From qualitative data to quantitative models: analysis of the phage shock protein stress response in Escherichia coli

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.

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.

Universal structural requirements for maximal robust perfect adaptation in biomolecular networks

Adaptation is a running theme in biology. It allows a living system to survive and thrive in the face of unpredictable environments by maintaining key physiological variables at their desired levels through tight regulation. When one such variable is maintained at a certain value at the steady state despite perturbations to a single input, this property is called robust perfect adaptation (RPA). Here we address and solve the fundamental problem of maximal RPA (maxRPA), whereby, for a designated output variable, RPA is achieved with respect to perturbations in virtually all network parameters. In particular, we show that the maxRPA property imposes certain structural constraints on the network. We then prove that these constraints are fully characterized by simple linear algebraic stoichiometric conditions which differ between deterministic and stochastic descriptions of the dynamics. We use our results to derive a new internal model principle (IMP) for biomolecular maxRPA networks, akin to the celebrated IMP in control theory. We exemplify our results through several known biological examples of robustly adapting networks and construct examples of such networks with the aid of our linear algebraic characterization. Our results reveal the universal requirements for maxRPA in all biological systems, and establish a foundation for studying adaptation in general biomolecular networks, with important implications for both systems and synthetic biology.

The design principles of discrete turing patterning systems

The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the question of how they may be adopted and realised in naturally evolved systems. The vast majority of mathematical studies of Turing patterns have used continuous models specified in terms of partial differential equations. Here, we complement this work by studying Turing patterns using discrete cellular automata models. We perform a large-scale study on all possible two-species networks and find the same Turing pattern producing networks as in the continuous framework. In contrast to continuous models, however, we find these Turing pattern topologies to be substantially more robust to changes in the parameters of the model. We also find that diffusion-driven instabilities are substantially weaker predictors for Turing patterns in our discrete modelling framework in comparison to the continuous case, in the sense that the presence of an instability does not guarantee a pattern emerging in simulations. We show that a more refined criterion constitutes a stronger predictor. The similarity of the results for the two modelling frameworks suggests a deeper underlying principle of Turing mechanisms in nature. Together with the larger robustness in the discrete case this suggests that Turing patterns may be more robust than previously thought.

Efficient gradient-based parameter estimation for dynamic models using qualitative data

MOTIVATION

Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence.

RESULTS

Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data.

AVAILABILITY AND IMPLEMENTATION

The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Model comparison via simplicial complexes and persistent homology

In many scientific and technological contexts, we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal statistical model selection to compare and contrast the ability of different mathematical models to describe such data. There is, however, a lack of rigorous methods to compare different models a priori. Here, we develop and illustrate two such approaches that allow us to compare model structures in a systematic way by representing models as simplicial complexes. Using well-developed concepts from simplicial algebraic topology, we define a distance between models based on their simplicial representations. Employing persistent homology with a flat filtration provides for alternative representations of the models as persistence intervals, which represent model structure, from which the model distances are also obtained. We then expand on this measure of model distance to study the concept of model equivalence to determine the conceptual similarity of models. We apply our methodology for model comparison to demonstrate an equivalence between a positional-information model and a Turing-pattern model from developmental biology, constituting a novel observation for two classes of models that were previously regarded as unrelated.

Efficient gradient-based parameter estimation for dynamic models using qualitative data

Motivation

Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence.

Results

Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data.

Availability and implementation

The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

Supplementary information

Supplementary data are available at Bioinformatics online.

Between roost contact is essential for maintenance of European bat lyssavirus type-2 in Myotis daubentonii bat reservoir: 'The Swarming Hypothesis'

Many high-consequence human and animal pathogens persist in wildlife reservoirs. An understanding of the dynamics of these pathogens in their reservoir hosts is crucial to inform the risk of spill-over events, yet our understanding of these dynamics is frequently insufficient. Viral persistence in a wild bat population was investigated by combining empirical data and in-silico analyses to test hypotheses on mechanisms for viral persistence. A fatal zoonotic virus, European Bat lyssavirus type 2 (EBLV-2), in Daubenton’s bats (Myotis daubentonii) was used as a model system. A total of 1839 M. daubentonii were sampled for evidence of virus exposure and excretion during a prospective nine year serial cross-sectional survey. Multivariable statistical models demonstrated age-related differences in seroprevalence, with significant variation in seropositivity over time and among roosts. An Approximate Bayesian Computation approach was used to model the infection dynamics incorporating the known host ecology. The results demonstrate that EBLV-2 is endemic in the study population, and suggest that mixing between roosts during seasonal swarming events is necessary to maintain EBLV-2 in the population. These findings contribute to understanding how bat viruses can persist despite low prevalence of infection, and why infection is constrained to certain bat species in multispecies roosts and ecosystems.

Contribution of YthA, a PspC Family Transcriptional Regulator of Lactococcus lactis F44 Acid Tolerance and Nisin Yield: a Transcriptomic Approach

To overcome the adverse impacts of environmental stresses during growth, different adaptive regulation mechanisms can be activated in Lactococcus lactis In this study, the transcription levels of eight transcriptional regulators of L. lactis subsp. lactis F44 under acid stress were analyzed using quantitative reverse transcription-PCR. Eight gene-overexpressing strains were then constructed to examine their influences on acid-resistant capability. Overexpressing ythA, a PspC family transcriptional regulator, increased the survival rate by 3.2-fold compared to the control at the lethal pH 3.0 acid shock. Moreover, the nisin yield was increased by 45.50%. The ythA-overexpressing strain FythA appeared to have higher intracellular pH stability and nisin-resistant ability. Subsequently, transcriptome analysis revealed that the vast majority of genes associated with amino acid biosynthesis, including arginine, serine, phenylalanine, and tyrosine, were predominantly upregulated in FythA. Arginine biosynthesis (argG and argH), arginine deiminase pathway, and polar amino acid transport (ysfE and ysfF) were proposed to be the main regulation mechanisms of YthA. Furthermore, the transcription of genes associated with pyrimidine and exopolysaccharide biosynthesis were upregulated. The transcriptional levels of nisIPRKFEG genes were substantially higher in FythA, which directly contributed to the yield and resistance of nisin. Three potential DNA-binding sequences were predicted by computer analysis using the upstream regions of genes with prominent changes. This study showed that YthA could increase acid resistance and nisin yield and revealed a putative regulation mechanism of YthA.IMPORTANCE Nisin, produced by Lactococcus lactis subsp. lactis, is widely used as a safe food preservative. Acid stress becomes the primary restrictive factor of cell growth and nisin yield. In this research, we found that the transcriptional regulator YthA was conducive to enhancing the acid resistance of L. lactis F44. Overexpressing ythA could significantly improve the survival rate and nisin yield. The stability of intracellular pH and nisin resistance were also increased. Transcriptome analysis showed that nisin immunity and the biosynthesis of some amino acids, pyrimidine, and exopolysaccharides were enhanced in the engineered strain. This study elucidates the regulation mechanism of YthA and provides a novel strategy for constructing robust industrial L. lactis strains.

Contribution of YthA, a PspC Family Transcriptional Regulator of Lactococcus lactis F44 Acid Tolerance and Nisin Yield: a Transcriptomic Approach

To overcome the adverse impacts of environmental stresses during growth, different adaptive regulation mechanisms can be activated in Lactococcus lactis In this study, the transcription levels of eight transcriptional regulators of L. lactis subsp. lactis F44 under acid stress were analyzed using quantitative reverse transcription-PCR. Eight gene-overexpressing strains were then constructed to examine their influences on acid-resistant capability. Overexpressing ythA, a PspC family transcriptional regulator, increased the survival rate by 3.2-fold compared to the control at the lethal pH 3.0 acid shock. Moreover, the nisin yield was increased by 45.50%. The ythA-overexpressing strain FythA appeared to have higher intracellular pH stability and nisin-resistant ability. Subsequently, transcriptome analysis revealed that the vast majority of genes associated with amino acid biosynthesis, including arginine, serine, phenylalanine, and tyrosine, were predominantly upregulated in FythA. Arginine biosynthesis (argG and argH), arginine deiminase pathway, and polar amino acid transport (ysfE and ysfF) were proposed to be the main regulation mechanisms of YthA. Furthermore, the transcription of genes associated with pyrimidine and exopolysaccharide biosynthesis were upregulated. The transcriptional levels of nisIPRKFEG genes were substantially higher in FythA, which directly contributed to the yield and resistance of nisin. Three potential DNA-binding sequences were predicted by computer analysis using the upstream regions of genes with prominent changes. This study showed that YthA could increase acid resistance and nisin yield and revealed a putative regulation mechanism of YthA.IMPORTANCE Nisin, produced by Lactococcus lactis subsp. lactis, is widely used as a safe food preservative. Acid stress becomes the primary restrictive factor of cell growth and nisin yield. In this research, we found that the transcriptional regulator YthA was conducive to enhancing the acid resistance of L. lactis F44. Overexpressing ythA could significantly improve the survival rate and nisin yield. The stability of intracellular pH and nisin resistance were also increased. Transcriptome analysis showed that nisin immunity and the biosynthesis of some amino acids, pyrimidine, and exopolysaccharides were enhanced in the engineered strain. This study elucidates the regulation mechanism of YthA and provides a novel strategy for constructing robust industrial L. lactis strains.

Parameter estimation for dynamical systems with discrete events and logical operations

Motivation

Ordinary differential equation (ODE) models are frequently used to describe the dynamic behaviour of biochemical processes. Such ODE models are often extended by events to describe the effect of fast latent processes on the process dynamics. To exploit the predictive power of ODE models, their parameters have to be inferred from experimental data. For models without events, gradient based optimization schemes perform well for parameter estimation, when sensitivity equations are used for gradient computation. Yet, sensitivity equations for models with parameter- and state-dependent events and event-triggered observations are not supported by existing toolboxes.

Results

In this manuscript, we describe the sensitivity equations for differential equation models with events and demonstrate how to estimate parameters from event-resolved data using event-triggered observations in parameter estimation. We consider a model for GFP expression after transfection and a model for spiking neurons and demonstrate that we can improve computational efficiency and robustness of parameter estimation by using sensitivity equations for systems with events. Moreover, we demonstrate that, by using event-outputs, it is possible to consider event-resolved data, such as time-to-event data, for parameter estimation with ODE models. By providing a user-friendly, modular implementation in the toolbox AMICI, the developed methods are made publicly available and can be integrated in other systems biology toolboxes.

Availability and Implementation

We implement the methods in the open-source toolbox Advanced MATLAB Interface for CVODES and IDAS (AMICI, https://github.com/ICB-DCM/AMICI ).

Contact

jan.hasenauer@helmholtz-muenchen.de.

Supplementary information

Supplementary data are available at Bioinformatics online.

Parallelization and High-Performance Computing Enables Automated Statistical Inference of Multi-scale Models

Mechanistic understanding of multi-scale biological processes, such as cell proliferation in a changing biological tissue, is readily facilitated by computational models. While tools exist to construct and simulate multi-scale models, the statistical inference of the unknown model parameters remains an open problem. Here, we present and benchmark a parallel approximate Bayesian computation sequential Monte Carlo (pABC SMC) algorithm, tailored for high-performance computing clusters. pABC SMC is fully automated and returns reliable parameter estimates and confidence intervals. By running the pABC SMC algorithm for ∼10⁶ hr, we parameterize multi-scale models that accurately describe quantitative growth curves and histological data obtained in vivo from individual tumor spheroid growth in media droplets. The models capture the hybrid deterministic-stochastic behaviors of 10⁵-10⁶ of cells growing in a 3D dynamically changing nutrient environment. The pABC SMC algorithm reliably converges to a consistent set of parameters. Our study demonstrates a proof of principle for robust, data-driven modeling of multi-scale biological systems and the feasibility of multi-scale model parameterization through statistical inference.

Anionic lipids and the cytoskeletal proteins MreB and RodZ define the spatio-temporal distribution and function of membrane stress controller PspA in Escherichia coli

All cell types must maintain the integrity of their membranes. The conserved bacterial membrane-associated protein PspA is a major effector acting upon extracytoplasmic stress and is implicated in protection of the inner membrane of pathogens, formation of biofilms and multi-drug-resistant persister cells. PspA and its homologues in Gram-positive bacteria and archaea protect the cell envelope whilst also supporting thylakoid biogenesis in cyanobacteria and higher plants. In enterobacteria, PspA is a dual function protein negatively regulating the Psp system in the absence of stress and acting as an effector of membrane integrity upon stress. We show that in Escherichia coli the low-order oligomeric PspA regulatory complex associates with cardiolipin-rich, curved polar inner membrane regions. There, cardiolipin and the flotillin 1 homologue YqiK support the PspBC sensors in transducing a membrane stress signal to the PspA-PspF inhibitory complex. After stress perception, PspA high-order oligomeric effector complexes initially assemble in polar membrane regions. Subsequently, the discrete spatial distribution and dynamics of PspA effector(s) in lateral membrane regions depend on the actin homologue MreB and the peptidoglycan machinery protein RodZ. The consequences of loss of cytoplasmic membrane anionic lipids, MreB, RodZ and/or YqiK suggest that the mode of action of the PspA effector is closely associated with cell envelope organization.

Structure and assembly of filamentous bacteriophages

Filamentous bacteriophages are interesting paradigms in structural molecular biology, in part because of the unusual mechanism of filamentous phage assembly. During assembly, several thousand copies of an intracellular DNA-binding protein bind to each copy of the replicating phage DNA, and are then displaced by membrane-spanning phage coat proteins as the nascent phage is extruded through the bacterial plasma membrane. This complicated process takes place without killing the host bacterium. The bacteriophage is a semi-flexible worm-like nucleoprotein filament. The virion comprises a tube of several thousand identical major coat protein subunits around a core of single-stranded circular DNA. Each protein subunit is a polymer of about 50 amino-acid residues, largely arranged in an α-helix. The subunits assemble into a helical sheath, with each subunit oriented at a small angle to the virion axis and interdigitated with neighbouring subunits. A few copies of "minor" phage proteins necessary for infection and/or extrusion of the virion are located at each end of the completed virion. Here we review both the structure of the virion and aspects of its function, such as the way the virion enters the host, multiplies, and exits to prey on further hosts. In particular we focus on our understanding of the way the components of the virion come together during assembly at the membrane. We try to follow a basic rule of empirical science, that one should chose the simplest theoretical explanation for experiments, but be prepared to modify or even abandon this explanation as new experiments add more detail.

A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation

As modeling becomes a more widespread practice in the life sciences and biomedical sciences, researchers need reliable tools to calibrate models against ever more complex and detailed data. Here we present an approximate Bayesian computation (ABC) framework and software environment, ABC-SysBio, which is a Python package that runs on Linux and Mac OS X systems and that enables parameter estimation and model selection in the Bayesian formalism by using sequential Monte Carlo (SMC) approaches. We outline the underlying rationale, discuss the computational and practical issues and provide detailed guidance as to how the important tasks of parameter inference and model selection can be performed in practice. Unlike other available packages, ABC-SysBio is highly suited for investigating, in particular, the challenging problem of fitting stochastic models to data. In order to demonstrate the use of ABC-SysBio, in this protocol we postulate the existence of an imaginary reaction network composed of seven interrelated biological reactions (involving a specific mRNA, the protein it encodes and a post-translationally modified version of the protein), a network that is defined by two files containing 'observed' data that we provide as supplementary information. In the first part of the PROCEDURE, ABC-SysBio is used to infer the parameters of this system, whereas in the second part we use ABC-SysBio's relevant functionality to discriminate between two different reaction network models, one of them being the 'true' one. Although computationally expensive, the additional insights gained in the Bayesian formalism more than make up for this cost, especially in complex problems.

Bayesian design strategies for synthetic biology

We discuss how statistical inference techniques can be applied in the context of designing novel biological systems. Bayesian techniques have found widespread application and acceptance in the systems biology community, where they are used for both parameter estimation and model selection. Here we show that the same approaches can also be used in order to engineer synthetic biological systems by inferring the structure and parameters that are most likely to give rise to the dynamics that we require a system to exhibit. Problems that are shared between applications in systems and synthetic biology include the vast potential spaces that need to be searched for suitable models and model parameters; the complex forms of likelihood functions; and the interplay between noise at the molecular level and nonlinearity in the dynamics owing to often complex feedback structures. In order to meet these challenges, we have to develop suitable inferential tools and here, in particular, we illustrate the use of approximate Bayesian computation and unscented Kalman filtering-based approaches. These partly complementary methods allow us to tackle a number of recurring problems in the design of biological systems. After a brief exposition of these two methodologies, we focus on their application to oscillatory systems.