Conservation of dynamic characteristics of transcriptional regulatory elements in periodic biological processes.

BACKGROUND: Cell and circadian cycles control a large fraction of cell and organismal physiology by regulating large periodic transcriptional programs that encompass anywhere from 15 to 80% of the genome despite performing distinct functions. In each case, these large periodic transcriptional programs are controlled by gene regulatory networks (GRNs), and it has been shown through genetics and chromosome mapping approaches in model systems that at the core of these GRNs are small sets of genes that drive the transcript dynamics of the GRNs. However, it is unlikely that we have identified all of these core genes, even in model organisms. Moreover, large periodic transcriptional programs controlling a variety of processes certainly exist in important non-model organisms where genetic approaches to identifying networks are expensive, time-consuming, or intractable. Ideally, the core network components could be identified using data-driven approaches on the transcriptome dynamics data already available. RESULTS: This study shows that a unified set of quantified dynamic features of high-throughput time series gene expression data are more prominent in the core transcriptional regulators of cell and circadian cycles than in their outputs, in multiple organism, even in the presence of external periodic stimuli. Additionally, we observe that the power to discriminate between core and non-core genes is largely insensitive to the particular choice of quantification of these features. CONCLUSIONS: There are practical applications of the approach presented in this study for network inference, since the result is a ranking of genes that is enriched for core regulatory elements driving a periodic phenotype. In this way, the method provides a prioritization of follow-up genetic experiments. Furthermore, these findings reveal something unexpected-that there are shared dynamic features of the transcript abundance of core components of unrelated GRNs that control disparate periodic phenotypes.

Genetic networks encode secrets of their past.

Research shows that gene duplication followed by either repurposing or removal of duplicated genes is an important contributor to evolution of gene and protein interaction networks. We aim to identify which characteristics of a network can arise through this process, and which must have been produced in a different way. To model the network evolution, we postulate vertex duplication and edge deletion as evolutionary operations on graphs. Using the novel concept of an ancestrally distinguished subgraph, we show how features of present-day networks require certain features of their ancestors. In particular, ancestrally distinguished subgraphs cannot be introduced by vertex duplication. Additionally, if vertex duplication and edge deletion are the only evolutionary mechanisms, then a graph's ancestrally distinguished subgraphs must be contained in all of the graph's ancestors. We analyze two experimentally derived genetic networks and show that our results accurately predict lack of large ancestrally distinguished subgraphs, despite this feature being statistically improbable in associated random networks. This observation is consistent with the hypothesis that these networks evolved primarily via vertex duplication. The tools we provide open the door for analyzing ancestral networks using current networks. Our results apply to edge-labeled (e.g. signed) graphs which are either undirected or directed.

Modeling Transport Regulation in Gene Regulatory Networks.

A gene regulatory network summarizes the interactions between a set of genes and regulatory gene products. These interactions include transcriptional regulation, protein activity regulation, and regulation of the transport of proteins between cellular compartments. DSGRN is a network modeling approach that builds on traditions of discrete-time Boolean models and continuous-time switching system models. When all interactions are transcriptional, DSGRN uses a combinatorial approximation to describe the entire range of dynamics that is compatible with network structure. Here we present an extension of the DGSRN approach to transport regulation across a boundary between compartments, such as a cellular membrane. We illustrate our approach by searching a model of the p53-Mdm2 network for the potential to admit two experimentally observed distinct stable periodic cycles.

Multistability in the epithelial-mesenchymal transition network.

BACKGROUND: The transitions between epithelial (E) and mesenchymal (M) cell phenotypes are essential in many biological processes like tissue development and cancer metastasis. Previous studies, both modeling and experimental, suggested that in addition to E and M states, the network responsible for these phenotypes exhibits intermediate phenotypes between E and M states. The number and importance of such states is subject to intense discussion in the epithelial-mesenchymal transition (EMT) community. RESULTS: Previous modeling efforts used traditional bifurcation analysis to explore the number of the steady states that correspond to E, M and intermediate states by varying one or two parameters at a time. Since the system has dozens of parameters that are largely unknown, it remains a challenging problem to fully describe the potential set of states and their relationship across all parameters. We use the computational tool DSGRN (Dynamic Signatures Generated by Regulatory Networks) to explore the intermediate states of an EMT model network by computing summaries of the dynamics across all of parameter space. We find that the only attractors in the system are equilibria, that E and M states dominate across parameter space, but that bistability and multistability are common. Even at extreme levels of some of the known inducers of the transition, there is a certain proportion of the parameter space at which an E or an M state co-exists with other stable steady states. CONCLUSIONS: Our results suggest that the multistability is broadly present in the EMT network across parameters and thus response of cells to signals may strongly depend on the particular cell line and genetic background.

Using extremal events to characterize noisy time series.

Experimental time series provide an informative window into the underlying dynamical system, and the timing of the extrema of a time series (or its derivative) contains information about its structure. However, the time series often contain significant measurement errors. We describe a method for characterizing a time series for any assumed level of measurement error [Formula: see text] by a sequence of intervals, each of which is guaranteed to contain an extremum for any function that [Formula: see text]-approximates the time series. Based on the merge tree of a continuous function, we define a new object called the normalized branch decomposition, which allows us to compute intervals for any level [Formula: see text]. We show that there is a well-defined total order on these intervals for a single time series, and that it is naturally extended to a partial order across a collection of time series comprising a dataset. We use the order of the extracted intervals in two applications. First, the partial order describing a single dataset can be used to pattern match against switching model output (Cummins et al. in SIAM J Appl Dyn Syst 17(2):1589-1616, 2018), which allows the rejection of a network model. Second, the comparison between graph distances of the partial orders of different datasets can be used to quantify similarity between biological replicates.

Identifying robust hysteresis in networks.

We present a new modeling and computational tool that computes rigorous summaries of network dynamics over large sets of parameter values. These summaries, organized in a database, can be searched for observed dynamics, e.g., bistability and hysteresis, to discover parameter regimes over which they are supported. We illustrate our approach on several networks underlying the restriction point of the cell cycle in humans and yeast. We rank networks by how robustly they support hysteresis, which is the observed phenotype. We find that the best 6-node human network and the yeast network share similar topology and robustness of hysteresis, in spite of having no homology between the corresponding nodes of the network. Our approach provides a new tool linking network structure and dynamics.

Comparison of Combinatorial Signatures of Global Network Dynamics Generated by Two Classes of ODE Models.

Modeling the dynamics of biological networks introduces many challenges, among them the lack of first principle models, the size of the networks, and difficulties with parameterization. Discrete time Boolean networks and related continuous time switching systems provide a computationally accessible way to translate the structure of the network to predictions about the dynamics. Recent work has shown that the parameterized dynamics of switching systems can be captured by a combinatorial object, called a Dynamic Signatures Generated by Regulatory Networks (DSGRN) database, that consists of a parameter graph characterizing a finite parameter space decomposition, whose nodes are assigned a Morse graph that captures global dynamics for all corresponding parameters. We show that for a given network there is a way to associate the same type of object by considering a continuous time ODE system with a continuous right-hand side, which we call an L-system. The main goal of this paper is to compare the two DSGRN databases for the same network. Since the L-systems can be thought of as perturbations (not necessarily small) of the switching systems, our results address the correspondence between global parameterized dynamics of switching systems and their perturbations. We show that, at corresponding parameters, there is an order preserving map from the Morse graph of the switching system to that of the L-system that is surjective on the set of attractors and bijective on the set of fixed-point attractors. We provide important examples showing why this correspondence cannot be strengthened.

The ecology of movement and behaviour: a saturated tripartite network for describing animal contacts.

Ecologists regularly use animal contact networks to describe interactions underlying pathogen transmission, gene flow, and information transfer. However, empirical descriptions of contact often overlook some features of individual movement, and decisions about what kind of network to use in a particular setting are commonly ad hoc Here, we relate individual movement trajectories to contact networks through a tripartite network model of individual, space, and time nodes. Most networks used in animal contact studies (e.g. individual association networks, home range overlap networks, and spatial networks) are simplifications of this tripartite model. The tripartite structure can incorporate a broad suite of alternative ecological metrics like home range sizes and patch occupancy patterns into inferences about contact network metrics such as modularity and degree distribution. We demonstrate the model's utility with two simulation studies using alternative forms of ecological data to constrain the tripartite network's structure and inform expectations about the harder-to-measure metrics related to contact.

Model Rejection and Parameter Reduction via Time Series.

We show how a graph algorithm for finding matching labeled paths in pairs of labeled directed graphs can be used to perform model invalidation for a class of dynamical systems including regulatory network models of relevance to systems biology. In particular, given a partial order of events describing local minima and local maxima of observed quantities from experimental time series data, we produce a labeled directed graph we call the pattern graph for which every path from root to leaf corresponds to a plausible sequence of events. We then consider the regulatory network model, which can itself be rendered into a labeled directed graph we call the search graph via techniques previously developed in computational dynamics. Labels on the pattern graph correspond to experimentally observed events, while labels on the search graph correspond to mathematical facts about the model. We give a theoretical guarantee that failing to find a match invalidates the model. As an application we consider gene regulatory models for the yeast S. cerevisiae.

Global dynamics for switching systems and their extensions by linear differential equations.

Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.

Convergence Properties of Posttranslationally Modified Protein-Protein Switching Networks with Fast Decay Rates.

A significant conceptual difficulty in the use of switching systems to model regulatory networks is the presence of so-called "black walls," co-dimension 1 regions of phase space with a vector field pointing inward on both sides of the hyperplane. Black walls result from the existence of direct negative self-regulation in the system. One biologically inspired way of removing black walls is the introduction of intermediate variables that mediate the negative self-regulation. In this paper, we study such a perturbation. We replace a switching system with a higher-dimensional switching system with rapidly decaying intermediate proteins, and compare the dynamics between the two systems. We find that the while the individual solutions of the original system can be approximated for a finite time by solutions of a sufficiently close perturbed system, there are always solutions that are not well approximated for any fixed perturbation. We also study a particular example, where global basins of attraction of the perturbed system have a strikingly different form than those of the original system. We perform this analysis using techniques that are adapted to dealing with non-smooth systems.

Combinatorial representation of parameter space for switching networks.

We describe the theoretical and computational framework for the Dynamic Signatures for Genetic Regulatory Network ( DSGRN) database. The motivation stems from urgent need to understand the global dynamics of biologically relevant signal transduction/gene regulatory networks that have at least 5 to 10 nodes, involve multiple interactions, and decades of parameters. The input to the database computations is a regulatory network, i.e. a directed graph with edges indicating up or down regulation. A computational model based on switching networks is generated from the regulatory network. The phase space dimension of this model equals the number of nodes and the associated parameter space consists of one parameter for each node (a decay rate), and three parameters for each edge (low level of expression, high level of expression, and threshold at which expression levels change). Since the nonlinearities of switching systems are piece-wise constant, there is a natural decomposition of phase space into cells from which the dynamics can be described combinatorially in terms of a state transition graph. This in turn leads to a compact representation of the global dynamics called an annotated Morse graph that identifies recurrent and nonrecurrent dynamics. The focus of this paper is on the construction of a natural computable finite decomposition of parameter space into domains where the annotated Morse graph description of dynamics is constant. We use this decomposition to construct an SQL database that can be effectively searched for dynamical signatures such as bistability, stable or unstable oscillations, and stable equilibria. We include two simple 3-node networks to provide small explicit examples of the type of information stored in the DSGRN database. To demonstrate the computational capabilities of this system we consider a simple network associated with p53 that involves 5 nodes and a 29-dimensional parameter space.

A spatial model of mosquito host-seeking behavior.

Mosquito host-seeking behavior and heterogeneity in host distribution are important factors in predicting the transmission dynamics of mosquito-borne infections such as dengue fever, malaria, chikungunya, and West Nile virus. We develop and analyze a new mathematical model to describe the effect of spatial heterogeneity on the contact rate between mosquito vectors and hosts. The model includes odor plumes generated by spatially distributed hosts, wind velocity, and mosquito behavior based on both the prevailing wind and the odor plume. On a spatial scale of meters and a time scale of minutes, we compare the effectiveness of different plume-finding and plume-tracking strategies that mosquitoes could use to locate a host. The results show that two different models of chemotaxis are capable of producing comparable results given appropriate parameter choices and that host finding is optimized by a strategy of flying across the wind until the odor plume is intercepted. We also assess the impact of changing the level of host aggregation on mosquito host-finding success near the end of the host-seeking flight. When clusters of hosts are more tightly associated on smaller patches, the odor plume is narrower and the biting rate per host is decreased. For two host groups of unequal number but equal spatial density, the biting rate per host is lower in the group with more individuals, indicative of an attack abatement effect of host aggregation. We discuss how this approach could assist parameter choices in compartmental models that do not explicitly model the spatial arrangement of individuals and how the model could address larger spatial scales and other probability models for mosquito behavior, such as Lévy distributions.

Round Trip: An Automated Pipeline for Experimental Design, Execution, and Analysis.

Synthetic biology is a complex discipline that involves creating detailed, purpose-built designs from genetic parts. This process is often phrased as a Design-Build-Test-Learn loop, where iterative design improvements can be made, implemented, measured, and analyzed. Automation can potentially improve both the end-to-end duration of the process and the utility of data produced by the process. One of the most important considerations for the development of effective automation and quality data is a rigorous description of implicit knowledge encoded as a formal knowledge representation. The development of knowledge representation for the process poses a number of challenges, including developing effective human-machine interfaces, protecting against and repairing user error, providing flexibility for terminological mismatches, and supporting extensibility to new experimental types. We address these challenges with the DARPA SD2 Round Trip software architecture. The Round Trip is an open architecture that automates many of the key steps in the Test and Learn phases of a Design-Build-Test-Learn loop for high-throughput laboratory science. The primary contribution of the Round Trip is to assist with and otherwise automate metadata creation, curation, standardization, and linkage with experimental data. The Round Trip's focus on metadata supports fast, automated, and replicable analysis of experiments as well as experimental situational awareness and experimental interpretability. We highlight the major software components and data representations that enable the Round Trip to speed up the design and analysis of experiments by 2 orders of magnitude over prior ad hoc methods. These contributions support a number of experimental protocols and experimental types, demonstrating the Round Trip's breadth and extensibility. We describe both an illustrative use case using the Round Trip for an on-the-loop experimental campaign and overall contributions to reducing experimental analysis time and increasing data product volume in the SD2 program.

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline.

Developing gene regulatory network models is a major challenge in systems biology. Several computational tools and pipelines have been developed to tackle this challenge, including the newly developed Inherent Dynamics Pipeline. The Inherent Dynamics Pipeline consists of several previously published tools that work synergistically and are connected in a linear fashion, where the output of one tool is then used as input for the following tool. As with most computational techniques, each step of the Inherent Dynamics Pipeline requires the user to make choices about parameters that don't have a precise biological definition. These choices can substantially impact gene regulatory network models produced by the analysis. For this reason, the ability to visualize and explore the consequences of various parameter choices at each step can help increase confidence in the choices and the results.The Inherent Dynamics Visualizer is a comprehensive visualization package that streamlines the process of evaluating parameter choices through an interactive interface within a web browser. The user can separately examine the output of each step of the pipeline, make intuitive changes based on visual information, and benefit from the automatic production of necessary input files for the Inherent Dynamics Pipeline. The Inherent Dynamics Visualizer provides an unparalleled level of access to a highly intricate tool for the discovery of gene regulatory networks from time series transcriptomic data.

An intrinsic oscillator drives the blood stage cycle of the malaria parasite Plasmodium falciparum.

The blood stage of the infection of the malaria parasite Plasmodium falciparum exhibits a 48-hour developmental cycle that culminates in the synchronous release of parasites from red blood cells, which triggers 48-hour fever cycles in the host. This cycle could be driven extrinsically by host circadian processes or by a parasite-intrinsic oscillator. To distinguish between these hypotheses, we examine the P. falciparum cycle in an in vitro culture system and show that the parasite has molecular signatures associated with circadian and cell cycle oscillators. Each of the four strains examined has a different period, which indicates strain-intrinsic period control. Finally, we demonstrate that parasites have low cell-to-cell variance in cycle period, on par with a circadian oscillator. We conclude that an intrinsic oscillator maintains Plasmodium's rhythmic life cycle.

DSGRN: Examining the Dynamics of Families of Logical Models.

We present a computational tool DSGRN for exploring the dynamics of a network by computing summaries of the dynamics of switching models compatible with the network across all parameters. The network can arise directly from a biological problem, or indirectly as the interaction graph of a Boolean model. This tool computes a finite decomposition of parameter space such that for each region, the state transition graph that describes the coarse dynamical behavior of a network is the same. Each of these parameter regions corresponds to a different logical description of the network dynamics. The comparison of dynamics across parameters with experimental data allows the rejection of parameter regimes or entire networks as viable models for representing the underlying regulatory mechanisms. This in turn allows a search through the space of perturbations of a given network for networks that robustly fit the data. These are the first steps toward discovering a network that optimally matches the observed dynamics by searching through the space of networks.

Interaction between arthropod filiform hairs in a fluid environment.

Many arthropods use filiform hairs as mechanoreceptors to detect air motion. In common house crickets (Acheta domestica) the hairs cover two antenna-like appendages called cerci at the rear of the abdomen. The biomechanical stimulus-response properties of individual filiform hairs have been investigated and modeled extensively in several earlier studies. However, only a few previous studies have considered viscosity-mediated coupling between pairs of hairs, and only in particular configurations. Here, we present a model capable of calculating hair-to-hair coupling in arbitrary configurations. We simulate the coupled motion of a small group of mechanosensory hairs on a cylindrical section of cercus. We have found that the coupling effects are non-negligible, and likely constrain the operational characteristics of the cercal sensory array.