Measurements and Simulations of the Acidity Dependence of the Kinetics of the Iron-Catalyzed Belousov-Zhabotinsky Reaction: Proton-Catalysis in the Electron Transfer Reaction Involving the [Fe(phen)3]3+ Species.

The acidity dependence of the iron-catalyzed bromate-malonic acid Belousov-Zhabotinsky reaction was studied in the range 0.36 M < [H2SO4]0 < 1.20 M, and the temporal evolutions of the oscillation patterns were analyzed. The experimental results show that the period times PT i decrease exponentially with increasing acidity and that the period times parallel the decrease of the reduction times RT with increasing acidity. Simulations using the reactions of the commonly accepted core reaction mechanism failed to match the measurements even in a qualitative fashion. However, we found that compelling agreement between the experiments and the simulations can be achieved over the entire range with the inclusion of second-order proton-catalysis of the oxidation of bromomalonic acid (BrMA) by the [Fe(phen)3]3+ species in the reaction identified in this paper as reaction 9 (R9), and this [H+] dependence is informative about the species involved in the outer sphere electron transfer reaction. The trication [Fe(phen)3]3+ species is stabilized by ion pairing and solvation, and one may anticipate the presence of [Fe(phen)3(HSO4) n(H2O) m](3- n)+ species ( n = 0-3). Our results suggest that the removal of aggregating HSO4- ions by protonation creates a better oxidant and facilitates the approach of the reductant BrMA, and the second-order [H+] dependence further suggests that BrMA is primarily oxidized by a doubly charged [Fe(phen)3(HSO4)1(L) k]2+ species. Considering the complexity of the BZ system and the uncertainties in the many reaction rate constants, we were somewhat surprised to find this high level of agreement by (just) the replacement of R9 by R9'. In fact, the near-quantitative agreement presents a powerful corroboration of the core reaction mechanism of the BrMA-rich BZ reaction, and the replacement of R9 by R9' extends the validity of this core reaction mechanism to acidities above and below the typical acidity of BZ reactions ([H+] ≈ 1 M).

Analytical optimal controls for the state constrained addition and removal of cryoprotective agents.

Cryobiology is a field with enormous scientific, financial, and even cultural impact. Successful cryopreservation of cells and tissues depends on the equilibration of these materials with high concentrations of permeating chemicals (CPAs) such as glycerol or 1,2 propylene glycol. Because cells and tissues are exposed to highly anisosmotic conditions, the resulting gradients cause large volume fluctuations that have been shown to damage cells and tissues. On the other hand, there is evidence that toxicity to these high levels of chemicals is time dependent, and therefore it is ideal to minimize exposure time as well. Because solute and solvent flux is governed by a system of ordinary differential equations, CPA addition and removal from cells is an ideal context for the application of optimal control theory. Recently, we presented a mathematical synthesis of the optimal controls for the ODE system commonly used in cryobiology in the absence of state constraints and showed that controls defined by this synthesis were optimal. Here we define the appropriate model, analytically extend the previous theory to one encompassing state constraints, and as an example apply this to the critical and clinically important cell type of human oocytes, where current methodologies are either difficult to implement or have very limited success rates. We show that an enormous increase in equilibration efficiency can be achieved under the new protocols when compared to classic protocols, potentially allowing a greatly increased survival rate for human oocytes and pointing to a direction for the cryopreservation of many other cell types.

A general model for the dynamics of cell volume, global stability, and optimal control.

Cell volume and concentration regulation in the presence of changing extracellular environments has been studied for centuries, and recently a general nondimensional model was introduced that encompassed solute and solvent transmembrane flux for a wide variety of solutes and flux mechanisms. Moreover, in many biological applications it is of considerable interest to understand optimal controls for both volume and solute concentrations. Here we examine a natural extension of this general model to an arbitrary number of solutes or solute pathways, show that this system is globally asymptotically stable and controllable, define necessary conditions for time-optimal controls in the arbitrary-solute case, and using a theorem of Boltyanski prove sufficient conditions for these controls in the commonly encountered two-solute case.

Exact solutions of a two parameter flux model and cryobiological applications.

Solute-solvent transmembrane flux models are used throughout biological sciences with applications in plant biology, cryobiology (transplantation and transfusion medicine), as well as circulatory and kidney physiology. Using a standard two parameter differential equation model of solute and solvent transmembrane flux described by Jacobs [The simultaneous measurement of cell permeability to water and to dissolved substances, J. Cell. Comp. Physiol. 2 (1932) 427-444], we determine the functions that describe the intracellular water volume and moles of intracellular solute for every time t and every set of initial conditions. Here, we provide several novel biophysical applications of this theory to important biological problems. These include using this result to calculate the value of cell volume excursion maxima and minima along with the time at which they occur, a novel result that is of significant relevance to the addition and removal of permeating solutes during cryopreservation. We also present a methodology that produces extremely accurate sum of squares estimates when fitting data for cellular permeability parameter values. Finally, we show that this theory allows a significant increase in both accuracy and speed of finite element methods for multicellular volume simulations, which has critical clinical biophysical applications in cryosurgical approaches to cancer treatment.