The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises

Protein Pattern Formation

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms.Comment: 17 pages, 14 figures, review articl

Dynamic Regulation of Myosin Light Chain Phosphorylation by Rho-kinase

Myosin light chain (MLC) phosphorylation plays important roles in various cellular functions such as cellular morphogenesis, motility, and smooth muscle contraction. MLC phosphorylation is determined by the balance between activities of Rho-associated kinase (Rho-kinase) and myosin phosphatase. An impaired balance between Rho-kinase and myosin phosphatase activities induces the abnormal sustained phosphorylation of MLC, which contributes to the pathogenesis of certain vascular diseases, such as vasospasm and hypertension. However, the dynamic principle of the system underlying the regulation of MLC phosphorylation remains to be clarified. Here, to elucidate this dynamic principle whereby Rho-kinase regulates MLC phosphorylation, we developed a mathematical model based on the behavior of thrombin-dependent MLC phosphorylation, which is regulated by the Rho-kinase signaling network. Through analyzing our mathematical model, we predict that MLC phosphorylation and myosin phosphatase activity exhibit bistability, and that a novel signaling pathway leading to the auto-activation of myosin phosphatase is required for the regulatory system of MLC phosphorylation. In addition, on the basis of experimental data, we propose that the auto-activation pathway of myosin phosphatase occurs in vivo. These results indicate that bistability of myosin phosphatase activity is responsible for the bistability of MLC phosphorylation, and the sustained phosphorylation of MLC is attributed to this feature of bistability

Onset dynamics of type A botulinum neurotoxin-induced paralysis

Experimental studies have demonstrated that botulinum neurotoxin serotype A (BoNT/A) causes flaccid paralysis by a multi-step mechanism. Following its binding to specific receptors at peripheral cholinergic nerve endings, BoNT/A is internalized by receptor-mediated endocytosis. Subsequently its zinc-dependent catalytic domain translocates into the neuroplasm where it cleaves a vesicle-docking protein, SNAP-25, to block neurally evoked cholinergic neurotransmission. We tested the hypothesis that mathematical models having a minimal number of reactions and reactants can simulate published data concerning the onset of paralysis of skeletal muscles induced by BoNT/A at the isolated rat neuromuscular junction (NMJ) and in other systems. Experimental data from several laboratories were simulated with two different models that were represented by sets of coupled, first-order differential equations. In this study, the 3-step sequential model developed by Simpson (J Pharmacol Exp Ther 212:16–21,1980) was used to estimate upper limits of the times during which anti-toxins and other impermeable inhibitors of BoNT/A can exert an effect. The experimentally determined binding reaction rate was verified to be consistent with published estimates for the rate constants for BoNT/A binding to and dissociating from its receptors. Because this 3-step model was not designed to reproduce temporal changes in paralysis with different toxin concentrations, a new BoNT/A species and rate (kS) were added at the beginning of the reaction sequence to create a 4-step scheme. This unbound initial species is transformed at a rate determined by kS to a free species that is capable of binding. By systematically adjusting the values of kS, the 4-step model simulated the rapid decline in NMJ function (kS ≥0.01), the less rapid onset of paralysis in mice following i.m. injections (kS = 0.001), and the slow onset of the therapeutic effects of BoNT/A (kS < 0.001) in man. This minimal modeling approach was not only verified by simulating experimental results, it helped to quantitatively define the time available for an inhibitor to have some effect (tinhib) and the relation between this time and the rate of paralysis onset. The 4-step model predicted that as the rate of paralysis becomes slower, the estimated upper limits of (tinhib) for impermeable inhibitors become longer. More generally, this modeling approach may be useful in studying the kinetics of other toxins or viruses that invade host cells by similar mechanisms, e.g., receptor-mediated endocytosis

Chemical and Physical Environmental Conditions Underneath Mat- and Canopy-Forming Macroalgae, and Their Effects on Understorey Corals

Disturbed coral reefs are often dominated by dense mat- or canopy-forming assemblages of macroalgae. This study investigated how such dense macroalgal assemblages change the chemical and physical microenvironment for understorey corals, and how the altered environmental conditions affect the physiological performance of corals. Field measurements were conducted on macroalgal-dominated inshore reefs in the Great Barrier Reef in quadrats with macroalgal biomass ranging from 235 to 1029 g DW m−2 dry weight. Underneath mat-forming assemblages, the mean concentration of dissolved oxygen was reduced by 26% and irradiance by 96% compared with conditions above the mat, while concentrations of dissolved organic carbon and soluble reactive phosphorous increased by 26% and 267%, respectively. The difference was significant but less pronounced under canopy-forming assemblages. Dissolved oxygen declined and dissolved inorganic carbon and alkalinity increased with increasing algal biomass underneath mat-forming but not under canopy-forming assemblages. The responses of corals to conditions similar to those found underneath algal assemblages were investigated in an aquarium experiment. Coral nubbins of the species Acropora millepora showed reduced photosynthetic yields and increased RNA/DNA ratios when exposed to conditions simulating those underneath assemblages (pre-incubating seawater with macroalgae, and shading). The magnitude of these stress responses increased with increasing proportion of pre-incubated algal water. Our study shows that mat-forming and, to a lesser extent, canopy-forming macroalgal assemblages alter the physical and chemical microenvironment sufficiently to directly and detrimentally affect the metabolism of corals, potentially impeding reef recovery from algal to coral-dominated states after disturbance. Macroalgal dominance on coral reefs therefore simultaneously represents a consequence and cause of coral reef degradation

Monotone and near-monotone biochemical networks

Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a “small” number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion

Potent New Small-Molecule Inhibitor of Botulinum Neurotoxin Serotype A Endopeptidase Developed by Synthesis-Based Computer-Aided Molecular Design

Botulinum neurotoxin serotype A (BoNTA) causes a life-threatening neuroparalytic disease known as botulism. Current treatment for post exposure of BoNTA uses antibodies that are effective in neutralizing the extracellular toxin to prevent further intoxication but generally cannot rescue already intoxicated neurons. Effective small-molecule inhibitors of BoNTA endopeptidase (BoNTAe) are desirable because such inhibitors potentially can neutralize the intracellular BoNTA and offer complementary treatment for botulism. Previously we reported a serotype-selective, small-molecule BoNTAe inhibitor with a Kiapp value of 3.8±0.8 µM. This inhibitor was developed by lead identification using virtual screening followed by computer-aided optimization of a lead with an IC50 value of 100 µM. However, it was difficult to further improve the lead from micromolar to even high nanomolar potency due to the unusually large enzyme-substrate interface of BoNTAe. The enzyme-substrate interface area of 4,840 Å2 for BoNTAe is about four times larger than the typical protein-protein interface area of 750–1,500 Å2. Inhibitors must carry several functional groups to block the unusually large interface of BoNTAe, and syntheses of such inhibitors are therefore time-consuming and expensive. Herein we report the development of a serotype-selective, small-molecule, and competitive inhibitor of BoNTAe with a Ki value of 760±170 nM using synthesis-based computer-aided molecular design (SBCAMD). This new approach accounts the practicality and efficiency of inhibitor synthesis in addition to binding affinity and selectivity. We also report a three-dimensional model of BoNTAe in complex with the new inhibitor and the dynamics of the complex predicted by multiple molecular dynamics simulations, and discuss further structural optimization to achieve better in vivo efficacy in neutralizing BoNTA than those of our early micromolar leads. This work provides new insight into structural modification of known small-molecule BoNTAe inhibitors. It also demonstrates that SBCAMD is capable of improving potency of an inhibitor lead by nearly one order of magnitude, even for BoNTAe as one of the most challenging protein targets. The results are insightful for developing effective small-molecule inhibitors of protein targets with large active sites

Memory in Microbes: Quantifying History-Dependent Behavior in a Bacterium

Memory is usually associated with higher organisms rather than bacteria. However, evidence is mounting that many regulatory networks within bacteria are capable of complex dynamics and multi-stable behaviors that have been linked to memory in other systems. Moreover, it is recognized that bacteria that have experienced different environmental histories may respond differently to current conditions. These “memory” effects may be more than incidental to the regulatory mechanisms controlling acclimation or to the status of the metabolic stores. Rather, they may be regulated by the cell and confer fitness to the organism in the evolutionary game it participates in. Here, we propose that history-dependent behavior is a potentially important manifestation of memory, worth classifying and quantifying. To this end, we develop an information-theory based conceptual framework for measuring both the persistence of memory in microbes and the amount of information about the past encoded in history-dependent dynamics. This method produces a phenomenological measure of cellular memory without regard to the specific cellular mechanisms encoding it. We then apply this framework to a strain of Bacillus subtilis engineered to report on commitment to sporulation and degradative enzyme (AprE) synthesis and estimate the capacity of these systems and growth dynamics to ‘remember’ 10 distinct cell histories prior to application of a common stressor. The analysis suggests that B. subtilis remembers, both in short and long term, aspects of its cell history, and that this memory is distributed differently among the observables. While this study does not examine the mechanistic bases for memory, it presents a framework for quantifying memory in cellular behaviors and is thus a starting point for studying new questions about cellular regulation and evolutionary strategy