to deal with parameters for whole-cell modelling

Establishing a conceptual framework for holistic cell states and state transitions

Cell states were traditionally defined by how they looked, where they were located, and what functions they performed. In this post-genomic era, the field is largely focused on a molecular view of cell state. Moving forward, we anticipate that the observables used to define cell states will evolve again as single-cell imaging and analytics are advancing at a breakneck pace via the collection of large-scale, systematic cell image datasets and the application of quantitative image-based data science methods. This is, therefore, a key moment in the arc of cell biological research to develop approaches that integrate the spatiotemporal observables of the physical structure and organization of the cell with molecular observables toward the concept of a holistic cell state. In this perspective, we propose a conceptual framework for holistic cell states and state transitions that is data-driven, practical, and useful to enable integrative analyses and modeling across many data types.

Technologies for whole-cell modeling: Genome-wide reconstruction of a cell in silico

With advances in high-throughput, large-scale in vivo measurement and genome modification techniques at the single-nucleotide level, there is an increasing demand for the development of new technologies for the flexible design and control of cellular systems. Computer-aided design is a powerful tool to design new cells. Whole-cell modeling aims to integrate various cellular subsystems, determine their interactions and cooperative mechanisms, and predict comprehensive cellular behaviors by computational simulations on a genome-wide scale. It has been applied to prokaryotes, yeasts, and higher eukaryotic cells, and utilized in a wide range of applications, including production of valuable substances, drug discovery, and controlled differentiation. Whole-cell modeling, consisting of several thousand elements with diverse scales and properties, requires innovative model construction, simulation, and analysis techniques. Furthermore, whole-cell modeling has been extended to multiple scales, including high-resolution modeling at the single-nucleotide and single-amino acid levels and multicellular modeling of tissues and organs. This review presents an overview of the current state of whole-cell modeling, discusses the novel computational and experimental technologies driving it, and introduces further developments toward multihierarchical modeling on a whole-genome scale.

Multi-scale models of whole cells: progress and challenges

Whole-cell modeling is "the ultimate goal" of computational systems biology and "a grand challenge for 21st century" (Tomita, Trends in Biotechnology, 2001, 19(6), 205-10). These complex, highly detailed models account for the activity of every molecule in a cell and serve as comprehensive knowledgebases for the modeled system. Their scope and utility far surpass those of other systems models. In fact, whole-cell models (WCMs) are an amalgam of several types of "system" models. The models are simulated using a hybrid modeling method where the appropriate mathematical methods for each biological process are used to simulate their behavior. Given the complexity of the models, the process of developing and curating these models is labor-intensive and to date only a handful of these models have been developed. While whole-cell models provide valuable and novel biological insights, and to date have identified some novel biological phenomena, their most important contribution has been to highlight the discrepancy between available data and observations that are used for the parametrization and validation of complex biological models. Another realization has been that current whole-cell modeling simulators are slow and to run models that mimic more complex (e.g., multi-cellular) biosystems, those need to be executed in an accelerated fashion on high-performance computing platforms. In this manuscript, we review the progress of whole-cell modeling to date and discuss some of the ways that they can be improved.

FitMultiCell: simulating and parameterizing computational models of multi-scale and multi-cellular processes

MOTIVATION

Biological tissues are dynamic and highly organized. Multi-scale models are helpful tools to analyse and understand the processes determining tissue dynamics. These models usually depend on parameters that need to be inferred from experimental data to achieve a quantitative understanding, to predict the response to perturbations, and to evaluate competing hypotheses. However, even advanced inference approaches such as approximate Bayesian computation (ABC) are difficult to apply due to the computational complexity of the simulation of multi-scale models. Thus, there is a need for a scalable pipeline for modeling, simulating, and parameterizing multi-scale models of multi-cellular processes.

RESULTS

Here, we present FitMultiCell, a computationally efficient and user-friendly open-source pipeline that can handle the full workflow of modeling, simulating, and parameterizing for multi-scale models of multi-cellular processes. The pipeline is modular and integrates the modeling and simulation tool Morpheus and the statistical inference tool pyABC. The easy integration of high-performance infrastructure allows to scale to computationally expensive problems. The introduction of a novel standard for the formulation of parameter inference problems for multi-scale models additionally ensures reproducibility and reusability. By applying the pipeline to multiple biological problems, we demonstrate its broad applicability, which will benefit in particular image-based systems biology.

AVAILABILITY AND IMPLEMENTATION

FitMultiCell is available open-source at https://gitlab.com/fitmulticell/fit.

Deep Neural Networks for Predicting Single-Cell Responses and Probability Landscapes

Engineering biology relies on the accurate prediction of cell responses. However, making these predictions is challenging for a variety of reasons, including the stochasticity of biochemical reactions, variability between cells, and incomplete information about underlying biological processes. Machine learning methods, which can model diverse input-output relationships without requiring a priori mechanistic knowledge, are an ideal tool for this task. For example, such approaches can be used to predict gene expression dynamics given time-series data of past expression history. To explore this application, we computationally simulated single-cell responses, incorporating different sources of noise and alternative genetic circuit designs. We showed that deep neural networks trained on these simulated data were able to correctly infer the underlying dynamics of a cell response even in the presence of measurement noise and stochasticity in the biochemical reactions. The training set size and the amount of past data provided as inputs both affected prediction quality, with cascaded genetic circuits that introduce delays requiring more past data. We also tested prediction performance on a bistable auto-activation circuit, finding that our initial method for predicting a single trajectory was fundamentally ill-suited for multimodal dynamics. To address this, we updated the network architecture to predict the entire distribution of future states, showing it could accurately predict bimodal expression distributions. Overall, these methods can be readily applied to the diverse prediction tasks necessary to predict and control a variety of biological circuits, a key aspect of many synthetic biology applications.

Sensitivity analysis of biochemical systems using bond graphs

The sensitivity of systems biology models to parameter variation can give insights into which parameters are most important for physiological function, and also direct efforts to estimate parameters. However, in general, kinetic models of biochemical systems do not remain thermodynamically consistent after perturbing parameters. To address this issue, we analyse the sensitivity of biological reaction networks in the context of a bond graph representation. We find that the parameter sensitivities can themselves be represented as bond graph components, mirroring potential mechanisms for controlling biochemistry. In particular, a sensitivity system is derived which re-expresses parameter variation as additional system inputs. The sensitivity system is then linearized with respect to these new inputs to derive a linear system which can be used to give local sensitivity to parameters in terms of linear system properties such as gain and time constant. This linear system can also be used to find so-called sloppy parameters in biological models. We verify our approach using a model of the Pentose Phosphate Pathway, confirming the reactions and metabolites most essential to maintaining the function of the pathway.

scAEGAN: Unification of single-cell genomics data by adversarial learning of latent space correspondences

Recent progress in Single-Cell Genomics has produced different library protocols and techniques for molecular profiling. We formulate a unifying, data-driven, integrative, and predictive methodology for different libraries, samples, and paired-unpaired data modalities. Our design of scAEGAN includes an autoencoder (AE) network integrated with adversarial learning by a cycleGAN (cGAN) network. The AE learns a low-dimensional embedding of each condition, whereas the cGAN learns a non-linear mapping between the AE representations. We evaluate scAEGAN using simulated data and real scRNA-seq datasets, different library preparations (Fluidigm C1, CelSeq, CelSeq2, SmartSeq), and several data modalities as paired scRNA-seq and scATAC-seq. The scAEGAN outperforms Seurat3 in library integration, is more robust against data sparsity, and beats Seurat 4 in integrating paired data from the same cell. Furthermore, in predicting one data modality from another, scAEGAN outperforms Babel. We conclude that scAEGAN surpasses current state-of-the-art methods and unifies integration and prediction challenges.

A Practical Guide for the Efficient Formulation and Calibration of Large, Energy- and Rule-Based Models of Cellular Signal Transduction

Aberrant signal transduction leads to complex diseases such as cancer. To rationally design treatment strategies with small molecule inhibitors, computational models have to be employed. Energy- and rule-based models allow the construction of mechanistic ordinary differential equation models based on structural insights. The detailed, energy-based description often generates large models, which are difficult to calibrate on experimental data. In this chapter, we provide a detailed, interactive protocol for the programmatic formulation and calibration of such large, energy- and rule-based models of cellular signal transduction based on an example model describing the action of RAF inhibitors on MAPK signaling. An interactive version of this chapter is available as Jupyter Notebook at github.com/FFroehlich/energy_modeling_chapter .

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.

Bayesian parameter estimation for dynamical models in systems biology

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent advances in experimental measurements, including sensor development and '-omics' studies that have helped populate protein-protein interaction networks in great detail, modeling in systems biology lacks systematic methods to estimate kinetic parameters and quantify associated uncertainties. This is because of multiple reasons, including sparse and noisy experimental measurements, lack of detailed molecular mechanisms underlying the reactions, and missing biochemical interactions. Additionally, the inherent nonlinearities with respect to the states and parameters associated with the system of differential equations further compound the challenges of parameter estimation. In this study, we propose a comprehensive framework for Bayesian parameter estimation and complete quantification of the effects of uncertainties in the data and models. We apply these methods to a series of signaling models of increasing mathematical complexity. Systematic analysis of these dynamical systems showed that parameter estimation depends on data sparsity, noise level, and model structure, including the existence of multiple steady states. These results highlight how focused uncertainty quantification can enrich systems biology modeling and enable additional quantitative analyses for parameter estimation.

Interpretable machine learning of action potential duration restitution kinetics in single-cell models of atrial cardiomyocytes

Action potential duration (APD) restitution curve and its maximal slope (Smax) reflect single cell-level dynamic instability for inducing chaotic heart rhythms. However, conventional parameter sensitivity analysis often fails to describe nonlinear relationships between ion channel parameters and electrophysiological phenotypes, such as Smax. We explored the parameter-phenotype mapping in a population of 5000 single-cell atrial cell models through interpretable machine learning (ML) approaches. Parameter sensitivity analyses could explain the linear relationships between parameters and electrophysiological phenotypes, including APD₉₀, resting membrane potential, Vmax, refractory period, and APD/calcium alternans threshold, but not for Smax. However, neural network models had better prediction performance for Smax. To interpret the ML model, we evaluated the parameter importance at the global and local levels by computing the permutation feature importance and the local interpretable model-agnostic explanations (LIME) values, respectively. Increases in I_CaL, I_NCX, and I_Kr, and decreases in I_K1, I_b,Cl, I_Kur, I_SERCA, and I_to are correlated with higher Smax values. The LIME algorithm determined that I_NaK plays a significant role in determining Smax as well as I_to and I_Kur. The atrial cardiomyocyte population was hierarchically clustered into three distinct groups based on the LIME values and the single-cell simulation confirmed that perturbations in I_NaK resulted in different behaviors of APD restitution curves in three clusters. Our combined top-down interpretable ML and bottom-up mechanistic simulation approaches uncovered the role of I_NaK in heterogeneous behaviors of Smax in the atrial cardiomyocyte population.

An expanded whole-cell model of E. coli links cellular physiology with mechanisms of growth rate control

Growth and environmental responses are essential for living organisms to survive and adapt to constantly changing environments. In order to simulate new conditions and capture dynamic responses to environmental shifts in a developing whole-cell model of E. coli, we incorporated additional regulation, including dynamics of the global regulator guanosine tetraphosphate (ppGpp), along with dynamics of amino acid biosynthesis and translation. With the model, we show that under perturbed ppGpp conditions, small molecule feedback inhibition pathways, in addition to regulation of expression, play a role in ppGpp regulation of growth. We also found that simulations with dysregulated amino acid synthesis pathways provide average amino acid concentration predictions that are comparable to experimental results but on the single-cell level, concentrations unexpectedly show regular fluctuations. Additionally, during both an upshift and downshift in nutrient availability, the simulated cell responds similarly with a transient increase in the mRNA:rRNA ratio. This additional simulation functionality should support a variety of new applications and expansions of the E. coli Whole-Cell Modeling Project.

The chemical Langevin equation for biochemical systems in dynamic environments

Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly stem from the interplay of the network with many other - and mostly unknown - fluctuating processes, as well as with various random signals arising from the extracellular world; these sources contribute extrinsic noise. Here we provide a computational simulation method to probe the stochastic dynamics of biochemical systems subject to both intrinsic and extrinsic noise. We develop an extrinsic chemical Langevin equation-a physically motivated extension of the chemical Langevin equation- to model intrinsically noisy reaction networks embedded in a stochastically fluctuating environment. The extrinsic CLE is a continuous approximation to the Chemical Master Equation (CME) with time-varying propensities. In our approach, noise is incorporated at the level of the CME, and can account for the full dynamics of the exogenous noise process, irrespective of timescales and their mismatches. We show that our method accurately captures the first two moments of the stationary probability density when compared with exact stochastic simulation methods, while reducing the computational runtime by several orders of magnitude. Our approach provides a method that is practical, computationally efficient and physically accurate to study systems that are simultaneously subject to a variety of noise sources.

Viruses as Living Systems—A Metacybernetic View

The debate over whether viruses are living organisms tends to be paradigmatically determined. The metabolic paradigm denies that they are, while new research evidences the opposite. The purpose of this paper is to deliver a generic model for viral contexts that explains why viruses are alive. It will take a systems biology approach, with a qualitative part (using metacybernetics) to provide deeper explanations of viral contexts, and a quantitative part (using Fisher Information deriving from the variational principle of Extreme Physical Information) which is in principle able to take measurements and predict outcomes. The modelling process provides an extended view of the epigenetic processes of viruses. The generic systems biology model will depict viruses as autonomous entities with metaphysical processes of autopoietic self-organisation and adaptation, enabling them to maintain their physical viability and hence, within their populations, mutate and evolve. The autopoietic epigenetic processes are shown to describe their capability to change, and these are both qualitatively and quantitatively explored, the latter providing an approach to make measurements of physical phenomena under uncertainty. Viruses maintain their fitness when they are able to maintain their stability, and this is indicated by information flow efficacy. A brief case study is presented on the COVID-19 virus from the perspective that it is a living system, and this includes outcome predictions given Fisher Information conditions for known contexts.

Patient-specific Boolean models of signalling networks guide personalised treatments

Prostate cancer is the second most occurring cancer in men worldwide. To better understand the mechanisms of tumorigenesis and possible treatment responses, we developed a mathematical model of prostate cancer which considers the major signalling pathways known to be deregulated. We personalised this Boolean model to molecular data to reflect the heterogeneity and specific response to perturbations of cancer patients. A total of 488 prostate samples were used to build patient-specific models and compared to available clinical data. Additionally, eight prostate cell line-specific models were built to validate our approach with dose-response data of several drugs. The effects of single and combined drugs were tested in these models under different growth conditions. We identified 15 actionable points of interventions in one cell line-specific model whose inactivation hinders tumorigenesis. To validate these results, we tested nine small molecule inhibitors of five of those putative targets and found a dose-dependent effect on four of them, notably those targeting HSP90 and PI3K. These results highlight the predictive power of our personalised Boolean models and illustrate how they can be used for precision oncology.

Validation Through Collaboration: Encouraging Team Efforts to Ensure Internal and External Validity of Computational Models of Biochemical Pathways

Computational modelling of biochemical reaction pathways is an increasingly important part of neuroscience research. In order to be useful, computational models need to be valid in two senses: First, they need to be consistent with experimental data and able to make testable predictions (external validity). Second, they need to be internally consistent and independently reproducible (internal validity). Here, we discuss both types of validity and provide a brief overview of tools and technologies used to ensure they are met. We also suggest the introduction of new collaborative technologies to ensure model validity: an incentivised experimental database for external validity and reproducibility audits for internal validity. Both rely on FAIR principles and on collaborative science practices.

The E. coli Whole-Cell Modeling Project

The Escherichia coli whole-cell modeling project seeks to create the most detailed computational model of an E. coli cell in order to better understand and predict the behavior of this model organism. Details about the approach, framework, and current version of the model are discussed. Currently, the model includes the functions of 43% of characterized genes, with ongoing efforts to include additional data and mechanisms. As additional information is incorporated in the model, its utility and predictive power will continue to increase, which means that discovery efforts can be accelerated by community involvement in the generation and inclusion of data. This project will be an invaluable resource to the E. coli community that could be used to verify expected physiological behavior, to predict new outcomes and testable hypotheses for more efficient experimental design iterations, and to evaluate heterogeneous data sets in the context of each other through deep curation.

Modular assembly of dynamic models in systems biology

It is widely acknowledged that the construction of large-scale dynamic models in systems biology requires complex modelling problems to be broken up into more manageable pieces. To this end, both modelling and software frameworks are required to enable modular modelling. While there has been consistent progress in the development of software tools to enhance model reusability, there has been a relative lack of consideration for how underlying biophysical principles can be applied to this space. Bond graphs combine the aspects of both modularity and physics-based modelling. In this paper, we argue that bond graphs are compatible with recent developments in modularity and abstraction in systems biology, and are thus a desirable framework for constructing large-scale models. We use two examples to illustrate the utility of bond graphs in this context: a model of a mitogen-activated protein kinase (MAPK) cascade to illustrate the reusability of modules and a model of glycolysis to illustrate the ability to modify the model granularity.

Data Management and Modeling in Plant Biology

The study of plant-environment interactions is a multidisciplinary research field. With the emergence of quantitative large-scale and high-throughput techniques, amount and dimensionality of experimental data have strongly increased. Appropriate strategies for data storage, management, and evaluation are needed to make efficient use of experimental findings. Computational approaches of data mining are essential for deriving statistical trends and signatures contained in data matrices. Although, current biology is challenged by high data dimensionality in general, this is particularly true for plant biology. Plants as sessile organisms have to cope with environmental fluctuations. This typically results in strong dynamics of metabolite and protein concentrations which are often challenging to quantify. Summarizing experimental output results in complex data arrays, which need computational statistics and numerical methods for building quantitative models. Experimental findings need to be combined by computational models to gain a mechanistic understanding of plant metabolism. For this, bioinformatics and mathematics need to be combined with experimental setups in physiology, biochemistry, and molecular biology. This review presents and discusses concepts at the interface of experiment and computation, which are likely to shape current and future plant biology. Finally, this interface is discussed with regard to its capabilities and limitations to develop a quantitative model of plant-environment interactions.

Inferring kinetic parameters of oscillatory gene regulation from single cell time-series data

Gene expression dynamics, such as stochastic oscillations and aperiodic fluctuations, have been associated with cell fate changes in multiple contexts, including development and cancer. Single cell live imaging of protein expression with endogenous reporters is widely used to observe such gene expression dynamics. However, the experimental investigation of regulatory mechanisms underlying the observed dynamics is challenging, since these mechanisms include complex interactions of multiple processes, including transcription, translation and protein degradation. Here, we present a Bayesian method to infer kinetic parameters of oscillatory gene expression regulation using an auto-negative feedback motif with delay. Specifically, we use a delay-adapted nonlinear Kalman filter within a Metropolis-adjusted Langevin algorithm to identify posterior probability distributions. Our method can be applied to time-series data on gene expression from single cells and is able to infer multiple parameters simultaneously. We apply it to published data on murine neural progenitor cells and show that it outperforms alternative methods. We further analyse how parameter uncertainty depends on the duration and time resolution of an imaging experiment, to make experimental design recommendations. This work demonstrates the utility of parameter inference on time course data from single cells and enables new studies on cell fate changes and population heterogeneity.

A forecast for large-scale, predictive biology: Lessons from meteorology

Quantitative systems biology, in which predictive mathematical models are constructed to guide the design of experiments and predict experimental outcomes, is at an exciting transition point, where the foundational scientific principles are becoming established, but the impact is not yet global. The next steps necessary for mathematical modeling to transform biological research and applications, in the same way it has already transformed other fields, is not completely clear. The purpose of this perspective is to forecast possible answers to this question-what needs to happen next-by drawing on the experience gained in another field, specifically meteorology. We review here a number of lessons learned in weather prediction that are directly relevant to biological systems modeling, and that we believe can enable the same kinds of global impact in our field as atmospheric modeling makes today.

Forecasting cellular states: from descriptive to predictive biology via single-cell multiomics

As the single cell field races to characterize each cell type, state, and behavior, the complexity of the computational analysis approaches the complexity of the biological systems. Single cell and imaging technologies now enable unprecedented measurements of state transitions in biological systems, providing high-throughput data that capture tens-of-thousands of measurements on hundreds-of-thousands of samples. Thus, the definition of cell type and state is evolving to encompass the broad range of biological questions now attainable. To answer these questions requires the development of computational tools for integrated multi-omics analysis. Merged with mathematical models, these algorithms will be able to forecast future states of biological systems, going from statistical inferences of phenotypes to time course predictions of the biological systems with dynamic maps analogous to weather systems. Thus, systems biology for forecasting biological system dynamics from multi-omic data represents the future of cell biology empowering a new generation of technology-driven predictive medicine.

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.

CLUE: Exact maximal reduction of kinetic models by constrained lumping of differential equations

MOTIVATION

Detailed mechanistic models of biological processes can pose significant challenges for analysis and parameter estimations due to the large number of equations used to track the dynamics of all distinct configurations in which each involved biochemical species can be found. Model reduction can help tame such complexity by providing a lower-dimensional model in which each macro-variable can be directly related to the original variables.

RESULTS

We present CLUE, an algorithm for exact model reduction of systems of polynomial differential equations by constrained linear lumping. It computes the smallest dimensional reduction as a linear mapping of the state space such that the reduced model preserves the dynamics of user-specified linear combinations of the original variables. Even though CLUE works with nonlinear differential equations, it is based on linear algebra tools, which makes it applicable to high-dimensional models. Using case studies from the literature, we show how CLUE can substantially lower model dimensionality and help extract biologically intelligible insights from the reduction.

AVAILABILITY

An implementation of the algorithm and relevant resources to replicate the experiments herein reported are freely available for download at https://github.com/pogudingleb/CLUE.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

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.

Computer-Aided Whole-Cell Design: Taking a Holistic Approach by Integrating Synthetic With Systems Biology

Computer-aided design (CAD) for synthetic biology promises to accelerate the rational and robust engineering of biological systems. It requires both detailed and quantitative mathematical and experimental models of the processes to (re)design biology, and software and tools for genetic engineering and DNA assembly. Ultimately, the increased precision in the design phase will have a dramatic impact on the production of designer cells and organisms with bespoke functions and increased modularity. CAD strategies require quantitative models of cells that can capture multiscale processes and link genotypes to phenotypes. Here, we present a perspective on how whole-cell, multiscale models could transform design-build-test-learn cycles in synthetic biology. We show how these models could significantly aid in the design and learn phases while reducing experimental testing by presenting case studies spanning from genome minimization to cell-free systems. We also discuss several challenges for the realization of our vision. The possibility to describe and build whole-cells in silico offers an opportunity to develop increasingly automatized, precise and accessible CAD tools and strategies.

Understanding hormonal crosstalk in Arabidopsis root development via emulation and history matching

A major challenge in plant developmental biology is to understand how plant growth is coordinated by interacting hormones and genes. To meet this challenge, it is important to not only use experimental data, but also formulate a mathematical model. For the mathematical model to best describe the true biological system, it is necessary to understand the parameter space of the model, along with the links between the model, the parameter space and experimental observations. We develop sequential history matching methodology, using Bayesian emulation, to gain substantial insight into biological model parameter spaces. This is achieved by finding sets of acceptable parameters in accordance with successive sets of physical observations. These methods are then applied to a complex hormonal crosstalk model for Arabidopsis root growth. In this application, we demonstrate how an initial set of 22 observed trends reduce the volume of the set of acceptable inputs to a proportion of 6.1 × 10-7 of the original space. Additional sets of biologically relevant experimental data, each of size 5, reduce the size of this space by a further three and two orders of magnitude respectively. Hence, we provide insight into the constraints placed upon the model structure by, and the biological consequences of, measuring subsets of observations.

Inference of Multisite Phosphorylation Rate Constants and Their Modulation by Pathogenic Mutations

Multisite protein phosphorylation plays a critical role in cell regulation [1-3]. It is widely appreciated that the functional capabilities of multisite phosphorylation depend on the order and kinetics of phosphorylation steps, but kinetic aspects of multisite phosphorylation remain poorly understood [4-6]. Here, we focus on what appears to be the simplest scenario, when a protein is phosphorylated on only two sites in a strict, well-defined order. This scenario describes the activation of ERK, a highly conserved cell-signaling enzyme. We use Bayesian parameter inference in a structurally identifiable kinetic model to dissect dual phosphorylation of ERK by MEK, a kinase that is mutated in a large number of human diseases [7-12]. Our results reveal how enzyme processivity and efficiencies of individual phosphorylation steps are altered by pathogenic mutations. The presented approach, which connects specific mutations to kinetic parameters of multisite phosphorylation mechanisms, provides a systematic framework for closing the gap between studies with purified enzymes and their effects in the living organism.

Towards computer-aided design of cellular structure

Cells are complex machines with tremendous potential for applications in medicine and biotechnology. Although much effort has been devoted to engineering the metabolic, genetic, and signaling pathways of cells, methods for systematically engineering the physical structure of cells are less developed. Here we consider how coarse-grained models for cellular geometry at the organelle level can be used to build computer-aided design (CAD) tools for cellular structure.

Benchmarking optimization methods for parameter estimation in large kinetic models

Motivation

Kinetic models contain unknown parameters that are estimated by optimizing the fit to experimental data. This task can be computationally challenging due to the presence of local optima and ill-conditioning. While a variety of optimization methods have been suggested to surmount these issues, it is difficult to choose the best one for a given problem a priori. A systematic comparison of parameter estimation methods for problems with tens to hundreds of optimization variables is currently missing, and smaller studies provided contradictory findings.

Results

We use a collection of benchmarks to evaluate the performance of two families of optimization methods: (i) multi-starts of deterministic local searches and (ii) stochastic global optimization metaheuristics; the latter may be combined with deterministic local searches, leading to hybrid methods. A fair comparison is ensured through a collaborative evaluation and a consideration of multiple performance metrics. We discuss possible evaluation criteria to assess the trade-off between computational efficiency and robustness. Our results show that, thanks to recent advances in the calculation of parametric sensitivities, a multi-start of gradient-based local methods is often a successful strategy, but a better performance can be obtained with a hybrid metaheuristic. The best performer combines a global scatter search metaheuristic with an interior point local method, provided with gradients estimated with adjoint-based sensitivities. We provide an implementation of this method to render it available to the scientific community.

Availability and implementation

The code to reproduce the results is provided as Supplementary Material and is available at Zenodo https://doi.org/10.5281/zenodo.1304034.

Supplementary information

Supplementary data are available at Bioinformatics online.

Bayesian, Likelihood-Free Modelling of Phenotypic Plasticity and Variability in Individuals and Populations

There is a paradigm shift from the traditional focus on the “average” individual towards the definition and analysis of trait variation within individual life-history and among individuals in populations. This is a result of increasing availability of individual phenotypic data. The shift allows the use of genetic and environment-driven variations to assess robustness to challenge, gain greater understanding of organismal biological processes, or deliver individual-targeted treatments or genetic selection. These consequences apply, in particular, to variation in ontogenetic growth. We propose an approach to parameterise mathematical models of individual traits (e.g., reaction norms, growth curves) that address two challenges: 1) Estimation of individual traits while making minimal assumptions about data distribution and correlation, addressed via Approximate Bayesian Computation (a form of nonparametric inference). We are motivated by the fact that available information on distribution of biological data is often less precise than assumed by conventional likelihood functions. 2) Scaling-up to population phenotype distributions while facilitating unbiased use of individual data; this is addressed via a probabilistic framework where population distributions build on separately-inferred individual distributions and individual-trait interpretability is preserved. The approach is tested against Bayesian likelihood-based inference, by fitting weight and energy intake growth models to animal data and normal- and skewed-distributed simulated data. i) Individual inferences were accurate and robust to changes in data distribution and sample size; in particular, median-based predictions were more robust than maximum- likelihood-based curves. These results suggest that the approach gives reliable inferences using few observations and monitoring resources. ii) At the population level, each individual contributed via a specific data distribution, and population phenotype estimates were not disproportionally influenced by outlier individuals. Indices measuring population phenotype variation can be derived for study comparisons. The approach offers an alternative for estimating trait variability in biological systems that may be reliable for various applications, for example, in genetics, health, and individualised nutrition, while using fewer assumptions and fewer empirical observations. In livestock breeding, the potentially greater accuracy of trait estimation (without specification of multitrait variance-covariance parameters) could lead to improved selection and to more decisive estimates of trait heritability.

Network modeling of single-cell omics data: challenges, opportunities, and progresses

Single-cell multi-omics technologies are rapidly evolving, prompting both methodological advances and biological discoveries at an unprecedented speed. Gene regulatory network modeling has been used as a powerful approach to elucidate the complex molecular interactions underlying biological processes and systems, yet its application in single-cell omics data modeling has been met with unique challenges and opportunities. In this review, we discuss these challenges and opportunities, and offer an overview of the recent development of network modeling approaches designed to capture dynamic networks, within-cell networks, and cell-cell interaction or communication networks. Finally, we outline the remaining gaps in single-cell gene network modeling and the outlooks of the field moving forward.

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.

Human Systems Biology and Metabolic Modelling: A Review-From Disease Metabolism to Precision Medicine

In cell and molecular biology, metabolism is the only system that can be fully simulated at genome scale. Metabolic systems biology offers powerful abstraction tools to simulate all known metabolic reactions in a cell, therefore providing a snapshot that is close to its observable phenotype. In this review, we cover the 15 years of human metabolic modelling. We show that, although the past five years have not experienced large improvements in the size of the gene and metabolite sets in human metabolic models, their accuracy is rapidly increasing. We also describe how condition-, tissue-, and patient-specific metabolic models shed light on cell-specific changes occurring in the metabolic network, therefore predicting biomarkers of disease metabolism. We finally discuss current challenges and future promising directions for this research field, including machine/deep learning and precision medicine. In the omics era, profiling patients and biological processes from a multiomic point of view is becoming more common and less expensive. Starting from multiomic data collected from patients and N-of-1 trials where individual patients constitute different case studies, methods for model-building and data integration are being used to generate patient-specific models. Coupled with state-of-the-art machine learning methods, this will allow characterizing each patient's disease phenotype and delivering precision medicine solutions, therefore leading to preventative medicine, reduced treatment, and in silico clinical trials.

Ensemble optimization of microbial conversion of glycerol into 1, 3-propanediol by Klebsiella pneumoniae

Using mathematical model and computer simulation to predict biological processes and optimize the target production is an important strategy for optimizing fermentation process. However, the inherent uncertainty of the kinetic model severely limits the predictive capability. In this study, optimize target production, such as productivity and yield of 1, 3-propanediol produced by Klebsiella pneumoniae using glycerol as substrate, the ensemble modeling approach was used to reduce the model's uncertainty for fermentation process as much as possible, and effectively improve its prediction performance. Firstly, through sensitivity analysis, the parameters having significant influence on the model were determined as the adjustable parameters for the ensemble modeling. After comparison, the appropriate threshold coefficient of the model error was determined, and the sampling method was used to generate as many equivalent parameter sets as possible. Each set of parameters was separately applied for the simulation, and all the predicted values were integrated for the weighted average. Therefore, the expected value of the prediction was obtained. Compared with the traditional simulation using single parameter set, the ensemble modeling method achieved the lower relative error between the prediction and the experimental value and the greatly improved model prediction performance. Moreover, the optimal productivity and yield of 1, 3-propanediol and the corresponding operating conditions were obtained, respectively. The ensemble modeling approach effectively compensates for the uncertainties of the model, making its prediction performance more practical, which is important for computer simulations to predict and guide the actual production process.

Defining informative priors for ensemble modeling in systems biology

Ensemble modeling in molecular systems biology requires the reproducible translation of kinetic parameter data into informative probability distributions (priors), as well as approaches that sample parameters from these distributions without violating the thermodynamic consistency of the overall model. Although a number of pioneering frameworks for ensemble modeling have been published, the issue of generating informative priors has not yet been addressed. Here, we present a protocol that aims to fill this gap. This protocol discusses the collection of parameter values from a diverse range of sources (literature, databases and experiments), assessment of their plausibility, and creation of log-normal probability distributions that can be used as informative priors in ensemble modeling. Furthermore, the protocol enables sampling from the generated distributions while maintaining thermodynamic consistency. Once all parameter values have been retrieved from literature and databases, the protocol can be implemented within ~5-10 min per parameter. The aim of this protocol is to facilitate the design and use of informative distributions for ensemble modeling, especially in fields such as synthetic biology and systems medicine.

Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes

Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about the behavior of latent variables or the process under new experimental conditions. Complementarily, inference of model structure can be used to identify the most plausible model structure from a set of candidates, and, thus, gain novel biological insight. Several toolboxes can infer model parameters and structure for small- to medium-scale mechanistic models out of the box. However, models for highly multiplexed datasets can require hundreds to thousands of state variables and parameters. For the analysis of such large-scale models, most algorithms require intractably high computation times. This chapter provides an overview of the state-of-the-art methods for parameter and model inference, with an emphasis on scalability.

Integrating -omics data into genome-scale metabolic network models: principles and challenges

At genome scale, it is not yet possible to devise detailed kinetic models for metabolism because data on the in vivo biochemistry are too sparse. Predictive large-scale models for metabolism most commonly use the constraint-based framework, in which network structures constrain possible metabolic phenotypes at steady state. However, these models commonly leave many possibilities open, making them less predictive than desired. With increasingly available -omics data, it is appealing to increase the predictive power of constraint-based models (CBMs) through data integration. Many corresponding methods have been developed, but data integration is still a challenge and existing methods perform less well than expected. Here, we review main approaches for the integration of different types of -omics data into CBMs focussing on the methods' assumptions and limitations. We argue that key assumptions - often derived from single-enzyme kinetics - do not generally apply in the context of networks, thereby explaining current limitations. Emerging methods bridging CBMs and biochemical kinetics may allow for -omics data integration in a common framework to provide more accurate predictions.

A thermodynamic framework for modelling membrane transporters

Membrane transporters contribute to the regulation of the internal environment of cells by translocating substrates across cell membranes. Like all physical systems, the behaviour of membrane transporters is constrained by the laws of thermodynamics. However, many mathematical models of transporters, especially those incorporated into whole-cell models, are not thermodynamically consistent, leading to unrealistic behaviour. In this paper we use a physics-based modelling framework, in which the transfer of energy is explicitly accounted for, to develop thermodynamically consistent models of transporters. We then apply this methodology to model two specific transporters: the cardiac sarcoplasmic/endoplasmic Ca²⁺ ATPase (SERCA) and the cardiac Na⁺/K⁺ ATPase.

Uncertainpy: A Python Toolbox for Uncertainty Quantification and Sensitivity Analysis in Computational Neuroscience

Computational models in neuroscience typically contain many parameters that are poorly constrained by experimental data. Uncertainty quantification and sensitivity analysis provide rigorous procedures to quantify how the model output depends on this parameter uncertainty. Unfortunately, the application of such methods is not yet standard within the field of neuroscience. Here we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it quick and easy to get started with uncertainty analysis, without any need for detailed prior knowledge. The toolbox allows uncertainty quantification and sensitivity analysis to be performed on already existing models without needing to modify the model equations or model implementation. Uncertainpy bases its analysis on polynomial chaos expansions, which are more efficient than the more standard Monte-Carlo based approaches. Uncertainpy is tailored for neuroscience applications by its built-in capability for calculating characteristic features in the model output. The toolbox does not merely perform a point-to-point comparison of the "raw" model output (e.g., membrane voltage traces), but can also calculate the uncertainty and sensitivity of salient model response features such as spike timing, action potential width, average interspike interval, and other features relevant for various neural and neural network models. Uncertainpy comes with several common models and features built in, and including custom models and new features is easy. The aim of the current paper is to present Uncertainpy to the neuroscience community in a user-oriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis of three case studies relevant for neuroscience: the original Hodgkin-Huxley point-neuron model for action potential generation, a multi-compartmental model of a thalamic interneuron implemented in the NEURON simulator, and a sparsely connected recurrent network model implemented in the NEST simulator.

Bond graph modelling of the cardiac action potential: implications for drift and non-unique steady states

Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with respect to charge conservation in specific models. Here, we propose a general and systematic method of identifying conservation laws hidden in models of cardiac electrophysiology by using bond graphs, and develop a bond graph model of the cardiac action potential to study long-term behaviour. Bond graphs provide an explicit energy-based framework for modelling physical systems, which makes them well suited for examining conservation within electrophysiological models. We find that the charge conservation laws derived in previous studies are examples of the more general concept of a 'conserved moiety'. Conserved moieties explain model drift and non-unique steady states, generalizing the results from previous studies. The bond graph approach provides a rigorous method to check for drift and non-unique steady states in a wide range of cardiac action potential models, and can be extended to examine behaviours of other excitable systems.

Delay models for the early embryonic cell cycle oscillator

Time delays are known to play a crucial role in generating biological oscillations. The early embryonic cell cycle in the frog Xenopus laevis is one such example. Although various mathematical models of this oscillating system exist, it is not clear how to best model the required time delay. Here, we study a simple cell cycle model that produces oscillations due to the presence of an ultrasensitive, time-delayed negative feedback loop. We implement the time delay in three qualitatively different ways, using a fixed time delay, a distribution of time delays, and a delay that is state-dependent. We analyze the dynamics in all cases, and we use experimental observations to interpret our results and put constraints on unknown parameters. In doing so, we find that different implementations of the time delay can have a large impact on the resulting oscillations.

Opportunities and Challenges in Building a Spatiotemporal Multi-scale Model of the Human Pancreatic β Cell

The construction of a predictive model of an entire eukaryotic cell that describes its dynamic structure from atomic to cellular scales is a grand challenge at the intersection of biology, chemistry, physics, and computer science. Having such a model will open new dimensions in biological research and accelerate healthcare advancements. Developing the necessary experimental and modeling methods presents abundant opportunities for a community effort to realize this goal. Here, we present a vision for creation of a spatiotemporal multi-scale model of the pancreatic β-cell, a relevant target for understanding and modulating the pathogenesis of diabetes.