What can be stated by the Glansdorff–Prigogine criterion concerning the stability of mass-action kinetic systems?

1999 ◽  
Vol 110 (13) ◽  
pp. 6128-6134 ◽  
Author(s):  
Thomas Wilhelm ◽  
Peter Hänggi
Keyword(s):  
Mass Action ◽  
Mass Action Kinetic ◽  
The Stability

scholarly journals Three-dimensional stochastic model of actin–myosin binding in the sarcomere lattice

2016 ◽  
Vol 148 (6) ◽  
pp. 459-488 ◽  
Author(s):  
Srboljub M. Mijailovich ◽  
Oliver Kayser-Herold ◽  
Boban Stojanovic ◽  
Djordje Nedic ◽  
Thomas C. Irving ◽  
...  
Keyword(s):  
Kinetic Models ◽  
Striated Muscle ◽  
Three Dimensional ◽  
Limited Range ◽  
Mass Action ◽  
Myosin Filament ◽  
Mass Action Kinetic ◽  
Cross Bridge ◽  
Myosin Binding ◽  
Cross Bridges

The effect of molecule tethering in three-dimensional (3-D) space on bimolecular binding kinetics is rarely addressed and only occasionally incorporated into models of cell motility. The simplest system that can quantitatively determine this effect is the 3-D sarcomere lattice of the striated muscle, where tethered myosin in thick filaments can only bind to a relatively small number of available sites on the actin filament, positioned within a limited range of thermal movement of the myosin head. Here we implement spatially explicit actomyosin interactions into the multiscale Monte Carlo platform MUSICO, specifically defining how geometrical constraints on tethered myosins can modulate state transition rates in the actomyosin cycle. The simulations provide the distribution of myosin bound to sites on actin, ensure conservation of the number of interacting myosins and actin monomers, and most importantly, the departure in behavior of tethered myosin molecules from unconstrained myosin interactions with actin. In addition, MUSICO determines the number of cross-bridges in each actomyosin cycle state, the force and number of attached cross-bridges per myosin filament, the range of cross-bridge forces and accounts for energy consumption. At the macroscopic scale, MUSICO simulations show large differences in predicted force-velocity curves and in the response during early force recovery phase after a step change in length comparing to the two simplest mass action kinetic models. The origin of these differences is rooted in the different fluxes of myosin binding and corresponding instantaneous cross-bridge distributions and quantitatively reflects a major flaw of the mathematical description in all mass action kinetic models. Consequently, this new approach shows that accurate recapitulation of experimental data requires significantly different binding rates, number of actomyosin states, and cross-bridge elasticity than typically used in mass action kinetic models to correctly describe the biochemical reactions of tethered molecules and their interaction energetics.

scholarly journals Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yongli Cai ◽  
Xixi Wang ◽  
Weiming Wang ◽  
Min Zhao
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Stochastic Dynamics ◽  
Complex Dynamics ◽  
Deterministic Model ◽  
Mass Action ◽  
Sirs Epidemic Model ◽  
Stochastic Epidemic ◽  
The Stability ◽  
Disease Free

We investigate the complex dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectious individuals to that of susceptible individuals. We first deal with the boundedness, dissipation, persistence, and the stability of the disease-free and endemic points of the deterministic model. And then we prove the existence and uniqueness of the global positive solutions, stochastic boundedness, and permanence for the stochastic epidemic model. Furthermore, we perform some numerical examples to validate the analytical findings. Needless to say, both deterministic and stochastic epidemic models have their important roles.

scholarly journals Spectrophotometric study of competitive complexation equilibria involving overlapped spectral responding species: Determination of the stability constant of bismuth-pyrophosphate complex

2012 ◽  
Vol 10 (6) ◽  
pp. 1875-1881
Author(s):  
Tsvetanka Nedeltcheva ◽  
Andriana Surleva ◽  
Liliya Nikolova ◽  
Rahila Borissova ◽  
Stela Georgieva
Keyword(s):  
Stability Constant ◽  
Spectrophotometric Study ◽  
Mass Action ◽  
Competitive Reaction ◽  
Species Determination ◽  
Complex Formation Equilibria ◽  
Mass Action Law ◽  
Multivariable Regression ◽  
Equilibrium Concentrations ◽  
The Stability

AbstractSpectrophotometric study of competitive complex formation equilibria involving overlapped spectral responding species applying a simple and versatile algorithm was carried out. The algorithm involves multivariable regression for calculation of equilibrium concentrations from multiwavelength data and mass action law for the stability constant calculation. The used regression functions are part of common statistical software. Stability constants and complex stoichiometry of competing equilibria were simultaneously determined. The species concentration profiles at several spectral overlapping and α-coefficient of competing reaction were obtained. Non-absorbing bismuth — pyrophosphate (PPh) system was studied as a competitive reaction of bismuth — 4-(2-Pyridylazo) resorcinol (PAR) complex. The formation of Bi-PPh complex with 1:1 stoichiometry was proved in the studied concentration region (CBi = 1×10−5 mol L−1; CPPh = 5×10−6 − 1×10−4 mol L−1). The stability constant of the complex at pH 1 and µ = 1.0 have been determined: logβ = 4.2±0.2.

The KOH-Number Test and Its Application to the Compounding of Zinc Oxide in Rubber Latex

1939 ◽  
Vol 12 (3) ◽  
pp. 590-603
Author(s):  
H. F. Jordan
Keyword(s):  
Zinc Oxide ◽  
Gum Arabic ◽  
Ammonia Concentration ◽  
Zinc Ion ◽  
Mass Action ◽  
Zinc Hydroxide ◽  
Latex Particles ◽  
Electrometric Titration ◽  
Maximum Stability ◽  
The Stability

Abstract 1. From measurements of the cataphoretic mobility of latex particles in potassium and calcium buffers, respectively, it has been calculated that in order to obtain high stability in latex compounds, the concentration of divalent ions must be of the order of 0.002 M or less. 2. Measurements of the cataphoretic mobility of latex particles suspended in solutions of constant zinc and ammonia concentrations indicate that in the presence of dissolved zinc oxide the stability of latex is increased with increasing pH above pH 9.6. This is attributed to conversion of divalent zinc ammonia ion (Zn(NH3)4++) into monovalent zinc ammonia hydroxide ion (Zn(NH3)3OH+). 3. A consideration of the mass action equations for zinc hydroxide and zinc ammonia hydroxide shows that the concentration of divalent zinc ion decreases rapidly as the ammonia concentration is reduced or as the pH is increased. 4. The EOH number of latex is defined as the number of grams of KOH per 100 grams of rubber corresponding to the end point (at pH 10.7–11) in the electrometric titration of latex with KOH. Experimental precautions in determining the KOH number are discussed. 5. Data are given which show that the KOH number of a normal latex may be reduced more than tenfold by creaming three times from 33% T.S. to 62% T.S. 6. The KOH numbers of commercially available normal latices have been found to vary between 1.2 and 2.4, and those of creamed or centrifuged latices between 0.55 and 0.95. 7. The amount of KOH for optimum stabilization (i.e., maximum stability, minimum viscosity and minimum change of properties with time) of zinc oxide compounds containing no added buffering ingredients varies with the latex, and is numerically equal to the KOH number. This quantity of KOH produces a pH of 10.7–11.0. 8. If appreciable amounts of protective ingredients such as casein, glue or gum arabic are added in compounding, sufficient additional KOH must be added to maintain a pH of 10.7–11 in the latex compound. The amounts of KOH required may be determined by electrometric titration of the protective ingredients.

scholarly journals Routes to Multiple Equilibria for Mass-Action Kinetic Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Antonio A. Alonso ◽  
Irene Otero-Muras ◽  
Manuel Pájaro
Keyword(s):  
State Space ◽  
Dynamic Systems ◽  
Multiple Equilibria ◽  
Space Form ◽  
Explicit Representation ◽  
Mass Action ◽  
Positive Parameter ◽  
Mass Action Kinetics ◽  
Mass Action Kinetic ◽  
Parameter Dependent

In this work we explore two potential mechanisms inducing multiple equilibria for weakly reversible networks with mass-action kinetics. The study is performed on a class of polynomial dynamic systems that, under some mild assumptions, are able to accommodate in their state-space form weakly reversible mass-action kinetic networks. The contribution is twofold. We provide an explicit representation of the set of all positive equilibria attained by the system class in terms of a set of (positive parameter dependent) algebraic relations. With this in hand, we prove that deficiency-one networks can only admit multiple equilibria via folding of the equilibrium manifold, whereas a bifurcation leading to multiple branches is only possible in networks with deficiencies larger than one. Interestingly, some kinetic networks within this latter class are capable of sustaining multiple equilibria for any reaction simplex, as we illustrate with one example.

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