On Propagation of Excitation Waves in Moving Media: The FitzHugh-Nagumo Model

BACKGROUND: Existence of flows and convection is an essential and integral feature of many excitable media with wave propagation modes, such as blood coagulation or bioreactors. METHODS/RESULTS: Here, propagation of two-dimensional waves is studied in parabolic channel flow of excitable medium of the FitzHugh-Nagumo type. Even if the stream velocity is hundreds of times higher that the wave velocity in motionless medium (), steady propagation of an excitation wave is eventually established. At high stream velocities, the wave does not span the channel from wall to wall, forming isolated excited regions, which we called "restrictons". They are especially easy to observe when the model parameters are close to critical ones, at which waves disappear in still medium. In the subcritical region of parameters, a sufficiently fast stream can result in the survival of excitation moving, as a rule, in the form of "restrictons". For downstream excitation waves, the axial portion of the channel is the most important one in determining their behavior. For upstream waves, the most important region of the channel is the near-wall boundary layers. The roles of transversal diffusion, and of approximate similarity with respect to stream velocity are discussed. CONCLUSIONS: These findings clarify mechanisms of wave propagation and survival in flow

An Allosteric Mechanism for Switching between Parallel Tracks in Mammalian Sulfur Metabolism

Methionine (Met) is an essential amino acid that is needed for the synthesis of S-adenosylmethionine (AdoMet), the major biological methylating agent. Methionine used for AdoMet synthesis can be replenished via remethylation of homocysteine. Alternatively, homocysteine can be converted to cysteine via the transsulfuration pathway. Aberrations in methionine metabolism are associated with a number of complex diseases, including cancer, anemia, and neurodegenerative diseases. The concentration of methionine in blood and in organs is tightly regulated. Liver plays a key role in buffering blood methionine levels, and an interesting feature of its metabolism is that parallel tracks exist for the synthesis and utilization of AdoMet. To elucidate the molecular mechanism that controls metabolic fluxes in liver methionine metabolism, we have studied the dependencies of AdoMet concentration and methionine consumption rate on methionine concentration in native murine hepatocytes at physiologically relevant concentrations (40–400 µM). We find that both [AdoMet] and methionine consumption rates do not change gradually with an increase in [Met] but rise sharply (∼10-fold) in the narrow Met interval from 50 to 100 µM. Analysis of our experimental data using a mathematical model reveals that the sharp increase in [AdoMet] and the methionine consumption rate observed within the trigger zone are associated with metabolic switching from methionine conservation to disposal, regulated allosterically by switching between parallel pathways. This regulatory switch is triggered by [Met] and provides a mechanism for stabilization of methionine levels in blood over wide variations in dietary methionine intake

A Novel Multiplex Cell Viability Assay for High-Throughput RNAi Screening

Cell-based high-throughput RNAi screening has become a powerful research tool in addressing a variety of biological questions. In RNAi screening, one of the most commonly applied assay system is measuring the fitness of cells that is usually quantified using fluorescence, luminescence and absorption-based readouts. These methods, typically implemented and scaled to large-scale screening format, however often only yield limited information on the cell fitness phenotype due to evaluation of a single and indirect physiological indicator. To address this problem, we have established a cell fitness multiplexing assay which combines a biochemical approach and two fluorescence-based assaying methods. We applied this assay in a large-scale RNAi screening experiment with siRNA pools targeting the human kinome in different modified HEK293 cell lines. Subsequent analysis of ranked fitness phenotypes assessed by the different assaying methods revealed average phenotype intersections of 50.7±2.3%–58.7±14.4% when two indicators were combined and 40–48% when a third indicator was taken into account. From these observations we conclude that combination of multiple fitness measures may decrease false-positive rates and increases confidence for hit selection. Our robust experimental and analytical method improves the classical approach in terms of time, data comprehensiveness and cost

Defining the Boundaries of Normal Thrombin Generation: Investigations into Hemostasis

In terms of its soluble precursors, the coagulation proteome varies quantitatively among apparently healthy individuals. The significance of this variability remains obscure, in part because it is the backdrop against which the hemostatic consequences of more dramatic composition differences are studied. In this study we have defined the consequences of normal range variation of components of the coagulation proteome by using a mechanism-based computational approach that translates coagulation factor concentration data into a representation of an individual's thrombin generation potential. A novel graphical method is used to integrate standard measures that characterize thrombin generation in both empirical and computational models (e.g max rate, max level, total thrombin, time to 2 nM thrombin (“clot time”)) to visualize how normal range variation in coagulation factors results in unique thrombin generation phenotypes. Unique ensembles of the 8 coagulation factors encompassing the limits of normal range variation were used as initial conditions for the computational modeling, each ensemble representing “an individual” in a theoretical healthy population. These “individuals” with unremarkable proteome composition was then compared to actual normal and “abnormal” individuals, i.e. factor ensembles measured in apparently healthy individuals, actual coagulopathic individuals or artificially constructed factor ensembles representing individuals with specific factor deficiencies. A sensitivity analysis was performed to rank either individual factors or all possible pairs of factors in terms of their contribution to the overall distribution of thrombin generation phenotypes. Key findings of these analyses include: normal range variation of coagulation factors yields thrombin generation phenotypes indistinguishable from individuals with some, but not all, coagulopathies examined; coordinate variation of certain pairs of factors within their normal ranges disproportionately results in extreme thrombin generation phenotypes, implying that measurement of a smaller set of factors may be sufficient to identify individuals with aberrant thrombin generation potential despite normal coagulation proteome composition

Regulation of early steps of GPVI signal transduction by phosphatases: a systems biology approach

We present a data-driven mathematical model of a key initiating step in platelet activation, a central process in the prevention of bleeding following Injury. In vascular disease, this process is activated inappropriately and causes thrombosis, heart attacks and stroke. The collagen receptor GPVI is the primary trigger for platelet activation at sites of injury. Understanding the complex molecular mechanisms initiated by this receptor is important for development of more effective antithrombotic medicines. In this work we developed a series of nonlinear ordinary differential equation models that are direct representations of biological hypotheses surrounding the initial steps in GPVI-stimulated signal transduction. At each stage model simulations were compared to our own quantitative, high-temporal experimental data that guides further experimental design, data collection and model refinement. Much is known about the linear forward reactions within platelet signalling pathways but knowledge of the roles of putative reverse reactions are poorly understood. An initial model, that includes a simple constitutively active phosphatase, was unable to explain experimental data. Model revisions, incorporating a complex pathway of interactions (and specifically the phosphatase TULA-2), provided a good description of the experimental data both based on observations of phosphorylation in samples from one donor and in those of a wider population. Our model was used to investigate the levels of proteins involved in regulating the pathway and the effect of low GPVI levels that have been associated with disease. Results indicate a clear separation in healthy and GPVI deficient states in respect of the signalling cascade dynamics associated with Syk tyrosine phosphorylation and activation. Our approach reveals the central importance of this negative feedback pathway that results in the temporal regulation of a specific class of protein tyrosine phosphatases in controlling the rate, and therefore extent, of GPVI-stimulated platelet activation

On the dynamics of the adenylate energy system: homeorhesis vs homeostasis.

Biochemical energy is the fundamental element that maintains both the adequate turnover of the biomolecular structures and the functional metabolic viability of unicellular organisms. The levels of ATP, ADP and AMP reflect roughly the energetic status of the cell, and a precise ratio relating them was proposed by Atkinson as the adenylate energy charge (AEC). Under growth-phase conditions, cells maintain the AEC within narrow physiological values, despite extremely large fluctuations in the adenine nucleotides concentration. Intensive experimental studies have shown that these AEC values are preserved in a wide variety of organisms, both eukaryotes and prokaryotes. Here, to understand some of the functional elements involved in the cellular energy status, we present a computational model conformed by some key essential parts of the adenylate energy system. Specifically, we have considered (I) the main synthesis process of ATP from ADP, (II) the main catalyzed phosphotransfer reaction for interconversion of ATP, ADP and AMP, (III) the enzymatic hydrolysis of ATP yielding ADP, and (IV) the enzymatic hydrolysis of ATP providing AMP. This leads to a dynamic metabolic model (with the form of a delayed differential system) in which the enzymatic rate equations and all the physiological kinetic parameters have been explicitly considered and experimentally tested in vitro. Our central hypothesis is that cells are characterized by changing energy dynamics (homeorhesis). The results show that the AEC presents stable transitions between steady states and periodic oscillations and, in agreement with experimental data these oscillations range within the narrow AEC window. Furthermore, the model shows sustained oscillations in the Gibbs free energy and in the total nucleotide pool. The present study provides a step forward towards the understanding of the fundamental principles and quantitative laws governing the adenylate energy system, which is a fundamental element for unveiling the dynamics of cellular life

Atomic-Scale Insights into Physical Mechanisms Driving Enzymes’ “Working Cycles”

10.1016/j.bpj.2018.04.005Biophysical Journal11492027-202