Uncovering the dual role of dimensionless radius in buckling of spherical shells with random geometric imperfections.

Localized deformation and randomly shaped imperfections are salient features of buckling-type instabilities in thin-walled load-bearing structures. However, it is generally agreed that their complex interactions in response to mechanical loading are not yet sufficiently understood, as evidenced by buckling-induced catastrophic failures which continue to today. This study investigates how the intimate coupling between localization mechanisms and geometric imperfections combine to determine the statistics of the pressure required to buckle (the illustrative example of) a hemispherical shell. The geometric imperfections, in the form of a surface, are defined by a random field generated over the nominally hemispherical shell geometry, and the probability distribution of the buckling pressure is computed via stochastic finite element analysis. Monte-Carlo simulations are performed for a wide range of the shell's radius to thickness ratio, as well as the correlation length of the spatial distribution of the imperfection. The results show that over this range, the buckling pressure is captured by the Weibull distribution. In addition, the analyses of the deformation patterns observed during the simulations provide insights into the effects of certain characteristic lengths on the local buckling that triggers global instability. In light of the simulation results, a probabilistic model is developed for the statistics of the buckling load that reveals how the dimensionless radius plays a dual role which remained hidden in previous deterministic analyses. The implications of the present model for reliability-based design of shell structures are discussed.

Dissecting Mechanisms of Epigenetic Memory Through Computational Modeling.

Understanding the mechanistic basis of epigenetic memory has proven to be a difficult task due to the underlying complexity of the systems involved in its establishment and maintenance. Here, we review the role of computational modeling in helping to unlock this complexity, allowing the dissection of intricate feedback dynamics. We focus on three forms of epigenetic memory encoded in gene regulatory networks, DNA methylation, and histone modifications and discuss the important advantages offered by plant systems in their dissection. We summarize the main modeling approaches involved and highlight the principal conceptual advances that the modeling has enabled through iterative cycles of predictive modeling and experiments. Lastly, we discuss remaining gaps in our understanding and how intertwined theory and experimental approaches might help in their resolution.

PREDIG: Web application to model and predict the enzymatic saccharification of plant cell wall.

Enzymatic digestion of lignocellulosic plant biomass is a key step in bio-refinery approaches for the production of biofuels and other valuable chemicals. However, the recalcitrance of this material in conjunction with its variability and heterogeneity strongly hampers the economic viability and profitability of biofuel production. To complement both academic and industrial experimental research in the field, we designed an advanced web application that encapsulates our in-house developed complex biophysical model of enzymatic plant cell wall degradation. PREDIG (https://predig.cs.hhu.de/) is a user-friendly, free, and fully open-source web application that allows the user to perform in silico experiments. Specifically, it uses a Gillespie algorithm to run stochastic simulations of the enzymatic saccharification of a lignocellulose microfibril, at the mesoscale, in three dimensions. Such simulations can for instance be used to test the action of distinct enzyme cocktails on the substrate. Additionally, PREDIG can fit the model parameters to uploaded experimental time-course data, thereby returning values that are intrinsically difficult to measure experimentally. This gives the user the possibility to learn which factors quantitatively explain the recalcitrance to saccharification of their specific biomass material.

Kinetic control of liposome size by direct lipid transfer.

Spontaneous lipid vesiculation and related size distribution are traditionally studied in the framework of equilibrium thermodynamics and continuum mechanics, overlooking the kinetic aspects of the process. In the scenario of liposomes consisting of different lipid molecules dispersed in the same medium - a non-equilibrium situation -, the system evolves driven by lipid monomer transfer among the different liposomes. This process encompasses time-dependent changes in liposome size and size distribution, thus predicting size and composition at a given time would entail the control of the size of liposomes by kinetic means, an asset in the framework of diagnostics and synthetic biology. We introduce a direct transfer model, based on the fact that monomers are highly reactive species and apply it to saturated phospholipid molecules differing in hydrophobic chain length. Considering a well-defined gamma-type liposome size distribution, we demonstrate a clear liposome size-composition correlation and are able to predict liposome size and size distribution at any time in the transfer process. The size-composition correlation opens up new prospects for the control of the self-assembling properties of lipids and thereby the control of the liposome size.

A stochastic B cell affinity maturation model to characterize mechanisms of protection for tetravalent dengue vaccine constructs.

Dengue annually infects millions of people from a regionally and seasonally varying dengue virus population circulating as four distinct serotypes. Effective protection against dengue infection and disease requires tetravalent vaccine formulations to stimulate a balanced protective immune response to all four serotypes. However, this has been a challenge to achieve, and several clinical trials with different leading vaccine candidates have demonstrated unbalanced replication and interference of interindividual serotype components, leading to low efficacy and enhanced disease severity for dengue-naïve populations. Production of serotype-specific neutralizing antibodies is largely viewed as a correlate of protection against severe dengue disease. However, the underlying mechanisms that lead to these protective immune responses are not clearly elucidated. In this work, using a stochastic model of B cell affinity maturation, we tested different live-attenuated vaccine constructs with varied viral replication rates and contrasted the initiation and progress of adaptive immune responses during tetravalent vaccination and after dengue virus challenge. Comparison of our model simulations across different disease-severity levels suggested that individual production of high levels of serotype-specific antibodies together with a lower cross-reactive antibody are better correlates for protection. Furthermore, evolution of these serotype-specific antibodies was dependent on the percent of viral attenuation in the vaccine, and production of initial B cell and T cell populations pre- and post-secondary dengue infection was crucial in providing protective immunity for dengue-naïve populations. Furthermore, contrasting disease severity with respect to different dengue serotypes, our model simulations showed that tetravalent vaccines fare better against DENV-4 serotype when compared to other serotypes.

Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data.

We propose a machine learning framework for the data-driven discovery of macroscopic chemotactic Partial Differential Equations (PDEs)-and the closures that lead to them- from high-fidelity, individual-based stochastic simulations of Escherichia coli bacterial motility. The fine scale, chemomechanical, hybrid (continuum-Monte Carlo) simulation model embodies the underlying biophysics, and its parameters are informed from experimental observations of individual cells. Using a parsimonious set of collective observables, we learn effective, coarse-grained "Keller-Segel class" chemotactic PDEs using machine learning regressors: (a) (shallow) feedforward neural networks and (b) Gaussian Processes. The learned laws can be black-box (when no prior knowledge about the PDE law structure is assumed) or gray-box when parts of the equation (e.g. the pure diffusion part) is known and "hardwired" in the regression process. More importantly, we discuss data-driven corrections (both additive and functional), to analytically known, approximate closures.

Locally adaptive aggregation of organisms under death risk in rock-paper-scissors models.

We run stochastic simulations of the spatial version of the rock-paper-scissors game, considering that individuals use sensory abilities to scan the environment to detect the presence of enemies. If the local dangerousness level is above a tolerable threshold, individuals aggregate instead of moving randomly on the lattice. We study the impact of the locally adaptive aggregation on the organisms' spatial organisation by measuring the characteristic length scale of the spatial domains occupied by organisms of a single species. Our results reveal that aggregation is beneficial if triggered when the local density of opponents does not exceed 30%; otherwise, the behavioural strategy may harm individuals by increasing the average death risk. We show that if organisms can perceive further distances, they can accurately scan and interpret the signals from the neighbourhood, maximising the effects of the locally adaptive aggregation on the death risk. Finally, we show that the locally adaptive aggregation behaviour promotes biodiversity independently of the organism's mobility. The coexistence probability rises if organisms join conspecifics, even in the presence of a small number of enemies. We verify that our conclusions hold for more complex systems by simulating the generalised rock-paper-scissors models with five and seven species. Our discoveries may be helpful to ecologists in understanding systems where organisms' self-defence behaviour adapts to local environmental cues.

Impact of population size on early adaptation in rugged fitness landscapes.

Owing to stochastic fluctuations arising from finite population size, known as genetic drift, the ability of a population to explore a rugged fitness landscape depends on its size. In the weak mutation regime, while the mean steady-state fitness increases with population size, we find that the height of the first fitness peak encountered when starting from a random genotype displays various behaviours versus population size, even among small and simple rugged landscapes. We show that the accessibility of the different fitness peaks is key to determining whether this height overall increases or decreases with population size. Furthermore, there is often a finite population size that maximizes the height of the first fitness peak encountered when starting from a random genotype. This holds across various classes of model rugged landscapes with sparse peaks, and in some experimental and experimentally inspired ones. Thus, early adaptation in rugged fitness landscapes can be more efficient and predictable for relatively small population sizes than in the large-size limit. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

A Compact and Power-Efficient Noise Generator for Stochastic Simulations.

This paper describes an adaptive noise generator circuit suitable for on-chip simulations of stochastic chemical kinetics. The circuit uses amplified BJT white noise and adaptive low-pass filtering to emulate the power spectrum and autocorrelation of random telegraph signals (RTS) with Poisson-distributed level transitions. A current-mode implementation in the AMS 0.35 µm BiCMOS process shows excellent agreement with theoretical results from the Gillespie stochastic simulation algorithm over a 60 dB range in mean current levels (modeling molecule count numbers). The circuit has an estimated layout area of 0.032 mm2 and typically consumes 400 µA, which are 73% and 50% less, respectively, than prior implementations. Moreover, it does not require any off-chip capacitors. Experimental results from a discrete board-level implementation of the circuit are in good agreement with theoretical predictions.

Assessing the relative importance of bacterial resistance, persistence and hyper-mutation for antibiotic treatment failure.

To curb the rising threat of antimicrobial resistance, we need to understand the routes to antimicrobial treatment failure. Bacteria can survive treatment by using both genetic and phenotypic mechanisms to diminish the effect of antimicrobials. We assemble empirical data showing that, for example, Pseudomonas aeruginosa infections frequently contain persisters, transiently non-growing cells unaffected by antibiotics (AB) and hyper-mutators, mutants with elevated mutation rates, and thus higher probability of genetic resistance emergence. Resistance, persistence and hyper-mutation dynamics are difficult to disentangle experimentally. Hence, we use stochastic population modelling and deterministic fitness calculations to investigate the relative importance of genetic and phenotypic mechanisms for immediate treatment failure and establishment of prolonged, chronic infections. We find that persistence causes 'hidden' treatment failure with very low cell numbers if antimicrobial concentrations prevent growth of genetically resistant cells. Persister cells can regrow after treatment is discontinued and allow for resistance evolution in the absence of AB. This leads to different mutational routes during treatment and relapse of an infection. By contrast, hyper-mutation facilitates resistance evolution during treatment, but rarely contributes to treatment failure. Our findings highlight the time and concentration dependence of different bacterial mechanisms to escape AB killing, which should be considered when designing 'failure-proof' treatments.

Supercoiling-mediated feedback rapidly couples and tunes transcription.

Transcription induces a wave of DNA supercoiling, altering the binding affinity of RNA polymerases and reshaping the biochemical landscape of gene regulation. As supercoiling rapidly diffuses, transcription dynamically reshapes the regulation of proximal genes, forming a complex feedback loop. However, a theoretical framework is needed to integrate biophysical regulation with biochemical transcriptional regulation. To investigate the role of supercoiling-mediated feedback within multi-gene systems, we model transcriptional regulation under the influence of supercoiling-mediated polymerase dynamics, allowing us to identify patterns of expression that result from physical inter-gene coupling. We find that gene syntax-the relative ordering and orientation of genes-defines the expression profiles, variance, burst dynamics, and inter-gene correlation of two-gene systems. Furthermore, supercoiling can enhance or weaken biochemical regulation. Our results suggest that supercoiling couples behavior between neighboring genes, providing a regulatory mechanism that tunes transcriptional variance in engineered gene networks and explains the behavior of co-localized native circuits.

Spatial organisation plasticity reduces disease infection risk in rock-paper-scissors models.

We study a three-species cyclic game system where organisms face a contagious disease whose virulence may change by a pathogen mutation. As a responsive defence strategy, organisms' mobility is restricted to reduce disease dissemination in the system. The impact of the collective self-preservation strategy on the disease infection risk is investigated by performing stochastic simulations of the spatial version of the rock-paper-scissors game. Our outcomes show that the mobility control strategy induces plasticity in the spatial patterns with groups of organisms of the same species inhabiting spatial domains whose characteristic length scales depend on the level of dispersal restrictions. The spatial organisation plasticity allows the ecosystems to adapt to minimise the individuals' disease contamination risk if an eventual pathogen alters the disease virulence. We discover that if a pathogen mutation makes the disease more transmissible or less lethal, the organisms benefit more if the mobility is not strongly restricted, thus forming large spatial domains. Conversely, the benefits of protecting against a pathogen causing a less contagious or deadlier disease are maximised if the average size of groups of individuals of the same species is significantly limited, reducing the dimensions of groups of organisms significantly. Our findings may help biologists understand the effects of dispersal control as a conservation strategy in ecosystems affected by epidemic outbreaks.

Non-genetic resistance facilitates survival while hindering the evolution of drug resistance due to intraspecific competition.

Rising rates of resistance to antimicrobial drugs threaten the effective treatment of infections across the globe. Drug resistance has been established to emerge from non-genetic mechanisms as well as from genetic mechanisms. However, it is still unclear how non-genetic resistance affects the evolution of genetic drug resistance. We develop deterministic and stochastic population models that incorporate resource competition to quantitatively investigate the transition from non-genetic to genetic resistance during the exposure to static and cidal drugs. We find that non-genetic resistance facilitates the survival of cell populations during drug treatment while hindering the development of genetic resistance due to competition between the non-genetically and genetically resistant subpopulations. Non-genetic resistance in the presence of subpopulation competition increases the fixation times of drug resistance mutations, while increasing the probability of mutation before population extinction during cidal drug treatment. Intense intraspecific competition during drug treatment leads to extinction of susceptible and non-genetically resistant subpopulations. Alternating between drug and no drug conditions results in oscillatory population dynamics, increased resistance mutation fixation timescales, and reduced population survival. These findings advance our fundamental understanding of the evolution of resistance and may guide novel treatment strategies for patients with drug-resistant infections.

Mathematical Modeling to Guide Experimental Design: T Cell Clustering as a Case Study.

Mathematical modeling provides a rigorous way to quantify immunological processes and discriminate between alternative mechanisms driving specific biological phenomena. It is typical that mathematical models of immunological phenomena are developed by modelers to explain specific sets of experimental data after the data have been collected by experimental collaborators. Whether the available data are sufficient to accurately estimate model parameters or to discriminate between alternative models is not typically investigated. While previously collected data may be sufficient to guide development of alternative models and help estimating model parameters, such data often do not allow to discriminate between alternative models. As a case study, we develop a series of power analyses to determine optimal sample sizes that allow for accurate estimation of model parameters and for discrimination between alternative models describing clustering of CD8 T cells around Plasmodium liver stages. In our typical experiments, mice are infected intravenously with Plasmodium sporozoites that invade hepatocytes (liver cells), and then activated CD8 T cells are transferred into the infected mice. The number of T cells found in the vicinity of individual infected hepatocytes at different times after T cell transfer is counted using intravital microscopy. We previously developed a series of mathematical models aimed to explain highly variable number of T cells per parasite; one of such models, the density-dependent recruitment (DDR) model, fitted the data from preliminary experiments better than the alternative models, such as the density-independent exit (DIE) model. Here, we show that the ability to discriminate between these alternative models depends on the number of parasites imaged in the analysis; analysis of about [Formula: see text] parasites at 2, 4, and 8 h after T cell transfer will allow for over 95% probability to select the correct model. The type of data collected also has an impact; following T cell clustering around individual parasites over time (called as longitudinal (LT) data) allows for a more precise and less biased estimates of the parameters of the DDR model than that generated from a more traditional way of imaging individual parasites in different liver areas/mice (cross-sectional (CS) data). However, LT imaging comes at a cost of a need to keep the mice alive under the microscope for hours which may be ethically unacceptable. We finally show that the number of time points at which the measurements are taken also impacts the precision of estimation of DDR model parameters; in particular, measuring T cell clustering at one time point does not allow accurately estimating all parameters of the DDR model. Using our case study, we propose a general framework on how mathematical modeling can be used to guide experimental designs and power analyses of complex biological processes.

LigninGraphs: lignin structure determination with multiscale graph modeling.

Lignin is an aromatic biopolymer found in ubiquitous sources of woody biomass. Designing and optimizing lignin valorization processes requires a fundamental understanding of lignin structures. Experimental characterization techniques, such as 2D-heteronuclear single quantum coherence (HSQC) nuclear magnetic resonance (NMR) spectra, could elucidate the global properties of the polymer molecules. Computer models could extend the resolution of experiments by representing structures at the molecular and atomistic scales. We introduce a graph-based multiscale modeling framework for lignin structure generation and visualization. The framework employs accelerated rejection-free polymerization and hierarchical Metropolis Monte Carlo optimization algorithms. We obtain structure libraries for various lignin feedstocks based on literature and new experimental NMR data for poplar wood, pinewood, and herbaceous lignin. The framework could guide researchers towards feasible lignin structures, efficient space exploration, and future kinetics modeling. Its software implementation in Python, LigninGraphs, is open-source and available on GitHub.

Combination of survival movement strategies in cyclic game systems during an epidemic.

Disease outbreaks affect many ecosystems threatening species that also fight against other natural enemies. We investigate a cyclic game system with 5 species, whose organisms outcompete according to the rules of a generalised spatial rock-paper-scissors game, during an epidemic. We study the effects of behavioural movement strategies that allow individuals of one out of the species to move towards areas with a low density of disease vectors and a high concentration of enemies of their enemies. We perform a series of stochastic simulations to discover the impact of self-preservation strategies in pattern formation, calculating the species' spatial autocorrelation functions. Considering organisms with different physical and cognitive abilities, we compute the benefits of each movement tactic to reduce selection and infection risks. Our findings show that the maximum profit in terms of territorial dominance in the cyclic game is achieved if both survival movement strategies are combined, with individuals prioritising social distancing. In the case of an epidemic causing symptomatic illness, the drop in infection risk when organisms identify and avoid disease vectors does not render a rise in the species population because many refuges are disregarded, limiting the benefits of safeguarding against natural enemies. Our results may be helpful to the understanding of the behavioural strategies in ecosystems where organisms adapt to face living conditions changes.

Modulation of nuclear and cytoplasmic mRNA fluctuations by time-dependent stimuli: Analytical distributions.

Temporal variation of environmental stimuli leads to changes in gene expression. Since the latter is noisy and since many reaction events occur between the birth and death of an mRNA molecule, it is of interest to understand how a stimulus affects the transcript numbers measured at various sub-cellular locations. Here, we construct a stochastic model describing the dynamics of signal-dependent gene expression and its propagation downstream of transcription. For any time-dependent stimulus and assuming bursty gene expression, we devise a procedure which allows us to obtain time-dependent distributions of mRNA numbers at various stages of its life-cycle, e.g. in its nascent form at the transcription site, post-splicing in the nucleus, and after it is exported to the cytoplasm. We also derive an expression for the error in the approximation whose accuracy is verified via stochastic simulation. We find that, depending on the frequency of oscillation and the time of measurement, a stimulus can lead to cytoplasmic amplification or attenuation of transcriptional noise.

Rules of Engagement: A Guide to Developing Agent-Based Models.

Agent-based models (ABM), also called individual-based models, first appeared several decades ago with the promise of nearly real-time simulations of active, autonomous individuals such as animals or objects. The goal of ABMs is to represent a population of individuals (agents) interacting with one another and their environment. Because of their flexible framework, ABMs have been widely applied to study systems in engineering, economics, ecology, and biology. This chapter is intended to guide the users in the development of an agent-based model by discussing conceptual issues, implementation, and pitfalls of ABMs from first principles. As a case study, we consider an ABM of the multi-scale dynamics of cellular interactions in a microbial community. We develop a lattice-free agent-based model of individual cells whose actions of growth, movement, and division are influenced by both their individual processes (cell cycle) and their contact with other cells (adhesion and contact inhibition).

Transcription factors and chaperone proteins play a role in launching a faster response to heat stress and aggregation.

Proteins, under conditions of cellular stress, typically tend to unfold and form lethal aggregates leading to neurological diseases like Parkinson's and Alzheimer's. A clear understanding of the conditions that favor dis-aggregation and restore the cell to its healthy state after they have been stressed is therefore important in dealing with these diseases. The heat shock response (HSR) mechanism is a signaling network that deals with these undue protein aggregates and aids in the maintenance of homeostasis within a cell. This framework, on its own, is a mathematically well studied mechanism. However, not much is known about how the various intermediate mis-folded protein states of the aggregation process interact with some of the key components of the HSR pathway such as the Heat Shock Protein (HSP), the Heat Shock Transcription Factor (HSF) and the HSP-HSF complex. In this article, using kinetic parameters from the literature, we propose and analyze two mathematical models for HSR that also include explicit reactions for the formation of protein aggregates. Deterministic analysis and stochastic simulations of these models show that the folded proteins and the misfolded aggregates exhibit bistability in a certain region of the parameter space. Further, the models also highlight the role of HSF and the HSF-HSP complex in reducing the time lag of response to stress and in re-folding all the mis-folded proteins back to their native state. These models, therefore, call attention to the significance of studying related pathways such as the HSR and the protein aggregation and re-folding process in conjunction with each other.

Electrophysiological Properties from Computations at a Single Voltage: Testing Theory with Stochastic Simulations.

We use stochastic simulations to investigate the performance of two recently developed methods for calculating the free energy profiles of ion channels and their electrophysiological properties, such as current-voltage dependence and reversal potential, from molecular dynamics simulations at a single applied voltage. These methods require neither knowledge of the diffusivity nor simulations at multiple voltages, which greatly reduces the computational effort required to probe the electrophysiological properties of ion channels. They can be used to determine the free energy profiles from either forward or backward one-sided properties of ions in the channel, such as ion fluxes, density profiles, committor probabilities, or from their two-sided combination. By generating large sets of stochastic trajectories, which are individually designed to mimic the molecular dynamics crossing statistics of models of channels of trichotoxin, p7 from hepatitis C and a bacterial homolog of the pentameric ligand-gated ion channel, GLIC, we find that the free energy profiles obtained from stochastic simulations corresponding to molecular dynamics simulations of even a modest length are burdened with statistical errors of only 0.3 kcal/mol. Even with many crossing events, applying two-sided formulas substantially reduces statistical errors compared to one-sided formulas. With a properly chosen reference voltage, the current-voltage curves can be reproduced with good accuracy from simulations at a single voltage in a range extending for over 200 mV. If possible, the reference voltages should be chosen not simply to drive a large current in one direction, but to observe crossing events in both directions.