Increasing the predictability and reducing the rate of side effects of oral anticoagulant treatment (OAT) requires further clarification of the cause of about 50% of the interindividual variability of OAT response that is currently unaccounted for. We explore numerically the hypothesis that the effect of the interindividual expression variability of coagulation proteins, which does not usually result in a variability of the coagulation times in untreated subjects, is unmasked by OAT.
We introduce systematic approaches to chemical kinetics based on the use of phase-phase (log-log) representations of the rate equations. For slow processes, we obtain a corrected form of the mass-action law, where the concentrations are replaced by kinetic activities. For fast reactions, delay expressions are derived. The phase-phase expansion is, in general, applicable to kinetic and transport processes. A mechanism is introduced for the occurrence of a generalized mass-action law as a result of self-similar recycling. We show that our self-similar recycling model applied to prothrombin assays reproduces the empirical equations for the International Normalized Ratio calibration (INR), as well as the Watala, Golanski, and Kardas relation (WGK) for the dependence of the INR on the concentrations of coagulation factors. Conversely, the experimental calibration equation for the INR, combined with the experimental WGK relation, without the use of theoretical models, leads to a generalized mass-action type kinetic law.
The Luo-Rudy I model, describing the electrophysiology of a ventricular cardiomyocyte, is associated with an 8-dimensional discontinuous dynamical system with logarithmic and exponential non-linearities depending on 15 parameters. The associated stationary problem was reduced to a nonlinear system in only two unknowns, the transmembrane potential V and the intracellular calcium concentration [Ca]( i ). By numerical approaches appropriate to bifurcation problems, sections in the static bifurcation diagram were determined. For a variable steady depolarizing or hyperpolarizing current (I (st)), the corresponding projection of the static bifurcation diagram in the (I (st), V) plane is complex, featuring three branches of stationary solutions joined by two limit points. On the upper branch oscillations can occur, being either damped at a stable focus or diverted to the lower branch of stable stationary solutions when reaching the unstable manifold of a homoclinic saddle, thus resulting in early after-depolarizations (EADs). The middle branch of solutions is a series of unstable saddle points, while the lower one a series of stable nodes. For variable slow inward and K(+) current maximal conductances (g (si) and g (K)), in a range between 0 and 4-fold normal values, the dynamics is even more complex, and in certain instances sustained oscillations tending to a limit cycle appear. All these types of behavior were correctly predicted by linear stability analysis and bifurcation theory methods, leading to identification of Hopf bifurcation points, limit points of cycles and period doubling bifurcations. In particular settings, e.g. one-fifth-of-normal g (si), EADs and sustained high amplitude oscillations due to an unstable resting state may occur simultaneously.
Articles have appeared that rely on the application of some form of "maximum local entropy production principle" (MEPP). This is usually an optimization principle that is supposed to compensate for the lack of structural information and measurements about complex systems, even systems as complex and as little characterized as the whole biosphere or the atmosphere of the Earth or even of less known bodies in the solar system. We select a number of claims from a few well-known papers that advocate this principle and we show that they are in error with the help of simple examples of well-known chemical and physical systems. These erroneous interpretations can be attributed to ignoring well-established and verified theoretical results such as (1) entropy does not necessarily increase in nonisolated systems, such as "local" subsystems; (2) macroscopic systems, as described by classical physics, are in general intrinsically deterministic-there are no "choices" in their evolution to be selected by using supplementary principles; (3) macroscopic deterministic systems are predictable to the extent to which their state and structure is sufficiently well-known; usually they are not sufficiently known, and probabilistic methods need to be employed for their prediction; and (4) there is no causal relationship between the thermodynamic constraints and the kinetics of reaction systems. In conclusion, any predictions based on MEPP-like principles should not be considered scientifically founded.
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