Ligand-gated ion channel currents in a nonstationary lyotropic model

Transmembrane currents in ligand-gated ion channels are calculated in a nonstationary, chemically open whole cell system or patch of a membrane. The model is lyotropic in the sense that dynamics, and parameters such as the ligand concentration for half-maximal response (scale of response), and threshold for firing, such as in neurons, become nonlinear functions of the reactant concentrations. The derived total currents fit recorded data significantly better than those derived from mass action, Ising, and other stationary type models, in which the derived response is often displaced from the assessed response by several orders in the ligand concentration. Also, the derived slope of response is in perfect agreement with the values assessed.     

Biocatalytic process optimization based on mechanistic modeling of cholic acid oxidation with cofactor regeneration

Reduction and oxidation of steroids in the human gut are catalyzed by hydroxysteroid dehydrogenases of microorganisms. For the production of 12-ketochenodeoxycholic acid (12-Keto-CDCA) from cholic acid the biocatalytic application of the 12α-hydroxysteroid dehydrogenase of Clostridium group P, strain C 48-50 (HSDH) is an alternative to chemical synthesis. However, due to the intensive costs the necessary cofactor (NADP(+) ) has to be regenerated. The alcohol dehydrogenase of Thermoanaerobacter ethanolicus (ADH-TE) was applied to catalyze the reduction of acetone while regenerating NADP(+) . A mechanistic kinetic model was developed for the process development of cholic acid oxidation using HSDH and ADH-TE. The process model was derived by identifying the parameters for both enzymatic models separately using progress curve measurements of batch processes over a broad range of concentrations and considering the underlying ordered bi-bi mechanism. Both independently derived kinetic models were coupled via mass balances to predict the production of 12-Keto-CDCA with HSDH and integrated cofactor regeneration with ADH-TE and acetone as co-substrate. The prediction of the derived model was suitable to describe the dynamics of the preparative 12-Keto-CDCA batch production with different initial reactant and enzyme concentrations. These datasets were used again for parameter identification. This led to a combined model which excellently described the reaction dynamics of biocatalytic batch processes over broad concentration ranges. Based on the identified process model batch process optimization was successfully performed in silico to minimize enzyme costs. By using 0.1 mM NADP(+) the HSDH concentration can be reduced to 3-4 μM and the ADH concentration to 0.4-0.6 μM to reach the maximal possible conversion of 100 mM cholic acid within 48 h. In conclusion, the identified mechanistic model offers a powerful tool for a cost-efficient process design.     

Kinetics of binding the mRNA cap analogues to the translation initiation factor eIF4E under second-order reaction conditions

The kinetics of binding of five analogues of the 5'-mRNA cap, differing in size and electric charge, to the eukaryotic initiation factor eIF4E, at 20 degrees C, pH 7.2, and ionic strength of 150 mM, were measured, after mixing solutions of comparable concentrations of the reagents, in a stopped-flow spectrofluorimeter. The registered stopped-flow signals were fitted using an efficient software package, called Dyna Fit, based on a numerical solution of the kinetic rate equations for assumed reaction mechanisms. One-, two-, and three-step binding models were considered. The quality of fits for these models were compared using two statistical criteria: Akaike's Information Criterion and Bayesian Information Criterion. Based on resulting probabilities of the models, it was concluded that for all investigated ligands a one-step binding model has essentially no support in the experimental observations. Our conclusions were also analysed from the perspective of kinetic transients obtained for cap-eIF4E systems under the so called pseudo-first order reaction condition, which result in the linear correlation of the observed association rate constant with ligand concentration. The existence of such a linear correlation is usually considered as proof of a one-step binding mechanism. The kinetic and optical parameters, derived from fitting a two-step cap-binding model with the DynaFit, were used to simulate kinetic transients under pseudo-first order reaction conditions. It appeared that the observed association rate constants derived from these simulated transients are also linearly correlated with the ligand concentration. This indicated that these linear dependencies are not sufficient to conclude a one-step binding.     

Copper complexation by naturally occurring organic matter: a multiligand model

ABSTRACT

Extending the fluorescence quenching single-ligand model of Ryan-Weber, a multiligand model that does not require a direct measurement of the free metal ion concentration is proposed. It is shown that the problem of inconsistent negative ligand concentrations, commonly predicted by single-ligand models, may be overcome by using multiligand models. Finally, particular results concerning the conditional stability constants and ligand concentrations for one-, two and three- ligand cases are presented for soil fulvic acid, both before and after reverse phase HPLC fractionation.     

Errors-in-variables in joint population pharmacokinetic/pharmacodynamic modeling

Pharmacokinetic (PK) models describe the relationship between the administered dose and the concentration of drug (and/or metabolite) in the blood as a function of time. Pharmacodynamic (PD) models describe the relationship between the concentration in the blood (or the dose) and the biologic response. Population PK/PD studies aim to determine the sources of variability in the observed concentrations/responses across groups of individuals. In this article, we consider the joint modeling of PK/PD data. The natural approach is to specify a joint model in which the concentration and response data are simultaneously modeled. Unfortunately, this approach may not be optimal if, due to sparsity of concentration data, an overly simple PK model is specified. As an alternative, we propose an errors-in-variables approach in which the observed-concentration data are assumed to be measured with error without reference to a specific PK model. We give an example of an analysis of PK/PD data obtained following administration of an anticoagulant drug. The study was originally carried out in order to make dosage recommendations. The prior for the distribution of the true concentrations, which may incorporate an individual's covariate information, is derived as a predictive distribution from an earlier study. The errors-in-variables approach is compared with the joint modeling approach and more naive methods in which the observed concentrations, or the separately modeled concentrations, are substituted into the response model. Throughout, a Bayesian approach is taken with implementation via Markov chain Monte Carlo methods.     

The importance of explicit chain representation in protein folding models: an examination of Ising-like models

A class of models that represents a protein chain as a sequence of "folded" and "unfolded" residues has recently been used to correlate rates and mechanisms of protein folding with the protein native structure. In order to better understand the conditions under which these "Ising-like" models apply, we compare results from this model to those obtained from an off-lattice model which uses the same potential function. We find that Ising-like models by construction impose folding via a highly sequential nucleation-condensation mechanism, which in turn leads to more rugged energy landscapes, fewer "pathways" to the native state, and in the specific case examined here, the cold shock protein A from Escherichia coli, a qualitative difference in the most likely order of events in folding.     

Importance of Initial Concentration of Factor VIII in a Mechanistic Model of In Vitro Coagulation

This computational study generates a hypothesis for the coagulation protein whose initial concentration greatly influences the course of coagulation. Many clinical malignancies of blood coagulation arise due to abnormal initial concentrations of coagulation factors. Sensitivity analysis of mechanistic models of blood coagulation is a convenient method to assess the effect of such abnormalities. Accordingly, the study presents sensitivity analysis, with respect to initial concentrations, of a recently developed mechanistic model of blood coagulation. Both the model and parameters to which model sensitivity is being analyzed provide newer insights into blood coagulation: the model incorporates distinct equations for plasma-phase and platelet membrane-bound species, and sensitivity to initial concentrations is a new dimension in sensitivity analysis. The results show that model predictions are most uncertain with respect to changes in initial concentration of factor VIII, and this hypothesis is supported by results from other models developed independently.     

Ligand-induced DNA condensation: choosing the model

We test and compare different models for ligand-induced DNA condensation. Using 14C-labeled spermidine3+, we measure the binding to condensed DNA at micromolar to molar polyamine concentrations. DNA aggregates at a critical polyamine concentration. Spermidine3+ binding becomes highly cooperative at the onset of aggregation. At higher concentrations, spermidine3+ binding to condensed DNA reaches a plateau with the degree of binding equal to 0.7 (NH(4+)/PO3-). Condensed DNA exists in a wide range of spermidine concentrations with the roughly constant degree of ligand binding. At greater concentrations, the degree of binding increases again. Further spermidine penetration between the double helices causes DNA resolubilization. We show that a simple two-state model without ligand-ligand interactions qualitatively predicts the reentrant aggregation-resolubilization behavior and the dependence on the ligand, Na+, and DNA concentrations. However, such models are inconsistent with the cooperative ligand binding to condensed DNA. Including the contact or long-range ligand-ligand interactions improves the coincidence with the experiments, if binding to condensed DNA is slightly more cooperative than to the starting DNA. For example, in the contact interaction model it is equivalent to an additional McGhee-von Hippel cooperativity parameter of approximately 2. Possible physical mechanisms for the observed cooperativity of ligand binding are discussed.     

What can we learn about protein folding from Ising-like models?

Ising-like models have been remarkably successful in reproducing all the experimental data available on the equilibrium and kinetics of secondary structure formation in short peptides. Over the past two years, very similar models have been used to predict the folding of complete proteins, with encouraging results. Although Ising-like models are probably too simple to describe all aspects of protein folding, the results obtained so far indicate that they can play a critical role in the study of protein folding by bridging the gap between experiment and more detailed theoretical approaches.     

Application of the one- and two-dimensional Ising models to studies of cooperativity between ion channels.

The Ising model of statistical physics provides a framework for studying systems of protomers in which nearest neighbors interact with each other. In this article, the Ising model is applied to the study of cooperative phenomena between ligand-gated ion channels. Expressions for the mean open channel probability, rho o, and the variance, sigma 2, are derived from the grand partition function. In the one-dimensional Ising model, interactions between neighboring open channels give rise to a sigmoidal rho o versus concentration curve and a nonquadratic relationship between sigma 2 and rho o. Positive cooperativity increases the slope at the midpoint of the rho o versus concentration curve, shifts the apparent binding affinity to lower concentrations, and increases the variance for a given rho o. Negative cooperativity has the opposite effects. Strong negative cooperativity results in a bimodal sigma 2 versus rho o curve. The slope of the rho o versus concentration curve increases linearly with the number of binding sites on a protomer, but the sigma 2 versus rho o relationship is independent of the number of ligand binding sites. Thus, the sigma 2 versus rho o curve provides unambiguous information about channel interactions. In the two-dimensional Ising model, rho o and sigma 2 are calculated numerically from a series expansion of the grand partition function appropriate for weak interactions. Virtually all of the features exhibited by the one-dimensional model are qualitatively present in the two-dimensional model. These models are also applicable to voltage-gated ion channels.     

Kinetic modelling of phototropism in maize coleoptiles

Blue-light-induced phototropism of maize (Zea mays L.) coleoptiles was studied with a view to kinetic models. Red-light-grown plants were used to eliminate complication arising from the activation by blue light of phytochrome-mediated phototropism. In the first part, mathematical models were developed to explain the phototropic fluence-response data, which were obtained for the responses induced by a single unilateral pulse (30 s) and those induced by a unilateral pulse (30 s) given immediately after a bilateral pulse (30 s, fixed fluences). These data showed bell-shaped fluence-response curves, characteristic of first positive curvature. Modelling began with the assumptions that the light gradient plays a fundamental role in phototropism and that the magnitude of the response is determined by the gradient, or the concentration difference, in a photoproduct between the irradiated and the shaded sides of the tissue. Minimal mathematical models were then derived, by defining chemical kinetics of the photoreaction and introducing the minimum of parameters needed to correlate the incident fluencerate to the functional fluence-rates within the tissue, the functional fluence-rate to the rate constant of the photoreaction, and the photoproduct concentration difference to the curvature response. The models were tested using a curve-fitting computer program. The model obtained by assigning first-order kinetics to the photoreaction failed to explain the fluence-response data, whereas application of second-order kinetics led to a successful fit of the model to the data. In the second part, temporal aspects of the photosystem were examined. Experimental results showed that a high-fluence bilateral pulse eliminated the bell-shaped fluence-response curve for an immediate unilateral pulse, and that the curve gradually reappeared as the time for unilateral stimulation elapsed after the bilateral pulse. The model based on a second-order photoreaction could be extended to explain the results, with assumed changes in two components: the concentration of the reactant for the photoproduct, and the light-sensitivity of the reaction. The reactant concentration, computed with the curvefitting program, showed a gradual increase from zero to a saturation level. This increase was then modelled in terms of regeneration of the reactant from the photoproduct, with an estimated first-order rate constant of about 0.001·s^-1. The computed value for the constant reflecting the light-sensitivity showed a sharp decline after the high-fluence pulse, followed by a gradual return to the initial level. From these analytical results, the appearance of second positive curvature was predicted.Abbreviations FPC first positive curvature - SPC second positive curvature CIW-DPB publication No. 884     

Kinetics for activated sludge process design: Experiment application to straw paper wastewater treatment

Degradation kinetics for the treatment of straw paper wastewater in an activated sludge process have been studied and a kinetic model has been derived for both batch and continuous experiments. These two methods are reasonably equivalent only when rather low concentrations of substrate are involved. In other cases batch and continuous results are quite different. Both models, however, show a dependence upon concentration corresponding to that which is typical of multicomponent substrate degradation. The kinetic model derived from continuous tests appears to be more suitable for designing industrial processes in that it avoids oversizing of the aeration unit.     

Lateral density of receptor arrays in the membrane plane influences sensitivity of the E. coli chemotaxis response

In chemotactic bacteria, transmembrane chemoreceptors, CheA and CheW form the core signalling complex of the chemotaxis sensory apparatus. These complexes are organized in extended arrays in the cytoplasmic membrane that allow bacteria to respond to changes in concentration of extracellular ligands via a cooperative, allosteric response that leads to substantial amplification of the signal induced by ligand binding. Here, we have combined cryo-electron tomographic studies of the 3D spatial architecture of chemoreceptor arrays in intact E. coli cells with computational modelling to develop a predictive model for the cooperativity and sensitivity of the chemotaxis response. The predictions were tested experimentally using fluorescence resonance energy transfer (FRET) microscopy. Our results demonstrate that changes in lateral packing densities of the partially ordered, spatially extended chemoreceptor arrays can modulate the bacterial chemotaxis response, and that information about the molecular organization of the arrays derived by cryo-electron tomography of intact cells can be translated into testable, predictive computational models of the chemotaxis response.     

The Onset of Double Diffusive Convection in a Viscoelastic Fluid-Saturated Porous Layer with Non-Equilibrium Model

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.     

Grand canonical Monte Carlo molecular and thermodynamic predictions of ion effects on binding of an oligocation (L8+) to the center of DNA oligomers.

Grand canonical Monte Carlo (GCMC) simulations are reported for aqueous solutions containing excess univalent salt (activities a +/- = 1.76-12.3 mM) and one of the following species: an octacationic rod-like ligand, L8+; a B-DNA oligomer with N phosphate charges (8 < or = N < or = 100); or a complex resulting from the binding of L8+ at the center of an N-mer (24 < or = N < or = 250). Simplified models of these multiply charged species are used in the GCMC simulations to predict the fundamental coulombic contributions to the following experimentally relevant properties: 1) the axial distance over which ligand binding affects local counterion concentrations at the surface of the N-mer; 2) the dependence on N of GCMC preferential interaction coefficients, gamma 32MC identical to delta C3/delta C2l a +/-, T, where C3 and C2 are, respectively, the molar concentrations of salt and the multiply charged species (ligand, N-mer or complex); and 3) the dependence on N of SaKobs identical to d in Kobs/d in a +/- = delta (magnitude of ZJ + 2 gamma 32J), where Kobs is the equilibrium concentration quotient for the binding of L8+ to the center of an N-mer and delta denotes the stoichiometric combination of terms, each of which pertains to a reactant or product J having magnitude of ZJ charges. The participation of electrolyte ions in the ligand binding interaction is quantified by the magnitude of SaKobs, which reflects the net (stoichiometrically weighted) difference in the extent of thermodynamic binding of salt ions to the products and reactants. Results obtained here from GCMC simulations yield a picture of the salient molecular consequences of binding a cationic ligand, as well as thermodynamic predictions whose applicability can be tested experimentally. Formation of the central complex is predicted to cause a dramatic reduction in the surface counterion (e.g., Na+) concentration over a region including but extending well beyond the location of the ligand binding site. For binding a cationic ligand, SaKobs is predicted to be negative, indicating net electrolyte ion release in the binding process. At small enough N, -SaKobs is predicted to decrease strongly toward zero with decreasing N. At intermediate N, -SaKobs appears to exceed its limiting value as N-->infinity.     

A Murine Model of Obesity With Accelerated Atherosclerosis

The epidemic of obesity sweeping developed nations is accompanied by an increase in atherosclerotic cardiovascular diseases. Dyslipidemia, diabetes, hypertension, and obesity are risk factors for cardiovascular disease. However, delineating the mechanism of obesity‐accelerated atherosclerosis has been hampered by a paucity of animal models. Similar to humans, apolipoprotein E–deficient (apoE^?/?) mice spontaneously develop atherosclerosis over their lifetime. To determine whether apoE^?/? mice would develop obesity with accelerated atherosclerosis, we fed mice diets containing 10 (low fat (LF)) or 60 (high fat (HF)) kcal % from fat for 17 weeks. Mice fed the HF diet had a marked increase in body weight and atherosclerotic lesion formation compared to mice fed the LF diet. There were no significant differences between groups in serum total cholesterol, triglycerides, or leptin concentrations. Plasma concentrations of the acute‐phase reactant serum amyloid A (SAA) are elevated in both obesity and cardiovascular disease. Accordingly, plasma SAA concentrations were increased fourfold (P < 0.01) in mice fed the HF diet. SAA was associated with both pro‐ and antiatherogenic lipoproteins in mice fed the HF diet compared to those fed the LF diet, in which SAA was primarily associated with the antiatherogenic lipoprotein high‐density lipoprotein (HDL). Moreover, SAA was localized with apoB‐containing lipoproteins and biglycan in the vascular wall. Taken together, these data suggest male apoE‐deficient mice are a model of metabolic syndrome and that chronic low level inflammation associated with increased SAA concentrations may mediate atherosclerotic lesion formation.     

Interpreting woody cover data in tropical and subtropical areas: Comparison between the equilibrium and the non-equilibrium assumption

We compared two basic assumptions about the woody cover distribution in tropical and subtropical areas: the equilibrium (woody cover always reaches a long-term steady state) vs the non-equilibrium assumption (woody cover fluctuates in response to fire disturbances). We considered two models each one representative of one of the two assumptions: an equilibrium and a non-equilibrium model. The equilibrium model considered fire as an a priori determined parameter, whereas the non-equilibrium model assumed fires as stochastic events whose probability increased with grass density. We compared the results of the models with large datasets containing woody cover values sampled at the continental and at the global scale. In particular, we focused on two evidences shown by data. The first evidence is that woody cover is limited by water scarcity for low rainfall values and by fire for high rainfall values (arid–moist savanna distinction). The second evidence is the bimodality of woody cover data observed for high rainfall values. The equilibrium model gave a static interpretation of the data. The non-equilibrium model, instead, gave a more general interpretation of the data. In particular, the non-equilibrium model detected the arid–moist savanna distinction as emergent along a rainfall gradient and demonstrated that the bimodality observed in the woody cover data could be obtained in the woody cover values exhibited by a vegetation system in different times. Thus, woody cover data do not necessarily represent steady states. Rather, they could represent snapshots of a vegetation system in certain time instants.