Effective connectivity determines the critical dynamics of biochemical networks

Living systems comprise interacting biochemical components in very large networks. Given their high connectivity, biochemical dynamics are surprisingly not chaotic but quite robust to perturbations—a feature C.H. Waddington named canalization. Because organisms are also flexible enough to evolve, they arguably operate in a critical dynamical regime between order and chaos. The established theory of criticality is based on networks of interacting automata where Boolean truth values model presence/absence of biochemical molecules. The dynamical regime is predicted using network connectivity and node bias (to be on/off) as tuning parameters. Revising this to account for canalization leads to a significant improvement in dynamical regime prediction. The revision is based on effective connectivity, a measure of dynamical redundancy that buffers automata response to some inputs. In both random and experimentally validated systems biology networks, reducing effective connectivity makes living systems operate in stable or critical regimes even though the structure of their biochemical interaction networks predicts them to be chaotic. This suggests that dynamical redundancy may be naturally selected to maintain living systems near critical dynamics, providing both robustness and evolvability. By identifying how dynamics propagates preferably via effective pathways, our approach helps to identify precise ways to design and control network models of biochemical regulation and signalling.     

An entropic characterization of protein interaction networks and cellular robustness.

The structure of molecular networks is believed to determine important aspects of their cellular function, such as the organismal resilience against random perturbations. Ultimately, however, cellular behaviour is determined by the dynamical processes, which are constrained by network topology. The present work is based on a fundamental relation from dynamical systems theory, which states that the macroscopic resilience of a steady state is correlated with the uncertainty in the underlying microscopic processes, a property that can be measured by entropy. Here, we use recent network data from large-scale protein interaction screens to characterize the diversity of possible pathways in terms of network entropy. This measure has its origin in statistical mechanics and amounts to a global characterization of both structural and dynamical resilience in terms of microscopic elements. We demonstrate how this approach can be used to rank network elements according to their contribution to network entropy and also investigate how this suggested ranking reflects on the functional data provided by gene knockouts and RNAi experiments in yeast and Caenorhabditis elegans. Our analysis shows that knockouts of proteins with large contribution to network entropy are preferentially lethal. This observation is robust with respect to several possible errors and biases in the experimental data. It underscores the significance of entropy as a fundamental invariant of the dynamical system, and as a measure of structural and dynamical properties of networks. Our analytical approach goes beyond the phenomenological studies of cellular robustness based on local network observables, such as connectivity. One of its principal achievements is to provide a rationale to study proxies of cellular resilience and rank proteins according to their importance within the global network context.     

Dynamics and processing in finite self-similar networks

A common feature of biological networks is the geometrical property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks show self-similar connectivity at multiple scales. We analyse the relationship between topology and signalling in contrasting classes of such topologies. We find that networks differ in their ability to contain or propagate signals between arbitrary nodes in a network depending on whether they possess branching or loop-like features. Networks also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise. Surprisingly, small-world topologies, with diameters logarithmic in system size, have slower dynamical time scales, and may be less integrated (more modular) than networks with longer path lengths. All of these phenomena are essentially mesoscopic, vanishing in the infinite limit but producing strong effects at sizes and time scales relevant to biology.     

Bifurcation analysis of bistable and oscillatory dynamics in biological networks using the root‐locus method

Most of the biological systems including gene regulatory networks can be described well by ordinary differential equation models with rational non‐linearities. These models are derived either based on the reaction kinetics or by curve fitting to experimental data. This study demonstrates the applicability of the root‐locus‐based bifurcation analysis method for studying the complex dynamics of such models. The effectiveness of the bifurcation analysis in determining the exact parameter regions in each of which the system shows a certain dynamical behaviour, such as bistability, oscillation, and asymptotically equilibrium dynamics is shown by considering two mostly studied gene regulatory networks, namely Gardner''s genetic toggle switch and p53 gene network possessing two‐phase (mono‐stable/oscillation) dynamics.Inspec keywords: oscillations, curve fitting, differential equations, bifurcation, genetics, nonlinear dynamical systemsOther keywords: nonlinearities, reaction kinetics, root‐locus‐based bifurcation analysis method, complex dynamics, exact parameter regions, dynamical behaviour, equilibrium dynamics, studied gene regulatory networks, p53 gene network, bistable dynamics, oscillatory dynamics, biological networks, root‐locus method, biological systems, ordinary differential equation models     

Mutually connected phase-locked loop networks: dynamical models and design parameters

Distribution of timing signals is an essential factor for the development of digital systems for telecommunication networks, integrated circuits and manufacturing automation. Originally, this distribution was implemented by using the master?slave architecture with a precise master clock generator sending signals to phaselocked loops (PLL) working as slave oscillators. Nowadays, wireless networks with dynamical connectivity and the increase in size and operation frequency of the integrated circuits suggest that the distribution of clock signals could be more efficient if mutually connected architectures were used. Here, mutually connected PLL networks are studied and conditions for synchronous states existence are analytically derived, depending on individual node parameters and network connectivity, considering that the nodes are nonlinear oscillators with nonlinear coupling conditions. An expression for the network synchronisation frequency is obtained. The lock-in range and the transmission error bounds are analysed providing hints to the design of this kind of clock distribution system.     

Safety models incorporating graph theory based transit indicators

There is a considerable need for tools to enable the evaluation of the safety of transit networks at the planning stage. One interesting approach for the planning of public transportation systems is the study of networks. Network techniques involve the analysis of systems by viewing them as a graph composed of a set of vertices (nodes) and edges (links). Once the transport system is visualized as a graph, various network properties can be evaluated based on the relationships between the network elements. Several indicators can be calculated including connectivity, coverage, directness and complexity, among others. The main objective of this study is to investigate the relationship between network-based transit indicators and safety. The study develops macro-level collision prediction models that explicitly incorporate transit physical and operational elements and transit network indicators as explanatory variables. Several macro-level (zonal) collision prediction models were developed using a generalized linear regression technique, assuming a negative binomial error structure. The models were grouped into four main themes: transit infrastructure, transit network topology, transit route design, and transit performance and operations. The safety models showed that collisions were significantly associated with transit network properties such as: connectivity, coverage, overlapping degree and the Local Index of Transit Availability. As well, the models showed a significant relationship between collisions and some transit physical and operational attributes such as the number of routes, frequency of routes, bus density, length of bus and 3+ priority lanes.     

Monotonicity in chemical reaction systems

This article discusses the question of when the dynamical systems arising from chemical reaction networks are monotone, preserving an order induced by some proper cone. The reaction systems studied are defined by the reaction network structure while the kinetics is only constrained very weakly. Necessary and sufficient conditions on cones preserved by these systems are presented. Linear coordinate changes which make a given reaction system cooperative are characterized. Also discussed is when a reaction system restricted to an invariant subspace is cone preserving, even when the system fails to be cone preserving on the whole of phase space. Many of the proofs allow explicit construction of preserved cones. Numerous examples of chemical reaction systems are presented to illustrate the results.     

Model validation of simple-graph representations of metabolism

The large-scale properties of chemical reaction systems, such as metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information, lists of chemical reactions, available in databases. Even for the simplest type of graph representation, this reduction can be done in several ways. We investigate different simple network representations by testing how well they encode information about one biologically important network structure—network modularity (the propensity for edges to be clustered into dense groups that are sparsely connected between each other). To achieve this goal, we design a model of reaction systems where network modularity can be controlled and measure how well the reduction to simple graphs captures the modular structure of the model reaction system. We find that the network types that best capture the modular structure of the reaction system are substrate–product networks (where substrates are linked to products of a reaction) and substance networks (with edges between all substances participating in a reaction). Furthermore, we argue that the proposed model for reaction systems with tunable clustering is a general framework for studies of how reaction systems are affected by modularity. To this end, we investigate statistical properties of the model and find, among other things, that it recreates correlations between degree and mass of the molecules.     

Social insect colony as a biological regulatory system: modelling information flow in dominance networks

Social insects provide an excellent platform to investigate flow of information in regulatory systems since their successful social organization is essentially achieved by effective information transfer through complex connectivity patterns among the colony members. Network representation of such behavioural interactions offers a powerful tool for structural as well as dynamical analysis of the underlying regulatory systems. In this paper, we focus on the dominance interaction networks in the tropical social wasp Ropalidia marginata—a species where behavioural observations indicate that such interactions are principally responsible for the transfer of information between individuals about their colony needs, resulting in a regulation of their own activities. Our research reveals that the dominance networks of R. marginata are structurally similar to a class of naturally evolved information processing networks, a fact confirmed also by the predominance of a specific substructure—the ‘feed-forward loop’—a key functional component in many other information transfer networks. The dynamical analysis through Boolean modelling confirms that the networks are sufficiently stable under small fluctuations and yet capable of more efficient information transfer compared to their randomized counterparts. Our results suggest the involvement of a common structural design principle in different biological regulatory systems and a possible similarity with respect to the effect of selection on the organization levels of such systems. The findings are also consistent with the hypothesis that dominance behaviour has been shaped by natural selection to co-opt the information transfer process in such social insect species, in addition to its primal function of mediation of reproductive competition in the colony.     

Network morphospace

The structure of complex networks has attracted much attention in recent years. It has been noted that many real-world examples of networked systems share a set of common architectural features. This raises important questions about their origin, for example whether such network attributes reflect common design principles or constraints imposed by selectional forces that have shaped the evolution of network topology. Is it possible to place the many patterns and forms of complex networks into a common space that reveals their relations, and what are the main rules and driving forces that determine which positions in such a space are occupied by systems that have actually evolved? We suggest that these questions can be addressed by combining concepts from two currently relatively unconnected fields. One is theoretical morphology, which has conceptualized the relations between morphological traits defined by mathematical models of biological form. The second is network science, which provides numerous quantitative tools to measure and classify different patterns of local and global network architecture across disparate types of systems. Here, we explore a new theoretical concept that lies at the intersection between both fields, the ‘network morphospace’. Defined by axes that represent specific network traits, each point within such a space represents a location occupied by networks that share a set of common ‘morphological’ characteristics related to aspects of their connectivity. Mapping a network morphospace reveals the extent to which the space is filled by existing networks, thus allowing a distinction between actual and impossible designs and highlighting the generative potential of rules and constraints that pervade the evolution of complex systems.     

Pros and Cons: Supramolecular or Macromolecular: What Is Best for Functional Hydrogels with Advanced Properties?

Hydrogels are fascinating soft materials with unique properties. Many biological systems are based on hydrogel-like structures, underlining their versatility and relevance. The properties of hydrogels strongly depend on the structure of the building blocks they are composed of, as well as the nature of interactions between them in the network structure. Herein, gel networks made by supramolecular interactions are compared to covalent macromolecular networks, drawing conclusions about their performance and application as responsive materials.     

Response cumulants of nonlinear systems subject to external and multiplicative excitations

A general framework is presented for deriving the differential equations governing the evolution of the response cumulants of linear and nonlinear dynamical systems subjected to external and multiplicative non-Gaussian delta-correlated processes. Significant simplifications of these equations are given based on using appropriate recursive relationships for joint cumulants involving products of one or more variables. A compact form of the equations for the response cumulants is presented which provides insight into the structure of the cumulant equations for specific types of dynamical systems. The procedure developed can easily be implemented in computer software to derive symbolic cumulant equations and to estimate numerically the response cumulants of systems with power-law nonlinearities using approximate cumulant-neglect closure schemes. Comparison between the equations for cumulants and the equations for moments are also presented, with particular emphasis on the advantages and disadvantages of each formulation. Suggestions are given regarding the choice to use cumulant or moment equations for analysing the stochastic response of dynamical systems. The preferred formulation is shown to depend on the type of system analysed (linear or nonlinear), the type of system nonlinearity (polynomial or non-polynomial), and the type of excitation (external or multiplicative, delta-correlated or filtered).     

Two-edge disjoint survivable network design problem with relays: a hybrid genetic algorithm and Lagrangian heuristic approach

This article presents a network design problem with relays considering the two-edge network connectivity. The problem arises in telecommunications and logistic networks where a constraint is imposed on the distance that a commodity can travel on a route without being processed by a relay, and the survivability of the network is critical in case of a component failure. The network design problem involves selecting two-edge disjoint paths between source and destination node pairs and determining the location of relays to minimize the network design cost. The formulated problem is solved by a hybrid approach of a genetic algorithm (GA) and a Lagrangian heuristic such that the GA searches for two-edge disjoint paths for each commodity, and the Lagrangian heuristic is used to determine relays on these paths. The performance of the proposed hybrid approach is compared to the previous approaches from the literature, with promising results.     

Efficient solutions to various routing issues involved in mobile ad hoc bio-sensor networks: applying appropriate motion trajectories

Ad hoc bio-sensor networks have a very characteristic structure with three types of nodes: the command centre, the sensor nodes (animals such as rats) and the relaying nodes. We have taken up such networks and measured the throughput of such systems and suggest ways in which the throughput can be increased. It was also found that to increase the throughput of such systems, no sophisticated routing techniques or expensive transmission techniques are needed. This can be achieved by simply adopting the appropriate motion trajectories of the nodes. We have also explained the structure of these networks in detail and the routing issues involved in these networks. A Hot-Spot problem at the command centre has also been discussed. The suggestions of appropriate motions target this problem and show how an even distribution of nodes can alleviate this problem to a large extent. In addition to this, a constraint on the number of messages the sensor node can send per unit time can also make the network more efficient.     

Controlling enzymatic reactions by geometry in a biomimetic nanoscale network

We demonstrate that a transition from a compact geometry (sphere) to a structured geometry (several spheres connected by nanoconduits) in nanotube-vesicle networks (NVNs) induces an ordinary enzyme-catalyzed reaction to display wavelike properties. The reaction dynamics can be controlled directly by the geometry of the network, and such networks can be used to generate wavelike patterns in product formation. The results have bearing for understanding catalytic reactions in biological systems as well as for designing emerging wet chemical nanotechnological devices.     

Performance Evaluation of Topological Infrastructure in Internet-of-Things-Enabled Serious Games

Serious games have recently enticed many researchers due to their wide range of capabilities. A serious game is a mean of gaming for a serious job such as healthcare, education, and entertainment purposes. With the advancement in the Internet of Things, new research directions are paving the way in serious games. However, the internet connectivity of players in Internet-of-things-enabled serious games is a matter of concern and has been worth investigating. Different studies on topologies, frameworks, and architecture of communication technologies are conducted to integrate them with serious games on machine and network levels. However, the Internet of things, whose core requirement is the provision of connectivity on the application layer, has different challenges for more dynamic applications such as serious games. The performance of Internet-of-things-enabled serious games depends on the type of infrastructure (wired, wireless) network and Mobile Ad-hoc Network (MANET) and is subtly different from one type of network to another. This paper investigates the connectivity challenges in the Internet-of-things-enabled serious games using the mentioned infrastructure and identifies the core requirements for these games. It also aims to evaluate various parameters such as reliability, scalability, response time, to name a few, with varying infrastructure and network types. Results highlight the preliminary infrastructure finding and highlight the core setup for which the games are deployed. Moreover, this work will be a steppingstone for architecting the connectivity in serious games in a typical smart space with many infrastructures such as wired networks, wireless networks, and MANET.     

On reaction network implementations of neural networks

This paper is concerned with the utilization of deterministically modelled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary differential equations (ODEs) associated with certain reaction network implementations of neural networks have desirable properties including (i) existence of unique positive fixed points that are smooth in the parameters of the model (necessary for gradient descent) and (ii) fast convergence to the fixed point regardless of initial condition (necessary for efficient implementation). We do so by first making a connection between neural networks and fixed points for systems of ODEs, and then by constructing reaction networks with the correct associated set of ODEs. We demonstrate the theory by constructing a reaction network that implements a neural network with a smoothed ReLU activation function, though we also demonstrate how to generalize the construction to allow for other activation functions (each with the desirable properties listed previously). As there are multiple types of ‘networks’ used in this paper, we also give a careful introduction to both reaction networks and neural networks, in order to disambiguate the overlapping vocabulary in the two settings and to clearly highlight the role of each network’s properties.