The role of G-proteins in the regulation of pacemaking activity.

This work is concerned with modeling the key interrelated biochemical reactions involved in initiating and inhibiting pacemaking activity in the mammalian sinoatrial node. A detailed model involving G-proteins was developed to better represent the activation pathway for adenylate cyclase. Concentration profiles of an activated G-protein complex [alpha(T)C] were established as a function of the membrane bound calcium calmodulin concentration. A previously developed model used to establish temporal profiles of cAMP was improved using the G-protein effects through the [alpha(T)C] functionality. Methods were also developed to model inhibition of G-protein by acetylcholine. Analytical solutions were developed to predict acetylcholine concentration profiles as a function of diffusion parameter and duration of acetylcholine pulses. The model was used to demonstrate suppression of cAMP by acetylcholine through G-protein pathways. It provides a basis for a tool to quantify key biochemical species during stimulation and inhibition of sinoatrial node pacemaking. A stability analysis of the model equations has potential application in studying the link between the biochemical species concentrations and abnormal effects in sinoatrial node pacemaking.

Dual role of calmodulin in excitable cells.

Consideration of the enzymatic reactions governing calcium channel phosphorylation and dephosphorylation leads one to deduce that there exist separate groups of enzymes, membrane-bound and cytoplasmic that are activated by a common mediator, calmodulin (CaM), whose time-dependent appearance (via diffusion) at both locales is controlled by both intracellular calcium levels and electrostatic interaction with the membrane. In brief, the change in the sign and extent of the electrical charge borne by the modulator in the presence of calcium (Ca) brings about the electrostatic attraction that enables the transport of [Ca-CaM] to the membrane. This translocation of Ca-CaM makes possible a sequential activation of cellular enzymes whose locations differ. The sequence, both spatial and temporal, of the activation of various cellular enzymes by Ca-CaM appears to be a control network shared in common by excitable cells containing a stimulus-response pathway mediated by second messengers.

Transport regulation of recombinant gene expression in E. coli and B. subtilis.

Expression kinetics of the lactose (lac) operon in Escherichia coli are reviewed for both wild-type and recombinant cell cultures under chemostatic conditions. A unified model which involves regulation of active inducer (lactose) transport, promoter-operator regulated expression of the lac operon, glucose-mediated inducer exclusion, and catabolite repression is summarized and supporting data is shown to verify its accuracy. The synthesis of alpha-amylase with a recombinant form of Bacillus subtilis is also reviewed to point out generic features in transport regulation, the lac operon model providing a point of departure. While there are many similarities in the influence of transport on both regulating models, there are also important differences. In a chemostat system, the synthesis of alpha-amylase is nongrowth associated, while beta-galactosidase is a growth-associated enzyme. Nevertheless, transport regulation is an important feature in both instances.

Fermentation of lactose to ethanol with recombinant yeast in an immobilized yeast membrane bioreactor.

A novel concept of membrane bioreactor in which living cells are sandwiched between ultrafiltration (UF) and reverse osmosis (RO) membranes was applied for lactose fermentation to ethanol by genetically engineered yeast cells. The productivity of the Lactophile 13B strains was higher than that of the Lactophile 13D strains. In both cases performance data similar to those for glucose fermentation to ethanol by Saccharomyces cerevisiae were obtained. However, the operational stability of recombinant yeast cells was improved in the new bioreactor in comparison to the stability of these cells in a shake flask.

Transport and kinetics in sandwiched membrane bioreactors.

A bioreactor in which living yeast cells are sandwiched between an ultrafiltration membrane and a reverse osmosis membrane was constructed, and experiments were performed for the conversion of substrate glucose to product ethanol. A set of equations that include both transport through a series of barrier layers and bioreaction rate were developed to predict the performance of the sandwich bioreactor. The above equations were solved by using numerical values for the transport parameter and the bioreaction rate constant, and the results are compared with the experimental data.

Regulation of lac operon expression in mixed sugar chemostat cultures.

Expression of the lactose (lac) operon in the Escherichia coli chromosome has been studied in mixed-sugar chemostat cultures under steady-state and transient conditions. A unified model has been formulated which involves regulation of active inducer (lactose) transport, promoter-operator regulated expression of the lac operon, glucose-mediated inducer exclusion, and catabolite repression. The model of the lac operon control system focuses on the molecular interactions among the regulatory species and the genetic control elements for the initiation of transcription. The role of catabolite modulator factor (CMF) in the regulation of transcription is described. The modeling of glucose-mediated regulation of intracellular cyclic adenosine monophosphate (cAMP) and inducer exclusion is based on the recently elucidated mechanisms of the involvement of the PTS (phosphoen-olpyruvate dependent sugar transport system) enzymes, in the presence of glucose, in regulation of adenylate cyclase and non-PTS sugar transport proteins (i.e. per-meases). The adequacy of the unified model was verified with experimental data.

Steady-state and transient behavior in microbial methanification: I. Experimental results.

The process of methanification of volatile fatty acids (VFA) was studied to elucidate its kinetics. An upflow anaerobic sludge bed (UASB) system was used to perform the experiments. At residence times of less than 2.5 h the UASB system was found to exhibit hysteresis with respect to acetic and propionic acid consumption but not with respect to butyric acid consumption. These hysteretic effects could be attributed to the manner in which the various VFA-consuming cultures were structured inside the flocculated biomass in light of the cross-inhibitory effects of the acetic- and propionic-acid-consuming fractions of the total culture. (Butyric acid proved to be non-interactive.) Production of methane was found to respond almost instantaneously to changes in the inlet conditions of the UASB system. This indicated that methane is not primarily growth associated, as has often been assumed, but is related to changes in the culture's maintenance energy requirements. Reactor operation was found to be stable even when the concentration of each VFA in the feed was simultaneously changed by 50%. Even at very high organic throughput rates (35 kg COD/day m(3)-reactor) conversions of 82% were observed.

Steady-state and transient behavior in microbial methanification: II. Mathematical modeling and verification.

It has been shown that the Upflow Anaerobic Sludge Bed (UASB) system data reported earlier(1) cannot be explained by simple Monod-type substrate consumption patterns. An autoinhibition model was also ruled out because the substrate concentration range over which hysteresis was observed was much larger than such a model would predict. However, propionic and acetic acids were found to inhibit each other's conversion machineries. Since in the UASB system the biocatalyst is flocculated, it was found that a model additionally incorporating this facet of the reactor set-up could explain the steady-state data very well. Using the parameters generated from steady-state data and data from butyric acid step change,(1) i.e., the entire set of parameters (Table I), a very good agreement between predicted and observed data was found. International Mathematical and Statistical Libraries (IMSL) and Upjohn's NONLIN library combined with various root-finding and integrating subroutines were used for parameter estimation. The model thus described was used to predict the response of the UASB system when acetic acid and propionic acid influent concentrations were stepped-up/down. The agreement between the predicted and observed data was found to be excellent in each case during the step-up schedule. During the step-down the data seemed to indicate that the UASB system, like any other chemostat, responded faster than predicted. This could be due to the fact that when the culture has to "gear up" part of the lag time is the time required for the cell to produce the requisite amount of enzymes. In the case of "gearing down" this time is not required and the system responds faster.

Transport of acetylcholine in a membrane. Laminate model of the neuromuscular junction.

A laminate model of the cleft-plus-postsynaptic membrane structure of the neuromuscular junction was studied. In order to prepare a model of the postsynaptic membrane, the properties of acetylcholine (Ach) receptor-rich vesicles purified from Torpedo fish were measured. Immobilization of vesicles was demonstrated by various methods, in particular, by investigating collagen and carrageenan matrices as models of the fluid-filled fibrous matrix of the cleft. It was found that a laminated system employing a liquid membrane-containing vesicle suspension, together with a swollen collagen membrane, is an appropriate model for examining important transport/reception aspects of the cleft-plus-postsynaptic membrane structure. Combined transport with immobilization of Ach in the liquid membrane system was elucidated and effective diffusivities in the vesicle suspension layer were calculated. Effective diffusivities of the composite system simulating the cleft and the postsynaptic membrane were evaluated as well. These data illustrate the importance of penetrant immobilization in retarding the diffusion process during neurotransmission.

Diffusional/kinetic analysis of the neurotransmission process at the nerve-muscle junction.

Transmission at the neuromuscular junction is known to comprise the following steps: vesicular release of Ach pulses; transport across the synaptic cleft; partial hydrolysis by Ach-ase; binding to Ach receptors; ion channel opening and closure, and, thereby, alteration of sodium and potassium conductances. Combining these elements, a unified model has been constructed that is effective in describing the relation between neurotransmitter arrival at receptor sites and channel openings, leading to simple relationships for sodium and potassium conduction at the neuromuscular junction. Application of the model to mepc and epp data has been successful.

Transport models of the neurotransmitter-receptor interaction.

Recently, in membrane transport studies, we have observed the duality of ligand-binding site interactions in a structural protein membrane. Separately, the role of membrane anisotropy in the transport/catalytic behavior of an enzyme-membrane was investigated and modeled by the present authors. In this work, we are combining the ideas of duality and anisotropy in a diffusional analysis of the phenomenon of migration of the neurotransmitter species acetylcholine (ACh) in the post-synaptic region of the neuromuscular junction. Employing the principle of mass conservation, a transient diffusion equation was formulated for ACh migration in this region; it was solved by numerical computation for the appropriate boundary conditions. Concentration profiles were generated and, with the aid of a simple linear coupling expressing regulation of the ion channel function by the ACh species bound to receptor sites in the active conformation, successful simulations of the nerve-muscle end-plate potential were obtained. Two subcases were considered: (a) static unilayer diffusional zone or "membrane." (b) moving active layer (multilayer or envelope membrane). Both models are capable of closely matching the normalized concentration profiles of the actively bound neurotransmitter species to the profile of normalized end-plate potential in reduced scale. A transport basis for the familiar two-state receptor-transmitter interaction is demonstrated and a plausible explanation of the role of geometry of the synaptic cleft and the function of junctional cholinesterases is provided. Arguments utilizing results from the literature, together with our simulation results, are employed in critical reexamination of the key concepts (diffusion, duality, anisotropy) and their validity is strengthened.

Modeling the role of cyclic AMP in catabolite repression of inducible enzyme biosynthesis in microbial cells.

Modeling the role of cyclic AMP (cAMP) in catabolite repression of inducible enzyme production in microbial cells was studied. A catabolite repression index, F, was defined based on the postulation that complex formation occurs between RNA polymerase (RNAP) and DNA, and shifting from the inert form to the open form of this complex (the latter form is required for transcription) is accelerated by the cAMP.CRP complex. The catabolite repression index, F, was incorporated into model equations of mRNA production. Empirical relationships between intracellular cAMP level and medium glucose concentration were established based on experimental data and introduced into the model. Computer simulation results were obtained for a number of interesting cases. The practical utility of the proposed model was demonstrated by comparing it with the experimental results on glucose isomerase biosynthesis.