A complex systems approach to Arabidopsis root stem-cell niche developmental mechanisms: from molecules, to networks, to morphogenesis

Recent reports have shown that the molecular mechanisms involved in root stem-cell niche development in Arabidopsis thaliana are complex and contain several feedback loops and non-additive interactions that need to be analyzed using computational and formal approaches. Complex systems cannot be understood in terms of the behavior of their isolated components, but they emerge as a consequence of largely non-linear interactions among their components. The study of complex systems has provided a useful approach for the exploration of system-level characteristics and behaviors of the molecular networks involved in cell differentiation and morphogenesis during development. We analyzed the complex molecular networks underlying stem-cell niche patterning in the A. thaliana root in terms of some of the key dynamic traits of complex systems: self-organization, modularity and structural properties. We use these analyses to integrate the available root stem-cell niche molecular mechanisms data and postulate novel hypotheses, missing components and interactions and explain apparent contradictions in the literature.     

Network modeling of signal transduction: establishing the global view

Embryonic development and adult tissue homeostasis are controlled through activation of intracellular signal transduction pathways by extracellular growth factors. In the past, signal transduction has largely been regarded as a linear process. However, more recent data from large-scale and high-throughput experiments indicate that there is extensive cross-talk between individual signaling cascades leading to the notion of a signaling network. The behavior of such complex networks cannot be predicted by simple intuitive approaches but requires sophisticated models and computational simulations. The purpose of such models is to generate experimentally testable hypotheses and to find explanations for unexpected experimental results. Here, we discuss the need for, and the future impact of, mathematical models for exploring signal transduction in different biological contexts such as for example development.     

Equation discovery for systems biology: finding the structure and dynamics of biological networks from time course data

Reconstructing biological networks, such as metabolic and signaling networks, is at the heart of systems biology. Although many approaches exist for reconstructing network structure, few approaches recover the full dynamic behavior of a network. We survey such approaches that originate from computational scientific discovery, a subfield of machine learning. These take as input measured time course data, as well as existing domain knowledge, such as partial knowledge of the network structure. We demonstrate the use of these approaches on illustrative tasks of finding the complete dynamics of biological networks, which include examples of rediscovering known networks and their dynamics, as well as examples of proposing models for unknown networks.     

Unsupervised quantification of naturalistic animal behaviors for gaining insight into the brain

Neural computation has evolved to optimize the behaviors that enable our survival. Although much previous work in neuroscience has focused on constrained task behaviors, recent advances in computer vision are fueling a trend toward the study of naturalistic behaviors. Automated tracking of fine-scale behaviors is generating rich datasets for animal models including rodents, fruit flies, zebrafish, and worms. However, extracting meaning from these large and complex data often requires sophisticated computational techniques. Here we review the latest methods and modeling approaches providing new insights into the brain from behavior. We focus on unsupervised methods for identifying stereotyped behaviors and for resolving details of the structure and dynamics of behavioral sequences.     

Meta-analysis for microarray studies of the genetics of complex traits

In comparison to other complex disease traits, alcoholism and alcohol abuse are influenced by the combined effects of many genes that alter susceptibility, phenotypic expression and associated morbidity, respectively. Many genetic studies, in both animal models and humans, have identified genetic intervals containing genes that influence alcoholism or behavioral responses to ethanol. Concurrently, a growing number of microarray studies have identified gene expression differences related to ethanol drinking or other ethanol behaviors. However, concerns about the statistical power of these experiments, combined with the complexity of the underlying phenotypes, have greatly hampered the identification of candidate genes underlying ethanol behaviors. Meta-analysis approaches using recent compilations of large datasets of microarray, behavioral and genetic data promise improved statistical power for detecting the genes or gene networks affecting ethanol behaviors and other complex traits.     

Individual-based modelling of bacterial ecologies and evolution

This paper presents two approaches to the individual-based modelling of bacterial ecologies and evolution using computational tools. The first approach is a fine-grained model that is based on networks of interactivity between computational objects representing genes and proteins. The second approach is a coarser-grained, agent-based model, which is designed to explore the evolvability of adaptive behavioural strategies in artificial bacteria represented by learning classifier systems. The structure and implementation of these computational models is discussed, and some results from simulation experiments are presented. Finally, the potential applications of the proposed models to the solution of real-world computational problems, and their use in improving our understanding of the mechanisms of evolution, are briefly outlined.     

Advances in the mechanical modeling of filamentous actin and its cross-linked networks on multiple scales

The protein actin is a part of the cytoskeleton and, therefore, responsible for the mechanical properties of the cells. Starting with the single molecule up to the final structure, actin creates a hierarchical structure of several levels exhibiting a remarkable behavior. The hierarchy spans several length scales and limitations in computational power; therefore, there is a call for different mechanical modeling approaches for the different scales. On the molecular level, we may consider each atom in molecular dynamics simulations. Actin forms filaments by combining the molecules into a double helix. In a model, we replace molecular subdomains using coarse-graining methods, allowing the investigation of larger systems of several atoms. These models on the nanoscale inform continuum mechanical models of large filaments, which are based on worm-like chain models for polymers. Assemblies of actin filaments are connected with cross-linker proteins. Models with discrete filaments, so-called Mikado models, allow us to investigate the dependence of the properties of networks on the parameters of the constituents. Microstructurally motivated continuum models of the networks provide insights into larger systems containing cross-linked actin networks. Modeling of such systems helps to gain insight into the processes on such small scales. On the other hand, they call for verification and hence trigger the improvement of established experiments and the development of new methods.     

Inferring dynamic signatures of microbes in complex host ecosystems

The human gut microbiota comprise a complex and dynamic ecosystem that profoundly affects host development and physiology. Standard approaches for analyzing time-series data of the microbiota involve computation of measures of ecological community diversity at each time-point, or measures of dissimilarity between pairs of time-points. Although these approaches, which treat data as static snapshots of microbial communities, can identify shifts in overall community structure, they fail to capture the dynamic properties of individual members of the microbiota and their contributions to the underlying time-varying behavior of host ecosystems. To address the limitations of current methods, we present a computational framework that uses continuous-time dynamical models coupled with Bayesian dimensionality adaptation methods to identify time-dependent signatures of individual microbial taxa within a host as well as across multiple hosts. We apply our framework to a publicly available dataset of 16S rRNA gene sequences from stool samples collected over ten months from multiple human subjects, each of whom received repeated courses of oral antibiotics. Using new diversity measures enabled by our framework, we discover groups of both phylogenetically close and distant bacterial taxa that exhibit consensus responses to antibiotic exposure across multiple human subjects. These consensus responses reveal a timeline for equilibration of sub-communities of micro-organisms with distinct physiologies, yielding insights into the successive changes that occur in microbial populations in the human gut after antibiotic treatments. Additionally, our framework leverages microbial signatures shared among human subjects to automatically design optimal experiments to interrogate dynamic properties of the microbiota in new studies. Overall, our approach provides a powerful, general-purpose framework for understanding the dynamic behaviors of complex microbial ecosystems, which we believe will prove instrumental for future studies in this field.     

An integrated approach for inference and mechanistic modeling for advancing drug development

An important challenge facing researchers in drug development is how to translate multi-omic measurements into biological insights that will help advance drugs through the clinic. Computational biology strategies are a promising approach for systematically capturing the effect of a given drug on complex molecular networks and on human physiology. This article discusses a two-pronged strategy for inferring biological interactions from large-scale multi-omic measurements and accounting for known biology via mechanistic dynamical simulations of pathways, cells, and organ- and tissue level models. These approaches are already playing a role in driving drug development by providing a rational and systematic computational framework.     

Directional and quantitative phosphorylation networks.

Directionality in protein signalling networks is due to modulated protein-protein interactions and is fundamental for proper signal progression and response to external and internal cues. This property is in part enabled by linear motifs embedding post-translational modification sites. These serve as recognition sites, guiding phosphorylation by kinases and subsequent binding of modular domains (e.g. SH2 and BRCT). Characterization of such modification-modulated interactions on a proteome-wide scale requires extensive computational and experimental analysis. Here, we review the latest advances in methods for unravelling phosphorylation-mediated cellular interaction networks. In particular, we will discuss how the combination of new quantitative mass-spectrometric technologies and computational algorithms together are enhancing mapping of these largely uncharted dynamic networks. By combining quantitative measurements of phosphorylation events with computational approaches, we argue that systems level models will help to decipher complex diseases through the ability to predict cellular systems trajectories.     

A Computational Model Predicting Disruption of Blood Vessel Development

Vascular development is a complex process regulated by dynamic biological networks that vary in topology and state across different tissues and developmental stages. Signals regulating de novo blood vessel formation (vasculogenesis) and remodeling (angiogenesis) come from a variety of biological pathways linked to endothelial cell (EC) behavior, extracellular matrix (ECM) remodeling and the local generation of chemokines and growth factors. Simulating these interactions at a systems level requires sufficient biological detail about the relevant molecular pathways and associated cellular behaviors, and tractable computational models that offset mathematical and biological complexity. Here, we describe a novel multicellular agent-based model of vasculogenesis using the CompuCell3D (http://www.compucell3d.org/) modeling environment supplemented with semi-automatic knowledgebase creation. The model incorporates vascular endothelial growth factor signals, pro- and anti-angiogenic inflammatory chemokine signals, and the plasminogen activating system of enzymes and proteases linked to ECM interactions, to simulate nascent EC organization, growth and remodeling. The model was shown to recapitulate stereotypical capillary plexus formation and structural emergence of non-coded cellular behaviors, such as a heterologous bridging phenomenon linking endothelial tip cells together during formation of polygonal endothelial cords. Molecular targets in the computational model were mapped to signatures of vascular disruption derived from in vitro chemical profiling using the EPA''s ToxCast high-throughput screening (HTS) dataset. Simulating the HTS data with the cell-agent based model of vascular development predicted adverse effects of a reference anti-angiogenic thalidomide analog, 5HPP-33, on in vitro angiogenesis with respect to both concentration-response and morphological consequences. These findings support the utility of cell agent-based models for simulating a morphogenetic series of events and for the first time demonstrate the applicability of these models for predictive toxicology.     

A rheological network model for the continuum anisotropic and viscoelastic behavior of soft tissue

The mechanical behavior of soft tissue demonstrates a number of complex features including nonlinearity, anisotropy, viscoelasticity, and growth. Characteristic features of the time-dependent and anisotropic behavior are related to the properties of various components of the tissue such as fibrous collagen and elastin networks, large proteins and sugars attached to these networks, and interstitial fluid. Attempts to model the elastic behavior of these tissues based on assumptions about the behavior of the underlying constituents have been reasonably successful, but the essential addition of viscoelasticity to these models has been met with varying success. Here, a new rheological network model is proposed using, as its basis, an orthotropic hyperelastic constitutive model for fibrous tissue and a viscoelastic reptation model for soft materials. The resulting model has been incorporated into numerical and computational models, and is shown to capture the mechanical behavior of soft tissue in various modes of deformation including uniaxial and biaxial tension and simple shear.     

Network Reconstruction Using Nonparametric Additive ODE Models

Network representations of biological systems are widespread and reconstructing unknown networks from data is a focal problem for computational biologists. For example, the series of biochemical reactions in a metabolic pathway can be represented as a network, with nodes corresponding to metabolites and edges linking reactants to products. In a different context, regulatory relationships among genes are commonly represented as directed networks with edges pointing from influential genes to their targets. Reconstructing such networks from data is a challenging problem receiving much attention in the literature. There is a particular need for approaches tailored to time-series data and not reliant on direct intervention experiments, as the former are often more readily available. In this paper, we introduce an approach to reconstructing directed networks based on dynamic systems models. Our approach generalizes commonly used ODE models based on linear or nonlinear dynamics by extending the functional class for the functions involved from parametric to nonparametric models. Concomitantly we limit the complexity by imposing an additive structure on the estimated slope functions. Thus the submodel associated with each node is a sum of univariate functions. These univariate component functions form the basis for a novel coupling metric that we define in order to quantify the strength of proposed relationships and hence rank potential edges. We show the utility of the method by reconstructing networks using simulated data from computational models for the glycolytic pathway of Lactocaccus Lactis and a gene network regulating the pluripotency of mouse embryonic stem cells. For purposes of comparison, we also assess reconstruction performance using gene networks from the DREAM challenges. We compare our method to those that similarly rely on dynamic systems models and use the results to attempt to disentangle the distinct roles of linearity, sparsity, and derivative estimation.     

Biochemical and statistical network models for systems biology

The normal and abnormal behavior of a living cell is governed by complex networks of interacting biomolecules. Models of these networks allow us to make predictions about cellular behavior under a variety of environmental cues. In this review, we focus on two broad classes of such models: biochemical network models and statistical inference models. In particular, we discuss a number of modeling approaches in the context of the assumptions that they entail, the types of data required for their inference, and the range of their applicability.     

Metabolic networks of microbial systems

In contrast to bioreactors the metabolites within the microbial cells are converted in an impure atmosphere, yet the productivity seems to be well regulated and not affected by changes in operation variables. These features are attributed to integral metabolic network within the microorganism. With the advent of neo-integrative proteomic approaches the understanding of integration of metabolic and protein-protein interaction networks have began. In this article we review the methods employed to determine the protein-protein interaction and their integration to define metabolite networks. We further present a review of current understanding of network properties, and benefit of studying the networks. The predictions using network structure, for example, in silico experiments help illustrate the importance of studying the network properties. The cells are regarded as complex system but their elements unlike complex systems interact selectively and nonlinearly to produce coherent rather than complex behaviors.     

Respiratory circuits: development, function and models

Breathing is a rhythmic motor behavior generated and controlled by hindbrain neuronal networks. Respiratory motor output arises from two distinct, but functionally interacting, rhythmogenic networks: the pre-B?tzinger complex (preB?tC) and the retrotrapezo?d nucleus/parafacial respiratory group (RTN/pFRG). This review outlines recent advances in delineating the genetic specification of the neuronal constituents of these two rhythmogenic networks, their respective roles in respiratory function and how they interact to constitute a functional respiratory circuit ensemble. The often lethal consequences of disruption to these networks found in naturally occurring developmental disorders, transgenic animals, and highly specific lesion studies are described. In addition, we discuss how recent computational models enhance our understanding of how respiratory networks generate and regulate respiratory behavior.