BioSystems

The exact mechanism controlling cell growth remains a grand challenge in developmental biology and regenerative medicine. The Drosophila wing disc tissue serves as an ideal biological model to study growth regulation due to similar features observed in other developmental systems. The mechanism of growth regulation in the wing disc remains a subject of intense debate. Most existing models to study tissue growth focus on either chemical signals or mechanical forces only. Here we developed a multiscale chemical-mechanical coupled model to test a growth regulation mechanism depending on the spatial range of the morphogen gradient. By comparing the spatial distribution of cell division and the overall shape of tissue obtained in the coupled model with experimental data, our results show that the distribution of the Dpp morphogen can be critical in resulting tissue size and shape. A larger tissue size with a faster growth rate and more symmetric shape can be achieved if the Dpp gradient spreads in a larger domain. Together with the absorbing boundary conditions, the feedback regulation that downregulates Dpp receptors on the cell membrane allows the further spread of the morphogen away from its source region, resulting in prolonged tissue growth at a more spatially homogeneous growth rate. Summary StatementA multiscale chemical-mechanical model was developed by coupling submodels representing dynamics of a morphogen gradient at the tissue level, intracellular chemical signals, and mechanical properties at the subcellular level. By applying this model to study the Drosophila wing disc, it was found that the spatial range of the morphogen gradient affected tissue growth in terms of the growth rate and the overall shape.

Biological complexity is defined as the number of modules that compose an organism or a biological system, the type of interactions between these modules, and new hierarchies that describe these interactions. These patterns in biological complexity are changing during the evolution of life-histories, such as the evolution of coloniality in animals. In relation to coloniality, it is possible to observe an increment in all the aspects defined in the concept of biological complexity. First, in colonial animals, there is an increment in the modules that compound the system (i.e. zooids) compared with a solitary organism in which the multicellular individual a unity. Consequently, this transformation of the multicellular individual, in a component of the modular architecture in colonies, involves an increase in the regulatory processes of colonial system. This is precisely the case of the colonial life history evolution from solitary ancestors in the Styelids tunicates. Therefore, the main question of this study is How is the regulation of the asexual developmental processes that occurred simultaneously in the modules of the colonies? This question was studied, by the research of colonial strategy in the styelid Symplegma. Using in vivo observations of the budding process, description and classification of the extra-corporeal blood vessels system and the blood cells, by cytohistological assays. The conclusion is that the regulation of the simultaneous developmental processes that occurred in Symplegma colonies is mediated by the system of extra-corporeal blood vessels, which maintain physically the cohesion of the individuals, the plasma, and migratory blood cells transport signals between the individuals of the colonies.

Capacitation is a complex maturation process mammalian sperm must undergo in the female genital tract to be able to fertilize an egg. This process involves, amongst others, physiological changes in flagellar beating pattern, membrane potential, intracellular ion concentrations and protein phosphorylation. Typically, in a capacitation medium, only a fraction of sperm achieve this state. The cause for this heterogeneous response is still not well understood and remains an open question. Here, one of our principal results is to develop a discrete regulatory network, with mostly deterministic dynamics in conjunction with some stochastic elements, for the main biochemical and biophysical processes involved in the early events of capacitation. The model criterion for capacitation requires the convergence of specific levels of a select set of nodes. Besides reproducing several experimental results and providing some insight on the network interrelations, the main contribution of the model is the suggestion that the degree of variability in the total amount and individual number of ion transporters among spermatozoa regulates the fraction of capacitated spermatozoa. This conclusion is consistent with recently reported experimental results. Based on this mathematical analysis, experimental clues are proposed for the control of capacitation levels. Furthermore, cooperative and interference traits that become apparent in the modelling among some components also call for future theoretical and experimental studies. Author summaryFertilization is one of the fundamental processes for the preservation of life. In mammals, sperm undergo a complex process during their passage through the female tract known as capacitation, which enables them for fertilization. At the present time, it is accepted from experimental observation, though not understood, that only a fraction of the sperm is capacitated. In this work, by means of a network mathematical model for regulatory sperm intracellular signaling processes involved in mice capacitation, we find that the variability in the distribution of the number of ion transporters intervenes in the regulation of the capacitation fraction. Experimental verification of this suggestion could open a line of research geared to the regulation of the degree of heterogeneity in the number of ion transporters as a fertility control. The model also uncovers, through in silico overactivation and loss of function of network nodes, synergetic traits which again call for experimental verification.

Phenotypic plasticity is usually defined as a property of individual genotypes to produce different phenotypes when exposed to different environmental conditions. While the benefits of plasticity for adaptation are well established, the costs associated with plasticity remain somewhat obscure. Understanding both why and how these costs occur could help us explain and predict the behaviour of living creatures as well as allow us to design more adaptable robotic systems. One of the challenges of conducting such investigations concerns the difficulty in isolating the effects of different types of costs and the lack of control over environmental conditions. The present study tackles these challenges by using virtual worlds (software) to investigate the environmentally regulated phenotypic plasticity of digital organisms: the experimental setup guarantees that possibly incurred genetic costs of plasticity are isolated from other plasticity-related costs. The hypothesis put forward here is that despite the potential benefits of plasticity, these benefits might be undermined by the genetic costs related to plasticity itself. This hypothesis was subsequently confirmed to be true. Author summaryPhenotypic plasticity is usually defined as a property of individual DNA that produces different bodies and brains when exposed to different environmental conditions. While the benefits of plasticity for adaptation are well established, there are also potential costs associated with plasticity: "Jack of all trades, master of none." Understanding both why and how these costs occur could help us explain and predict the behaviour of living creatures as well as allow us to design more adaptable robotic systems. While some studies have reported strong evidence for such costs, many other studies have observed no costs. One of the challenges associated with conducting such investigations concerns the difficulty of isolating the effects of the different types of costs. Artificial life (ALife) involves the design and investigation of artificial living systems in different levels of organisation and mediums. Importantly, ALife allows for the customisation of multiple properties of an artificial living system. In the present study, I investigate the environmentally regulated phenotypic plasticity of evolvable digital organisms using an ALife system. The experimental setup guarantees that possibly incurred genetic costs of plasticity are isolated from other plasticity-related costs. The hypothesis put forward here is that despite the potential benefits of plasticity, these benefits might be undermined by the genetic costs related to plasticity itself. This hypothesis was subsequently confirmed to be true.

Hepatitis B is the main public health problem of the whole world. In epidemiology, mathematical models perform a key role in understanding the dynamics of infectious diseases. This paper proposes Pade approximation (Pa) with Differential Evolution (DE) for obtaining solution of Hepatitis-B model which is nonlinear numerically. The proposed strategy transforms the nonlinear model into optimization problem by using Pade approximation. Initial conditions are converted into problem constraints and constraint problem become unconstraint by using penalty function. DE is obtained numerical solution of Hepatitis-B model by solving the established problem of optimization. There is no need to choose step lengths in proposed Pade-approximation based Differential Evolution (PaDE) technique and also PaDE converges to true steady state points. Finally, a convergence and error analysis evidence that the convergence speed of PaDE is greater than Non-Standard Finite Difference (NSFD) method for different time steps.

Antibiotic resistance is a compound effect of several factors in the infection to healing cycle, from molecular factors such as mutation rate of bacteria to habitual behaviors such as adherence to a prescribed drug. Usually each of these factors is modeled separately from biochemistry, evolutionary biology or population health perspectives. To develop an understanding for the drug resistance at a population level, which is of high global significance, it is important to weigh all these factors in an integrated model. We develop RASAID, a model for resistance considering bacterial adaptation, infection spread, population adherence, immunity, and drug dosage. We apply the model to antibiotic resistance in the spread of resistant strains of Streptococcus Pneumoniae (Sp) in a finite community. We analyze the contributions from several factors to resistance, with a goal towards asking how important is the pursuit of newer drug developments relative to improving the awareness about the good practices in drug usage.

The paper assumed that Nf2-Amot complex regulates the phosphorylation cascade so that each cell in the early mammalian embryo differentiates properly in silico. To confirm the validity of the assumption, it was necessary to verify whether Nf2-Amot complex has an impact on the resulting differentiation. The living embryo is unsuitable for the confirmation since the early mammalian embryo is too small to observe and too ethically sensitive to invade. In such cases, computational models can be used as experimental subjects for operations that cannot be applied to the living embryo. Previous models on the embryo, however, could not verify the assumption because they had not modeled Nf2-Amot complex, and they seldom modeled the Hippo signaling pathway. Therefore, the paper introduced a model of Nf2-Amot complex to the previous study that had modeled the Hippo signaling pathway. Testing the model under diverse conditions revealed that the existence of Nf2-Amot complex reproduces the ideal cell differentiation observed in the living embryo. In this sense, the validity of the model was confirmed. Furthermore, diverse cell-cell contacts that induce various concentrations of Nf2-Amot complex also resulted in ideal cell differentiation. These results suggested the correctness of the assumption in silico.

Pneumonia has been a major airborne transmitted disease and continues to pose a major public health burden in both developed and developing countries of the world. In this study, we constructed and analyzed a nonlinear deterministic compartmental mathematical model for assessing the community-level impacts of vaccination, other protection measures like practicing good hygiene, avoiding close contacts with sick people and limiting exposure to cigarette smoke, etc. and treatment on the transmission dynamics of pneumonia disease in a population of varying size. Our model exhibits two kinds of equilibrium points: pneumonia disease-free equilibrium point, and pneumonia endemic equilibrium point(s). Using center manifold criteria, we have verified that the pneumonia model exhibits backward bifurcations whenever its effective reproduction number [R]P < 1 and in the same region, the model shows the existence of more than one endemic equilibrium point where some of which are stable and others are unstable. Thus, for pneumonia infection, the necessity of the pneumonia effective reproduction number [R]P < 1, although essential, it might not be enough to completely eradicate the pneumonia infection from the considered community. Our examination of sensitivity analysis shows that the pneumonia infection transmission rate denoted by {beta} plays a crucial role to change the qualitative dynamics of pneumonia infection. By taking standard data from published literature, our numerical computations show that the numerical value of pneumonia infection model effective reproduction number is [R]P = 8.31 at {beta} = 4.21 it implies that the disease spreads throughout the community. Finally, our numerical simulations show that protection, vaccination, and treatment against pneumonia disease have the effect of decreasing pneumonia expansion.

In developing tissues, signal transduction from morphogen gradients conveys positional information to cells, resulting in cell specification and differentiation. One such morphogen is bone morphogenetic protein (BMP), of the TGF-{beta} superfamily, whose signaling network is highly conserved across many species. In Danio rerio (zebrafish), this signaling pathway directs dorsoventral axis formation during early embryogenesis. Many of the molecules that play a role in this network are well-understood; however, the mechanisms through which they achieve noise attenuation and gradient robustness have not been fully defined. Specifically, the heterodimer-heterotetramer complex has been shown to be required for signal transduction[1], but current understanding and modeling of the BMP membrane receptors at this stage has not given any insight into evolutionary drivers of the requirement. In this study, we develop a stochastic model of receptor oligomerization with the published reports of binding kinetics of BMP ligand-receptor interactions to mechanistically assess zebrafish phenotype variability related to the distributions of noise and stochasticity. We can also analyze time-dependent signaling and frequency metrics that are not available in traditional, deterministic modeling. Fast Fourier Transform and cumulative energy spectral density visualization show that the heterodimer-heterotetramer complex may function as part of a low-pass filter mechanism in the dorsal-ventral axis formation process, specifically tuned to the noise of the system. Under dynamic conditions such as the mid-blastula transition (MBT), wherein the morphogen gradient rapidly changes shape, established metrics of noise and information transduction, such as coefficient of variation and mutual information, overlook important temporal effects that may be particularly relevant during development. As the BMP signaling pathway is highly conserved and has been implicated in human bone growth and wound healing, its study in simpler systems stands to accelerate our comprehension of BMP network structure and molecular mechanisms with potential application in regenerative medical studies.

Molecular network modeling requires the use of mathematical and computational formalisms for a robust and accurate prediction of phenotypes. Furthermore, there is a need to extend these formalisms to be applied to large-scale molecular networks, thus helping in the understanding of biological complexity. In this work, we propose an extension to the modeling framework known as design principles, developed by M.A. Savageau, which is based on the Power Law Modeling. While valuable to understand several properties of molecular networks, the power law modeling cannot be used to infer kinetic orders, which are typically related to the number of binding sites present in molecules. We modified the traditional approach by incorporating the use of monoids generating a new methodological approach that we call Genotype Arithmetic. This approach solves local geometry, solving networks through monoids and varieties, reducing the computational complexity. The resulting combinatorial object contains a family of geometric points, whose fixed points in the exponent space define a set of constraints determining the correct kinetic order to be used in the power law modeling. This characteristic constitutes a prediction of the binding strength and/or the number of DNA binding sites in regulatory sequences, as well as the reaction orders in enzymatic kinetics. To show the applicability of the present approach, we show how the number of binding sites can be approximated in metabolic pathways formed by 3 to 9 reactions, in allosteric systems of end-product inhibition with intermediate catalytic reactions and one gene inhibition. Author summaryIn this work, was revised the Power Law Modeling to analyze and predict kinetic and genomic parameters in molecular networks. It was developed a new approach, called Genotype Arithmetic, which takes advantage from the properties of Monoids found within this formalism. Using this algebraic and geometric technique, were predicted the number of binding sites for various cases associated with the pathway length in the gene allosteric system for end-product inhibition.

The mechanisms underlying the scaling of the Bicoid morphogen gradient in Drosophila with the embryo size is not clearly understood. We propose a model with a spatially varying diffusion coefficient along the anterior-posterior axis, that is proportional to the nearly periodic spatial distribution of the nucleo-cytoplasmic domains and alternating between regions of fast and slow diffusion. We postulate that for specific interpretation of the heterogeneous environment, where the space available for free diffusion within an energid is assumed to be proportional to the embryo size, a change in the embryo size can lead to a size-dependent scaling of the gradient lengthscale. We further study a two component model with slow and fast diffusing Bicoid, and identify this model to be equivalent to the heterogeneous diffusion model further postulating that the fast-state occupancy which is a measure of the fraction of time spent in the fast diffusing state, should also scale with the embryo size via the energid size. Finally, we incorporate nuclear shuttling into our model to understand the effect of shuttling on the gradient lengthscale and scaling with embryo size. We argue that for the particular case where the degradation within the nucleus is low, nuclear shuttling does not perturb the Bicoid gradient. Our study suggests that scaling of the gradient length scale is possible due to spatial heterogeneity and does not depend on nuclear trapping as suggested previously.

Mammalian spermatogenesis occurs in the seminiferous tubules, which exhibit unique spatiotemporal differentiation patterns known as cellular association patterns. In mice, these patterns can be regarded as one-dimensional wavetrains that consistently propagate inward from both ends, resulting in one or more "sites of reversal." Segmented wavetrain pattern, in which the wave propagation direction spatially switches, was observed in our previous three-species reaction-diffusion model for interspecific species difference in spermatogenic waves (Kawamura et al., 2021). However, the biological mechanisms of the formation of sites of reversal and of this directional bias, as well as the principle of pattern formation, remain unknown. Here, we refined our previous model to match the actual biological spatiotemporal scale and examined its dynamics through extensive numerical simulations. The modified model frequently generated segmented wavetrain patterns, corresponding to the sites of reversal, but without directional bias. We systematically examined possible biological mechanisms for the bias and found that tubule elongation, especially near the rete testis, most effectively accounts for the bias among the tested. Extensive simulations revealed that the segmented pattern is numerically stable, emerges more frequently in longer domains, and shows an exponential segment size distribution with a lower limit for the stably existing segment length. These explorations imply that locally emerged unidirectional wavetrains serve as building blocks to generate the stable segmented wavetrains through their interactions. HighlightsO_LISegmented wavetrains reflect sites of reversal in seminiferous tubules. C_LIO_LISegmented patterns frequently emerge but show no inherent directional bias. C_LIO_LITubule elongation may contribute to inward propagation near the rete testis. C_LIO_LISegmented wavetrains are numerically stable and more frequent in longer domains. C_LIO_LIInteractions of local unidirectional wavetrains generate stable segmented structures. C_LI

Evolution optimizes cellular behavior throughout sequential generations by selecting the successful individual cells in a given context. As gene regulatory networks (GRNs) determine the behavior of single cells by ruling the activation of different processes - such as cell differentiation and death - how GRNs change from one generation to the other might have a relevant impact on the course of evolution. It is not clear, however, which mechanisms that affect GRNs effectively favor evolution and how. Here, we use a population of computational robotic models controlled by artificial gene regulatory networks (AGRNs) to evaluate the impact of different genetic modification strategies in the course of evolution. The virtual agent senses the ambient and acts on it as a bacteria in different phototaxis-like tasks - orientation to light, phototaxis, and phototaxis with obstacles. We studied how the strategies of gradual and abrupt changes on the AGRNs impact evolution considering multiple levels of task complexity. The results indicated that a gradual increase in the complexity of the performed tasks is beneficial for the evolution of the model. Furthermore, we have seen that larger gene regulatory networks are needed for more complex tasks, with single-gene duplication being an excellent evolutionary strategy for growing these networks, as opposed to full-genome duplication. Studying how GRNs evolved in a biological environment allows us to improve the computational models produced and provide insights into aspects and events that influenced the development of life on earth.

Correlation coefficients are abundantly used in the life sciences. Their use can be limited to simple exploratory analysis or to construct association networks for visualization but they are also basic ingredients for sophisticated multivariate data analysis methods. It is therefore important to have reliable estimates for correlation coefficients. In modern life sciences, comprehensive measurement techniques are used to measure metabolites, proteins, gene-expressions and other types of data. All these measurement techniques have errors. Whereas in the old days, with simple measurements, the errors were also simple, that is not the case anymore. Errors are heterogeneous, non-constant and not independent. This hampers the quality of the estimated correlation coefficients seriously. We will discuss the different types of errors as present in modern comprehensive life science data and show with theory, simulations and real-life data how these affect the correlation coefficients. We will briefly discuss ways to improve the estimation of such coefficients.

Geometric models allow us to quantify topography of the Waddington landscape and gain quantitative insights of gene interaction in cell fate differentiation. Often mutant phenotypes show partial penetrance and there is a dearth of quantitative models that can exploit this data and make predictions about new allelic combinations with no additional parameters. C. elegans with its invariant cell lineages has been a key model system for discovering the genes controlling development. Here we focus on the differentiation of the endoderm founder cell named E from its mother, the EMS cell. Mutants that convert E to its sister MS fate have figured prominently in deciphering the Wnt pathway in worm. We construct a bi-valued Waddington landscape model that predicts the effect on POP-1/TCF and SYS-1/beta-catenin levels based on the penetrance of mutant alleles and RNAi, and relates the levels to fate choice decisions. A subset of the available data is used to fit the model and remaining data is then correctly predicted. Simple kinetic arguments show that contrary to current belief the ratio of these two proteins alone is not indicative of fate outcomes. Furthermore, double mutants within a background reduction of POP-1 levels are predicted with no adjustable parameters and their relative penetrance can differ from the same mutants with the wild-type POP-1 level, which calls for further experimental investigations. Our model refines the content of existing gene networks and invites extensions to other manifestations of the Wnt pathway in worm.

The nematode Caenorhabditis elegans exhibits an invariant cell lineage during its development where the gene-molecular network that regulates the development is crucial for the biological process. While there are many molecular cell atlases describing the phenomena and key molecules involved in cell transformation, the underlying mechanisms from a systems biology perspective have received less attention. Based on an endogenous molecular-cellular theory that relates the molecular mechanisms to biological phenotypes, we constructed a model of core endogenous network to describe the early stages of embryonic development of the nematode. Different cell types and intermediate cell states during development from zygotes to founder cells correspond to the steady states of the network as a nonlinear stochastic dynamical system. Connections between steady states form a topological landscape that encompasses known developmental lineage trajectories. By regulating the expression of agents in the network, we quantitatively simulated the effects of the Wnt and Notch signaling pathway on cell fate transitions and predicted the possible trajectories of transdifferentiation of the AB cell across the lineage. The success of the current study may help advance our understanding of the fundamental principles of developmental biology and cell fate determination, offering an effective tool for quantitative analysis of cellular processes.

Evolutionary algorithms, a class of optimization techniques inspired by biological evolution, have emerged as powerful tools for the optimization of complex systems, including the evolution of mass-action chemical reaction networks. This work explores the application of evolutionary algorithms in this domain, presenting a novel approach inspired by neural network evolution methodologies. A key feature of the algorithm is speciation, which separates candidate reaction networks into groups based on their similarity, which maintains diversity and protects innovations. Crossover has also been shown to be an effective means of improving evolutionary success in other domains. However, crossover of mass-action networks is tested and found to be detrimental to the evolutionary process. This work goes beyond theoretical exploration by offering a practical contribution in the form of a user-friendly software module. This module encapsulates the newly devised algorithm, enabling researchers and practitioners to readily apply the speciation-based approach in their own investigations of mass-action chemical reaction networks. Author summaryEvolutionary algorithms are an optimization technique inspired by biological evolution. They can be used to solve complex multi-dimensional problems for which analytic solutions are infeasible. We developed a novel evolutionary algorithm for use with mass-action chemical reaction networks. This algorithm implements two features of biological evolution, speciation and crossover, in an effort to generate chemical reaction networks with specific behaviors. Here, this novel algorithm is demonstrated by generating chemical reaction networks whose chemical species oscillate in time. This algorithm is encapsulated in a julia package and is publicly available as ReactionNetworkEvolution.jl.

This work is based on the Equivalence between Molecular Dynamics and Neural Network. It provides learning proofs in a Lennard-Jones (LJ) fluid, presented as a network of particles having non-bonded interactions. I describe the fluids learning as the property of an order that emerges as an adaptation in establishing equilibrium with energy and thermal conservation. The experimental section demonstrates the fluid can be trained with logic-gates patterns. The work goes beyond Molecular Computings application, explaining how this model uses its intrinsic minimizing properties in learning and predicting outputs. Finally, it gives hints for a theory on real chemistrys computational universality.

Much progress has been made, and continues to be made, towards identifying candidate mutated driver pathways in cancer. However, no systematic approach to understanding how candidate pathways relate to each other for a given cancer (such as Acute myeloid leukemia), and how one type of cancer may be similar or different from another with regard to their respective pathways (Acute myeloid leukemia vs. Glioblastoma multiforme for instance), has emerged thus far. Our work attempts to contribute to the understanding of space of pathways through a novel topological framework. We illustrate our approach, using mutation data (obtained from TCGA) of two types of tumors: Acute myeloid leukemia (AML) and Glioblastoma multiforme (GBM). We find that the space of pathways for AML is homotopy equivalent to a sphere, while that of GBM is equivalent to a genus-2 surface. We hope to trigger new types of questions (i.e., allow for novel kinds of hypotheses) towards a more comprehensive grasp of cancer.

The exact mechanisms behind many morphogenic processes are still a mystery. Mechanical cues, such as curvature, play an important role when tissue or cell shape is formed. In this work, we derive and analyze a mechanochemical model. This particular spatially one-dimensional model describes the deformation of a tissue- or cell surface over time, which is driven by a morphogen that locally induces curvature. The model consists of two PDEs with periodic boundary conditions; one reaction-diffusion equation for the morphogen and one PDE that describes the dynamics of the curve, derived by taking the L2-gradient flow of the Helfrich energy. We analyze the possible steady states of this model using geometric singular perturbation theory. It turns out that the strength of interaction between the morphogen and the curvature plays a key role in the type of possible steady state solutions. In the case of weak interaction, the geometry of the slow manifolds allows only for (in space) slowly changing periodic orbits that lay completely on one slow manifold. In the case of strong interaction, there exist multiple front solutions: periodic orbits that jump between different slow manifolds. The singular skeletons of the steady state solutions do not meet the required consistency conditions for the curvature, a priori indicating that the solutions might not be observable. The observability and stability are investigated further using numerical simulation.