Sequential behavior and stability properties of enzymatic neuron networks

The cycle structure of enzymatic neural networks may be characterized in terms of number of cycles exhibited, size of cycle state sets and cycle lengths. Simulation experiments show that the stability properties of these networks have some unusual features which are not exhibited by networks of two-state switching elements or by randomly constructed ecosystem models. The behavioral and structural stability of these systems decreases with their structural complexity, as measured by the number of components. The behavioral and structural stability of enzymatic neural networks also decreases with structural complexity, as measured by the number of excitase types, but only up to the middle level of excitases per neuron. This is the point of highest potential responsiveness of the system to environmental stimuli. Beyond this point the behavioral and structural stability increase. This is due to the fact that the number of possible states increases up to this point and decreases beyond it. The number of possible states, not the number of components, serves as the useful measure of complexity in these types of systems. The selection circuits learning algorithm has been used to evolve networks whose cycle structures have desired features.     

Structure-Based Network Analysis of Activation Mechanisms in the ErbB Family of Receptor Tyrosine Kinases: The Regulatory Spine Residues Are Global Mediators of Structural Stability and Allosteric Interactions

The ErbB protein tyrosine kinases are among the most important cell signaling families and mutation-induced modulation of their activity is associated with diverse functions in biological networks and human disease. We have combined molecular dynamics simulations of the ErbB kinases with the protein structure network modeling to characterize the reorganization of the residue interaction networks during conformational equilibrium changes in the normal and oncogenic forms. Structural stability and network analyses have identified local communities integrated around high centrality sites that correspond to the regulatory spine residues. This analysis has provided a quantitative insight to the mechanism of mutation-induced “superacceptor” activity in oncogenic EGFR dimers. We have found that kinase activation may be determined by allosteric interactions between modules of structurally stable residues that synchronize the dynamics in the nucleotide binding site and the αC-helix with the collective motions of the integrating αF-helix and the substrate binding site. The results of this study have pointed to a central role of the conserved His-Arg-Asp (HRD) motif in the catalytic loop and the Asp-Phe-Gly (DFG) motif as key mediators of structural stability and allosteric communications in the ErbB kinases. We have determined that residues that are indispensable for kinase regulation and catalysis often corresponded to the high centrality nodes within the protein structure network and could be distinguished by their unique network signatures. The optimal communication pathways are also controlled by these nodes and may ensure efficient allosteric signaling in the functional kinase state. Structure-based network analysis has quantified subtle effects of ATP binding on conformational dynamics and stability of the EGFR structures. Consistent with the NMR studies, we have found that nucleotide-induced modulation of the residue interaction networks is not limited to the ATP site, and may enhance allosteric cooperativity with the substrate binding region by increasing communication capabilities of mediating residues.     

Implications of Network Topology on Stability

In analogy to chemical reaction networks, I demonstrate the utility of expressing the governing equations of an arbitrary dynamical system (interaction network) as sums of real functions (generalized reactions) multiplied by real scalars (generalized stoichiometries) for analysis of its stability. The reaction stoichiometries and first derivatives define the network’s “influence topology”, a signed directed bipartite graph. Parameter reduction of the influence topology permits simplified expression of the principal minors (sums of products of non-overlapping bipartite cycles) and Hurwitz determinants (sums of products of the principal minors or the bipartite cycles directly) for assessing the network’s steady state stability. Visualization of the Hurwitz determinants over the reduced parameters defines the network’s stability phase space, delimiting the range of its dynamics (specifically, the possible numbers of unstable roots at each steady state solution). Any further explicit algebraic specification of the network will project onto this stability phase space. Stability analysis via this hierarchical approach is demonstrated on classical networks from multiple fields.     

Regulation of cell proliferation and survival: Convergence of protein kinases and caspases

Intricate networks of protein kinases are intimately involved in the regulation of cellular events related to cell proliferation and survival. In addition to protein kinases, cells also contain networks of proteases including aspartic-acid directed caspases organized in cascades that play a major role in the regulation of cell survival through their involvement in the initiation and execution phases of apoptosis. Perturbations in regulatory protein kinase and caspase networks induce alterations in cell survival and frequently accompany transformation and tumorigenesis. Furthermore, recent studies have documented that caspases or their substrates are subject to phosphorylation in cells illustrating a potential convergence of protein kinase and caspase signaling pathways. Interestingly, a number of caspase substrates are protected from cleavage when they are phosphorylated at sites that are adjacent to caspase cleavage sites. While it is theoretically possible that many distinct protein kinases could protect proteins from caspase-mediated cleavage, protein kinase CK2 is of particular interest because acidic amino acids, including aspartic acid residues that are recognized by caspases, are its dominant specificity determinants.     

ATM and ATR: networking cellular responses to DNA damage

Maintenance of genome stability depends on the appropriate response to DNA damage. This response is based on complex networks of signaling pathways that activate numerous processes and lead ultimately to damage repair and cellular survival - or apoptosis. The protein kinases ATM and ATR are master controllers of some of these networks, acting either in concert or separately to orchestrate the responses to specific types of DNA damage or stalled replication. Understanding their mode of action is essential to our understanding of how cells cope with genotoxic stress.     

Spatial cycles in G‐protein crowd control

The nature of living systems and their apparent resilience to the second law of thermodynamics has been the subject of extensive investigation and imaginative speculation. The segregation and compartmentalization of proteins is one manifestation of this departure from equilibrium conditions; the effect of which is now beginning to be elucidated. This should not come as a surprise, as even a cursory inspection of cellular processes reveals the large amount of energetic cost borne to maintain cell‐scale patterns, separations and gradients of molecules. The G‐proteins, kinases, calcium‐responsive proteins have all been shown to contain reaction cycles that are inherently coupled to their signalling activities. G‐proteins represent an important and diverse toolset used by cells to generate cellular asymmetries. Many small G‐proteins in particular, are dynamically acylated to modify their membrane affinities, or localized in an activity‐dependent manner, thus manipulating the mobility modes of these proteins beyond pure diffusion and leading to finely tuned steady state partitioning into cellular membranes. The rates of exchange of small G‐proteins over various compartments, as well as their steady state distributions enrich and diversify the landscape of possibilities that GTPase‐dependent signalling networks can display over cellular dimensions. The chemical manipulation of spatial cycles represents a new approach for the modulation of cellular signalling with potential therapeutic benefits.     

The effects of reversibility and noise on stochastic phosphorylation cycles and cascades

The phosphorylation-dephosphorylation cycle is a common motif in cellular signaling networks. Previous work has revealed that, when driven by a noisy input signal, these cycles may exhibit bistable behavior. Here, a recently introduced theorem on network bistability is applied to prove that the existence of bistability is dependent on the stochastic nature of the system. Furthermore, the thermodynamics of simple cycles and cascades is investigated in the stochastic setting. Because these cycles are driven by the ATP hydrolysis potential, they may operate far from equilibrium. It is shown that sufficient high ATP hydrolysis potential is necessary for the existence of a bistable steady state. For the single-cycle system, the ensemble average behavior follows the ultrasensitive response expected from analysis of the corresponding deterministic system, but with significant fluctuations. For the two-cycle cascade, the average behavior begins to deviate from the expected response of the deterministic system. Examination of a two-cycle cascade reveals that the bistable steady state may be either propagated or abolished along a cascade, depending on the parameters chosen. Likewise, the variance in the response can be maximized or minimized by tuning the number of enzymes in the second cycle.     

Thermodynamics of Random Reaction Networks

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.     

Influence of Input Parameters on Dynamic Orbital Stability of Walking: In-Silico and Experimental Evaluation

Many measures aiming to assess the stability of human motion have been proposed in the literature, but still there is no commonly accepted way to define or quantify locomotor stability. Among these measures, orbital stability analysis via Floquet multipliers is still under debate. Some of the controversies concerning the use of this technique could lie in the absence of a standard implementation. The aim of this study was to analyse the influence of i) experimental measurement noise, ii) variables selected for the construction of the state space, and iii) number of analysed cycles on the outputs of orbital stability applied to walking. The analysis was performed on a 2-dimensional 5-link walking model and on a sample of 10 subjects performing long over-ground walks. Noise resulting from stereophotogrammetric and accelerometric measurement systems was simulated in the in-silico analysis. Maximum Floquet multipliers resulted to be affected by both number of analysed strides and state space composition. The effect of experimental noise was found to be slightly more potentially critical when analysing stereophotogrammetric data then when dealing with acceleration data. Experimental and model results were comparable in terms of overall trend, but a difference was found in the influence of the number of analysed cycles.     

The effect of negative feedback loops on the dynamics of boolean networks

Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distance-to-positive-feedback which, in essence, captures the number of independent negative feedback loops in the network, a property inherent in the network topology. Through a computational study using Boolean networks, it is shown that distance-to-positive-feedback has a strong influence on network dynamics and correlates very well with the number and length of limit cycles in the phase space of the network. To be precise, it is shown that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to decrease (increase). These conclusions are consistent with the fact that certain natural biological networks exhibit generally regular behavior and have fewer negative feedback loops than randomized networks with the same number of nodes and same connectivity.     

SQ/TQ cluster domains: concentrated ATM/ATR kinase phosphorylation site regions in DNA-damage-response proteins

ATM/ATR-like protein kinases play central roles in the maintenance of genome stability and phosphorylate numerous substrates in response to DNA damage, preferentially on SQ or TQ motifs. ATM/ATR substrates often contain several closely spaced SQ/TQ motifs in regions that have been termed SQ/TQ cluster domains (SCDs). SCDs are now considered a structural hallmark of DNA-damage-response proteins. Mutational analyses of a number of SCD-containing proteins indicate that multisite phosphorylation of SQ/TQ motifs is required for normal DNA-damage responses, most commonly by mediating protein-protein interactions in the formation of DNA-damage-induced complexes. SCD sequences are highly diverse and these domains may be largely unfolded in their native state rather than adopting a common three-dimensional fold. Structural disorder of SCDs could be advantageous for efficient phosphorylation by ATM/ATR kinases and also enable them to be molded into distinct conformations to facilitate flexible interactions with multiple binding partners.     

Maximum Number of Fixed Points in Regulatory Boolean Networks

Boolean networks (BNs) have been extensively used as mathematical models of genetic regulatory networks. The number of fixed points of a BN is a key feature of its dynamical behavior. Here, we study the maximum number of fixed points in a particular class of BNs called regulatory Boolean networks, where each interaction between the elements of the network is either an activation or an inhibition. We find relationships between the positive and negative cycles of the interaction graph and the number of fixed points of the network. As our main result, we exhibit an upper bound for the number of fixed points in terms of minimum cardinality of a set of vertices meeting all positive cycles of the network, which can be applied in the design of genetic regulatory networks.     

Calpain mediates integrin-induced signaling at a point upstream of Rho family members.

Integrin-induced adhesion leads to cytoskeletal reorganizations, cell migration, spreading, proliferation, and differentiation. The details of the signaling events that induce these changes in cell behavior are not well understood but they appear to involve activation of Rho family members which activate signaling molecules such as tyrosine kinases, serine/threonine kinases, and lipid kinases. The result is the formation of focal complexes, focal adhesions, and bundles and networks of actin filaments that allow the cell to spread. The present study shows that mu-calpain is active in adherent cells, that it cleaves proteins known to be present in focal complexes and focal adhesions, and that overexpression of mu-calpain increased the cleavage of these proteins, induced an overspread morphology and induced an increased number of stress fibers and focal adhesions. Inhibition of calpain with membrane permeable inhibitors or by expression of a dominant negative form of mu-calpain resulted in an inability of cells to spread or to form focal adhesions, actin filament networks, or stress fibers. Cells expressing constitutively active Rac1 could still form focal complexes and actin filament networks (but not focal adhesions or stress fibers) in the presence of calpain inhibitors; cells expressing constitutively active RhoA could form focal adhesions and stress fibers. Taken together, these data indicate that calpain plays an important role in regulating the formation of focal adhesions and Rac- and Rho-induced cytoskeletal reorganizations and that it does so by acting at sites upstream of both Rac1 and RhoA.     

Evolution of Osmosensory MAP Kinase Signaling Pathways

Mitogen-activated protein (MAP) kinases constitute a large familyof proteins with many functions. They are represented by a multitudeof paralogous isoforms in yeast, vertebrates, and other eukaryotes.A phylogenetically conserved function of MAP kinases is to carryosmotic signals from sensory to target elements of cells. Eventhough this function of MAP kinases is ubiquitous and characteristicof unicellular and multicellular eukaryotes alike the contingenciesbetween individual MAP kinases, sensor elements, and targetelements have been subject to vast modification during evolution.Extensive networking of MAP kinase cascades with other signalingpathways is reflected by the large number of diverse signalsthat can be carried by a single MAP kinase pathway and flexibleactivation kinetics. It is emerging that the most importantfunction of MAP kinase networks may not be signal amplificationbut integration of information about the setpoint of environmentalparameters (including osmolality) with other physiological processesto control cell function. Insight into how this cellular integrationof information is achieved by MAP kinase networks will shedlight on the principles of cell dynamics and adaptation.     

Typology of life cycles of ground beetles (Coleoptera,Carabidae) in Western Palaearctic

An original classification of the life cycles of ground beetles from Western Palaearctic is proposed. The classification is based on a combination of five criteria: duration, number of generations per season, phenology of reproduction, stability, and repeatability of reproduction. According to the individual lifespan, the cycles are subdivided into annual and biennial ones. The annual life cycles may be uni-and bivoltine, whereas biennial ones are always univoltine. By the time of reproduction, winter-spring, spring, spring-summer, early summer, summer, late summer, summer-autumnal, autumnal, autumn-winter, winter, and aseasonal species are distinguished. The biennial and bivoltine cycles may be of both facultative and obligate nature. Species living only one season and having a continuous reproductive period are designated as semelparous, while those breeding during two or more years or having several distinct periods of reproduction in one season, as iteroparous. By now, 30 variants of life cycles in Carabidae from western Palaearctic have been established. Repeated similarly directed modifications of the life cycle may produce essentially different seasonal rhythms in some individuals. In this case, two subpopulation groups usually appear within the population. Under the most unfavorable conditions, these groups become practically isolated and hibernate at different ontogenetic stages. The individual development in each of these groups takes two years with the same seasonal rhythm. Among the types considered, only obligate-bivoltine life cycles are always polyvariant, but annual univoltine and obligate-biennial ones are always univariant. The facultative-bivoltine and biennial life cycles may be realized as uni-and polyvariant ones, depending on the environmental conditions.     

Signaling cascades as cellular devices for spatial computations

Signaling networks usually include protein-modification cycles. Cascades of such cycles are the backbones of multiple signaling pathways. Protein gradients emerge from the spatial separation of opposing enzymes, such as kinases and phosphatases, or guanine nucleotide exchange factors (GEFs) and GTPase activating proteins (GAPs) for GTPase cycles. We show that different diffusivities of an active protein form and an inactive form leads to spatial gradients of protein abundance in the cytoplasm. For a cascade of cycles, using a discrete approximation of the space, we derive an analytical expression for the spatial gradients and show that it converges to an exact solution with decreasing the size of the quantization. Our results facilitate quantitative analysis of the dependence of spatial gradients on the network topology and reaction kinetics. We demonstrate how different cascade designs filter and process the input information to generate precise, complex spatial guidance for multiple GTPase effector processes. Thus, protein-modification cascades may serve as devices to compute complex spatial distributions of target proteins within intracellular space.