Analysis of Homeostatic Mechanisms in Biochemical Networks

Cell metabolism is an extremely complicated dynamical system that maintains important cellular functions despite large changes in inputs. This “homeostasis” does not mean that the dynamical system is rigid and fixed. Typically, large changes in external variables cause large changes in some internal variables so that, through various regulatory mechanisms, certain other internal variables (concentrations or velocities) remain approximately constant over a finite range of inputs. Outside that range, the mechanisms cease to function and concentrations change rapidly with changes in inputs. In this paper we analyze four different common biochemical homeostatic mechanisms: feedforward excitation, feedback inhibition, kinetic homeostasis, and parallel inhibition. We show that all four mechanisms can occur in a single biological network, using folate and methionine metabolism as an example. Golubitsky and Stewart have proposed a method to find homeostatic nodes in networks. We show that their method works for two of these mechanisms but not the other two. We discuss the many interesting mathematical and biological questions that emerge from this analysis, and we explain why understanding homeostatic control is crucial for precision medicine.     

Random Networks of Catalytic Biochemical Reactions

Formulae for the probabilities of cycles and components are obtained for large random networks by combinatorical considerations and computer experiments. Formulae for the occurrence and distribution of cycles and of components of certain number and size are received for random networks.     

Random Networks of Catalytie Biochemical Reactions

Formulae for the probabilities of components and cycles and of their numerical distribution are obtained for large random networks by computer experiments and combinatorical considerations. Probability considerations are made and formulae for the occurrence and distribution of cycles and of components of certain number, size and structure are received for random networks.     

An Autonomously Replicating Transforming Vector for Sulfolobus solfataricus

A plasmid able to transform and to be stably maintained both in Sulfolobus solfataricus and in Escherichia coli was constructed by insertion into an E. coli plasmid of the autonomously replicating sequence of the virus particle SSV1 and a suitable mutant of the hph (hygromycin phosphotransferase) gene as the transformation marker. The vector suffered no rearrangement and/or chromosome integration, and its copy number in Sulfolobus was increased by exposure of the cells to mitomycin C.     

Metastability and Inter-Band Frequency Modulation in Networks of Oscillating Spiking Neuron Populations

Groups of neurons firing synchronously are hypothesized to underlie many cognitive functions such as attention, associative learning, memory, and sensory selection. Recent theories suggest that transient periods of synchronization and desynchronization provide a mechanism for dynamically integrating and forming coalitions of functionally related neural areas, and that at these times conditions are optimal for information transfer. Oscillating neural populations display a great amount of spectral complexity, with several rhythms temporally coexisting in different structures and interacting with each other. This paper explores inter-band frequency modulation between neural oscillators using models of quadratic integrate-and-fire neurons and Hodgkin-Huxley neurons. We vary the structural connectivity in a network of neural oscillators, assess the spectral complexity, and correlate the inter-band frequency modulation. We contrast this correlation against measures of metastable coalition entropy and synchrony. Our results show that oscillations in different neural populations modulate each other so as to change frequency, and that the interaction of these fluctuating frequencies in the network as a whole is able to drive different neural populations towards episodes of synchrony. Further to this, we locate an area in the connectivity space in which the system directs itself in this way so as to explore a large repertoire of synchronous coalitions. We suggest that such dynamics facilitate versatile exploration, integration, and communication between functionally related neural areas, and thereby supports sophisticated cognitive processing in the brain.     

The Energy Costs of Insulators in Biochemical Networks

Complex networks of biochemical reactions, such as intracellular protein signaling pathways and genetic networks, are often conceptualized in terms of modules—semiindependent collections of components that perform a well-defined function and which may be incorporated in multiple pathways. However, due to sequestration of molecular messengers during interactions and other effects, collectively referred to as retroactivity, real biochemical systems do not exhibit perfect modularity. Biochemical signaling pathways can be insulated from impedance and competition effects, which inhibit modularity, through enzymatic futile cycles that consume energy, typically in the form of ATP. We hypothesize that better insulation necessarily requires higher energy consumption. We test this hypothesis through a combined theoretical and computational analysis of a simplified physical model of covalent cycles, using two innovative measures of insulation, as well as a possible new way to characterize optimal insulation through the balancing of these two measures in a Pareto sense. Our results indicate that indeed better insulation requires more energy. While insulation may facilitate evolution by enabling a modular plug-and-play interconnection architecture, allowing for the creation of new behaviors by adding targets to existing pathways, our work suggests that this potential benefit must be balanced against the metabolic costs of insulation necessarily incurred in not affecting the behavior of existing processes.     

Control of ATP-Dependent Binding of Saccharomyces cerevisiae Origin Recognition Complex to Autonomously Replicating DNA Sequences

Eukaryotic origin recognition complexes (ORCs) play pivotal roles in the initiation of chromosomal DNA replication. ORC from the yeast, Saccharomyces cerevisiae, recognizes and binds replication origins in the late G1 phase and the binding has profound implications in the progression of the cell cycle to the S-phase. Therefore, we have quantitatively analyzed the mechanism of recognition and interaction of the yeast ORC with various elements of a yeast origin of DNA replication, the autonomously replicating sequence 1 (ARS1). ORC bound all four individual A and B elements of ARS1 with reasonably high affinities. However, the highest affinity binding was observed with a DNA sequence containing both the A and B1 elements. In addition, ATP and ADP significantly modulated the binding of ORC to the combined elements as well as modulating the binding of ORC to the element A alone or in combination with the B1 element. However, binding of ORC to individual B1, B2, and B3 elements was not responsive to nucleotides. Thus, the consensus ARS sequence in element A appeared to play a pivotal role in the ATP-dependent binding of ORC to ARS1 and likely in other ARSs or origins of DNA replication.     

Origins of Stochasticity and Burstiness in High-Dimensional Biochemical Networks

Two major approaches are known in the field of stochastic dynamics of intracellular biochemical networks. The first one places the focus of attention on the fact that many biochemical constituents vitally important for the network functionality may be present only in small quantities within the cell, and therefore the regulatory process is essentially discrete and prone to relatively big fluctuations. The second approach treats the regulatory process as essentially continuous. Complex pseudostochastic behavior in such processes may occur due to multistability and oscillatory motions within limit cycles. In this paper we outline the third scenario of stochasticity in the regulatory process. This scenario is only conceivable in high-dimensional highly nonlinear systems. In particular, we show that burstiness, a well-known phenomenon in the biology of gene expression, is a natural consequence of high dimensionality coupled with high nonlinearity. In mathematical terms, burstiness is associated with heavy-tailed probability distributions of stochastic processes describing the dynamics of the system. We demonstrate how the "shot" noise originates from purely deterministic behavior of the underlying dynamical system. We conclude that the limiting stochastic process may be accurately approximated by the "heavy-tailed" generalized Pareto process which is a direct mathematical expression of burstiness.     

Autonomously Bioluminescent Mammalian Cells for Continuous and Real-time Monitoring of Cytotoxicity

Mammalian cell-based in vitro assays have been widely employed as alternatives to animal testing for toxicological studies but have been limited due to the high monetary and time costs of parallel sample preparation that are necessitated due to the destructive nature of firefly luciferase-based screening methods. This video describes the utilization of autonomously bioluminescent mammalian cells, which do not require the destructive addition of a luciferin substrate, as an inexpensive and facile method for monitoring the cytotoxic effects of a compound of interest. Mammalian cells stably expressing the full bacterial bioluminescence (luxCDABEfrp) gene cassette autonomously produce an optical signal that peaks at 490 nm without the addition of an expensive and possibly interfering luciferin substrate, excitation by an external energy source, or destruction of the sample that is traditionally performed during optical imaging procedures. This independence from external stimulation places the burden for maintaining the bioluminescent reaction solely on the cell, meaning that the resultant signal is only detected during active metabolism. This characteristic makes the lux-expressing cell line an excellent candidate for use as a biosentinel against cytotoxic effects because changes in bioluminescent production are indicative of adverse effects on cellular growth and metabolism. Similarly, the autonomous nature and lack of required sample destruction permits repeated imaging of the same sample in real-time throughout the period of toxicant exposure and can be performed across multiple samples using existing imaging equipment in an automated fashion.     

Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.     

Oscillations in Biochemical Reaction Networks Arising from Pairs of Subnetworks

Biochemical reaction models show a variety of dynamical behaviors, such as stable steady states, multistability, and oscillations. Biochemical reaction networks with generalized mass action kinetics are represented as directed bipartite graphs with nodes for species and reactions. The bipartite graph of a biochemical reaction network usually contains at least one cycle, i.e., a sequence of nodes and directed edges which starts and ends at the same species node. Cycles can be positive or negative, and it has been shown that oscillations can arise as a result of either a positive cycle or a negative cycle. In earlier work it was shown that oscillations associated with a positive cycle can arise from subnetworks with an odd number of positive cycles. In this article we formulate a similar graph-theoretic condition, which generalizes the negative cycle condition for oscillations. This new graph-theoretic condition for oscillations involves pairs of subnetworks with an even number of positive cycles. An example of a calcium reaction network with generalized mass action kinetics is discussed in detail.     

Application of the Percolation Theory to Random Networks of Biochemical Reactions

Percolation Theory is used to get statements about random networks. It can be seen that the probability distribution that vertices belong to a finite cluster in dependence on the mean catalytic activity C = K/N has an analogy to phase transition of second kind.     

CONSTRICTOR: Constraint Modification Provides Insight into Design of Biochemical Networks

Advances in computational methods that allow for exploration of the combinatorial mutation space are needed to realize the potential of synthetic biology based strain engineering efforts. Here, we present Constrictor, a computational framework that uses flux balance analysis (FBA) to analyze inhibitory effects of genetic mutations on the performance of biochemical networks. Constrictor identifies engineering interventions by classifying the reactions in the metabolic model depending on the extent to which their flux must be decreased to achieve the overproduction target. The optimal inhibition of various reaction pathways is determined by restricting the flux through targeted reactions below the steady state levels of a baseline strain. Constrictor generates unique in silico strains, each representing an “expression state”, or a combination of gene expression levels required to achieve the overproduction target. The Constrictor framework is demonstrated by studying overproduction of ethylene in Escherichia coli network models iAF1260 and iJO1366 through the addition of the heterologous ethylene-forming enzyme from Pseudomonas syringae. Targeting individual reactions as well as combinations of reactions reveals in silico mutants that are predicted to have as high as 25% greater theoretical ethylene yields than the baseline strain during simulated exponential growth. Altering the degree of restriction reveals a large distribution of ethylene yields, while analysis of the expression states that return lower yields provides insight into system bottlenecks. Finally, we demonstrate the ability of Constrictor to scan networks and provide targets for a range of possible products. Constrictor is an adaptable technique that can be used to generate and analyze disparate populations of in silico mutants, select gene expression levels and provide non-intuitive strategies for metabolic engineering.     

NEXCADE: Perturbation Analysis for Complex Networks

Recent advances in network theory have led to considerable progress in our understanding of complex real world systems and their behavior in response to external threats or fluctuations. Much of this research has been invigorated by demonstration of the 'robust, yet fragile' nature of cellular and large-scale systems transcending biology, sociology, and ecology, through application of the network theory to diverse interactions observed in nature such as plant-pollinator, seed-dispersal agent and host-parasite relationships. In this work, we report the development of NEXCADE, an automated and interactive program for inducing disturbances into complex systems defined by networks, focusing on the changes in global network topology and connectivity as a function of the perturbation. NEXCADE uses a graph theoretical approach to simulate perturbations in a user-defined manner, singly, in clusters, or sequentially. To demonstrate the promise it holds for broader adoption by the research community, we provide pre-simulated examples from diverse real-world networks including eukaryotic protein-protein interaction networks, fungal biochemical networks, a variety of ecological food webs in nature as well as social networks. NEXCADE not only enables network visualization at every step of the targeted attacks, but also allows risk assessment, i.e. identification of nodes critical for the robustness of the system of interest, in order to devise and implement context-based strategies for restructuring a network, or to achieve resilience against link or node failures. Source code and license for the software, designed to work on a Linux-based operating system (OS) can be downloaded at http://www.nipgr.res.in/nexcade_download.html. In addition, we have developed NEXCADE as an OS-independent online web server freely available to the scientific community without any login requirement at http://www.nipgr.res.in/nexcade.html.