A Chemistry-Inspired Framework for Achieving Consensus in Wireless Sensor Networks

The aim of this paper is to show how simple interaction mechanisms, inspired by chemical systems, can provide the basic tools to design and analyze a mathematical model for achieving consensus in wireless sensor networks, characterized by balanced directed graphs. The convergence and stability of the model are first proven by using new mathematical tools, which are borrowed directly from chemical theory, and then validated by means of simulation results, for different network topologies and number of sensors. The underlying chemical theory is also used to derive simple interaction rules that may account for practical issues, such as the estimation of the number of neighbors and the robustness against perturbations. Finally, the proposed chemical solution is validated under real-world conditions by means of a four-node hardware implementation where the exchange of information among nodes takes place in a distributed manner (with no need for any admission control and synchronism procedure), simply relying on the transmission of a pulse whose rate is proportional to the state of each sensor.Comment: 12 pages, 10 figures, submitted to IEEE Sensors Journa

How the global structure of protein interaction networks evolves

Two processes can influence the evolution of protein interaction networks: addition and elimination of interactions between proteins, and gene duplications increasing the number of proteins and interactions. The rates of these processes can be estimated from available Saccharomyces cerevisiae genome data and are sufficiently high to affect network structure on short time scales. For instance, more than 100 interactions may be added to the yeast network every million years, a substantial fraction of which adds previously unconnected proteins to the network. Highly connected proteins show a greater rate of interaction turnover than proteins with few interactions. From these observations one can explain ? without natural selection on global network structure ? the evolutionary sustenance of the most prominent network feature, the distribution of the frequency P(d) of proteins with d neighbors, which is a broad-tailed distribution. This distribution is independent of the experimental approach providing nformation on network structure

Biochemical Networks Across Planets and Scales

abstract: Biochemical reactions underlie all living processes. Their complex web of interactions is difficult to fully capture and quantify with simple mathematical objects. Applying network science to biology has advanced our understanding of the metabolisms of individual organisms and the organization of ecosystems, but has scarcely been applied to life at a planetary scale. To characterize planetary-scale biochemistry, I constructed biochemical networks using global databases of annotated genomes and metagenomes, and biochemical reactions. I uncover scaling laws governing biochemical diversity and network structure shared across levels of organization from individuals to ecosystems, to the biosphere as a whole. Comparing real biochemical reaction networks to random reaction networks reveals the observed biological scaling is not a product of chemistry alone, but instead emerges due to the particular structure of selected reactions commonly participating in living processes. I perform distinguishability tests across properties of individual and ecosystem-level biochemical networks to determine whether or not they share common structure, indicative of common generative mechanisms across levels. My results indicate there is no sharp transition in the organization of biochemistry across distinct levels of the biological hierarchy—a result that holds across different network projections. Finally, I leverage these large biochemical datasets, in conjunction with planetary observations and computational tools, to provide a methodological foundation for the quantitative assessment of biology’s viability amongst other geospheres. Investigating a case study of alkaliphilic prokaryotes in the context of Enceladus, I find that the chemical compounds observed on Enceladus thus far would be insufficient to allow even these extremophiles to produce the compounds necessary to sustain a viable metabolism. The environmental precursors required by these organisms provides a reference for the compounds which should be prioritized for detection in future planetary exploration missions. The results of this framework have further consequences in the context of planetary protection, and hint that forward contamination may prove infeasible without meticulous intent. Taken together these results point to a deeper level of organization in biochemical networks than what has been understood so far, and suggests the existence of common organizing principles operating across different levels of biology and planetary chemistry.Dissertation/ThesisDoctoral Dissertation Geological Sciences 201

Stochastic Ratcheting on a Funneled Energy Landscape is Necessary for Highly Efficient Contractility of Actomyosin Force Dipoles

Current understanding of how contractility emerges in disordered actomyosin networks of non-muscle cells is still largely based on the intuition derived from earlier works on muscle contractility. This view, however, largely overlooks the free energy gain following passive cross-linker binding, which, even in the absence of active fluctuations, provides a thermodynamic drive towards highly overlapping filamentous states. In this work, we shed light on this phenomenon, showing that passive cross-linkers, when considered in the context of two anti-parallel filaments, generate noticeable contractile forces. However, as binding free energy of cross-linkers is increased, a sharp onset of kinetic arrest follows, greatly diminishing effectiveness of this contractility mechanism, allowing the network to contract only with weakly resisting tensions at its boundary. We have carried out stochastic simulations elucidating this mechanism, followed by a mean-field treatment that predicts how contractile forces asymptotically scale at small and large binding energies, respectively. Furthermore, when considering an active contractile filament pair, based on non-muscle myosin II, we found that the non-processive nature of these motors leads to highly inefficient force generation, due to recoil slippage of the overlap during periods when the motor is dissociated. However, we discovered that passive cross-linkers can serve as a structural ratchet during these unbound motor time spans, resulting in vast force amplification. Our results shed light on the non-equilibrium effects of transiently binding proteins in biological active matter, as observed in the non-muscle actin cytoskeleton, showing that highly efficient contractile force dipoles result from synergy of passive cross-linker and active motor dynamics, via a ratcheting mechanism on a funneled energy landscape.Comment: 13 pages, 6 figure

Stochastic neural field theory and the system-size expansion

We analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and transition rates are chosen so that in the thermodynamic or deterministic limit (N → ∞) we recover standard activity–based or voltage–based rate models. We derive the lowest order corrections to these rate equations for large but finite N using two different approximation schemes, one based on the Van Kampen system-size expansion and the other based on path integral methods. Both methods yield the same series expansion of the moment equations, which at O(1/N ) can be truncated to form a closed system of equations for the first and second order moments. Taking a continuum limit of the moment equations whilst keeping the system size N fixed generates a system of integrodifferential equations for the mean and covariance of the corresponding stochastic neural field model. We also show how the path integral approach can be used to study large deviation or rare event statistics underlying escape from the basin of attraction of a stable fixed point of the mean–field dynamics; such an analysis is not possible using the system-size expansion since the latter cannot accurately\ud determine exponentially small transitions