652 research outputs found
Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes
Enyzme kinetics are cyclic. We study a Markov renewal process model of
single-enzyme turnover in nonequilibrium steady-state (NESS) with sustained
concentrations for substrates and products. We show that the forward and
backward cycle times have idential non-exponential distributions:
\QQ_+(t)=\QQ_-(t). This equation generalizes the Haldane relation in
reversible enzyme kinetics. In terms of the probabilities for the forward
() and backward () cycles, is shown to be the
chemical driving force of the NESS, . More interestingly, the moment
generating function of the stochastic number of substrate cycle ,
follows the fluctuation theorem in the form of
Kurchan-Lebowitz-Spohn-type symmetry. When $\lambda$ = $\Delta\mu/k_BT$, we
obtain the Jarzynski-Hatano-Sasa-type equality:
1 for all , where is the fluctuating chemical work
done for sustaining the NESS. This theory suggests possible methods to
experimentally determine the nonequilibrium driving force {\it in situ} from
turnover data via single-molecule enzymology.Comment: 4 pages, 3 figure
Michaelis-Menten Relations for Complex Enzymatic Networks
All biological processes are controlled by complex systems of enzymatic
chemical reactions. Although the majority of enzymatic networks have very
elaborate structures, there are many experimental observations indicating that
some turnover rates still follow a simple Michaelis-Menten relation with a
hyperbolic dependence on a substrate concentration. The original
Michaelis-Menten mechanism has been derived as a steady-state approximation for
a single-pathway enzymatic chain. The validity of this mechanism for many
complex enzymatic systems is surprising. To determine general conditions when
this relation might be observed in experiments, enzymatic networks consisting
of coupled parallel pathways are investigated theoretically. It is found that
the Michaelis-Menten equation is satisfied for specific relations between
chemical rates, and it also corresponds to the situation with no fluxes between
parallel pathways. Our results are illustrated for simple models. The
importance of the Michaelis-Menten relationship and derived criteria for
single-molecule experimental studies of enzymatic processes are discussed.Comment: 10 pages, 4 figure
Shear induced grain boundary motion for lamellar phases in the weakly nonlinear regime
We study the effect of an externally imposed oscillatory shear on the motion
of a grain boundary that separates differently oriented domains of the lamellar
phase of a diblock copolymer. A direct numerical solution of the
Swift-Hohenberg equation in shear flow is used for the case of a
transverse/parallel grain boundary in the limits of weak nonlinearity and low
shear frequency. We focus on the region of parameters in which both transverse
and parallel lamellae are linearly stable. Shearing leads to excess free energy
in the transverse region relative to the parallel region, which is in turn
dissipated by net motion of the boundary toward the transverse region. The
observed boundary motion is a combination of rigid advection by the flow and
order parameter diffusion. The latter includes break up and reconnection of
lamellae, as well as a weak Eckhaus instability in the boundary region for
sufficiently large strain amplitude that leads to slow wavenumber readjustment.
The net average velocity is seen to increase with frequency and strain
amplitude, and can be obtained by a multiple scale expansion of the governing
equations
Blood coagulation dynamics: mathematical modeling and stability results
The hemostatic system is a highly complex multicomponent biosystem that under normal physiologic conditions maintains the fluidity of blood. Coagulation is initiated in response to endothelial surface vascular injury or certain biochemical stimuli, by the exposure of plasma to Tissue Factor (TF), that activates platelets and the coagulation cascade, inducing clot formation, growth and lysis. In recent years considerable advances have contributed to understand this highly complex process and some mathematical and numerical models have been developed. However, mathematical models that are both rigorous and comprehensive in terms of meaningful experimental data, are not available yet. In this paper a mathematical model of coagulation and fibrinolysis in flowing blood that integrates biochemical, physiologic and rheological factors, is revisited. Three-dimensional numerical simulations are performed in an idealized stenosed blood vessel where clot formation and growth are initialized through appropriate boundary conditions on a prescribed region of the vessel wall. Stability results are obtained for a simplified version of the clot model in quiescent plasma, involving some of the most relevant enzymatic reactions that follow Michaelis-Menten kinetics, and having a continuum of equilibria.CEMAT/IST through FCT [PTDC/MAT/68166/2006]; Czech Science Foundation [201/09/0917]; Grant Agency of the Academy of Sciences of the CR [IAA100190804]; Ministry of Education of Czech Republic [6840770010]info:eu-repo/semantics/publishedVersio
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Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations
We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated
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: the Michaelis-Menten approximation of
noisy enzymatic reactions, which we show to be applicable also in co-presence
of both intrinsic and extrinsic noise, a model of enzymatic futile cycle
and a genetic toggle switch. In and 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
Moment Closure - A Brief Review
Moment closure methods appear in myriad scientific disciplines in the
modelling of complex systems. The goal is to achieve a closed form of a large,
usually even infinite, set of coupled differential (or difference) equations.
Each equation describes the evolution of one "moment", a suitable
coarse-grained quantity computable from the full state space. If the system is
too large for analytical and/or numerical methods, then one aims to reduce it
by finding a moment closure relation expressing "higher-order moments" in terms
of "lower-order moments". In this brief review, we focus on highlighting how
moment closure methods occur in different contexts. We also conjecture via a
geometric explanation why it has been difficult to rigorously justify many
moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in
mathematics, physics, chemistry and quantitative biolog
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
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