Kinetics of non-equilibrium metabolism-coupled passive transport in biosystems

Expressions for time course of solute concentration in an arbitrary compartment of a biosystem were derived using simplifying assumptions of unidirectional transport and first order metabolism kinetics. The coefficients of the resulting exponential-summation function comprise, in addition to the volumes and the connecting areas of individual compartments, the rate parameters of the processes mentioned. The equations presented were verified using results obtained in drug potency testing.     

Effect of passive transport of water through plasma membrane in production of extracellular enzyme

Bioprocess and Biosystems Engineering - In this article, availability and control of water in solid-state fermentation (SSF) were investigated. Based on passive transport of water through plasma...     

Ca2+ transport in human platelet membranes. Kinetics of active transport and passive release

Active Ca2+ transport and passive release were characterized in crude and purified human platelet membranes to facilitate comparison with skeletal muscle sarcoplasmic reticulum. Endoplasmic reticulum markers were enriched from 3- to 14-fold in the purified membranes, while surface membrane antigens were reduced 4-fold and mitochondrial contamination was completely eliminated. The pH optimum for active Ca2+ transport in platelet membranes was 7.6, and the optimum for Ca2+-ATPase activity ranged from 7.6 to 8.0. Upon addition of MgATP there was a burst in active Ca2+ transport activity. In the absence of phosphate, steady state was reached within 20 s; added phosphate promoted continued uptake for greater than 1 h. The maximum pump stoichiometry was 2.0 Ca2+/ATP. The Ca2+ ionophore A23187 caused rapid release of 90% of the sequestered Ca2+ in the presence of phosphate. The dependence of Ca2+ transport on MgATP was biphasic with apparent Km values of 0.6 mM and 9.5 microM. Kinetic measurements with varied external Ca2+ yielded a single Km of 0.1 microM. Mg2+ stimulated Ca2+ transport and Ca2+-ATPase activities. Results with crude and purified membranes were similar, and comparison with the Ca2+ pump from sarcoplasmic reticulum revealed nearly identical enzymatic properties. In contrast to the results of comparing active Ca2+ transport, the characteristics of Ca2+ release from platelet membranes were quite different from those of sarcoplasmic reticulum. External Ca2+ did not promote release of sequestered Ca2+ from platelet membranes in contrast to sarcoplasmic reticulum. In addition, spontaneous release of Ca2+ from platelet membranes did not occur after ATP depletion. Inositol trisphosphate induced rapid partial release of Ca2+ from platelet membranes but had no effect on sarcoplasmic reticulum under identical conditions. Thus active Ca2+ transport is quite similar in internal membranes of platelet and skeletal muscle, but the mechanism of Ca2+ release appears to be entirely different.     

Kinetics of water transport in sickle cells

This paper reports the results of stopped-flow studies on differences in the kinetics of osmotic water transport of sickle and normal erythrocytes. The kinetics of inward osmotic water permeability are similar in sickle and normal red blood cells. In contrast, the kinetics of outward water flux are significantly (approx. 38%) decreased in sickle cells. Deoxygenation does not modify the water influx kinetics in either type of cells, but accelerates considerably the rate of water efflux in sickle cells. No significant variation of water transport kinetics was observed in density-separated cell fractions of either type. The results suggest that membrane-associated hemoglobin may decrease the outward water permeability and that in deoxygenated sickle cells the fraction of hemoglobin S near the lipid bilayer is lower than in oxygenated conditions.     

A mathematical description of recombinant yeast

A model was formulated to examine specific experimental data of growth and heterologous product formation with recombinant Saccharomyces cerevisiae while incorporating available literature. The model simulated dry cell weight, glucose, ethanol, dissolved oxygen, human Epidermal Growth Factor (hEGF) production, fraction of recombinant cells, oxygen uptake rate, and carbon dioxide production rate for batch, fed batch, and hollow fiber bioreactor configurations. Nineteen differential equations, 24 analytical equations, and 48 parameters were required. Due to the lack of detailed studies needed for the ADH-II and the TCA enzyme pool, 8 of the 48 parameters were adjustable. Simulation results are presented for verification of the model which successfully described the observed phenomena for the fermentations of S. cerevisiae strain AB103. 1 pYalphaEF-25. Also presented is a statistical analysis of the model's fit and model parameter sensitivity.     

A mathematical model for membrane transport of amino acid and Na+ in vesicles

Summary A model with a carrier having sites for both amino acid and Na⁺ can account for AIB (-aminoisobutyric acid) transport kinetics observed in membrane vesicles from SV3T3 (simian virus 40-tranformed Balb/c3T3 cells) and 3T3 (the parent cell line). The main feature of this cotransport model is that Na⁺ binding to carrier decreases the effectiveK _m for AIB transport, Na⁺ transport kinetics observed in both vesicle systems can be described by passive (possibly facilitated) diffusion. The lag of Na⁺ transport across the membrane compared to that for AIB, coupled to the Na⁺-dependent decrease in theK _m for AIB, accounts for the overshoot in intravesicular AIB observed for SV3T3 in the presence of an initial Na⁺ gradient. Extra-vesicular Na⁺ maintains a derease in theK _m for AIB influx before intra-vesicular Na⁺ has accumulated to balance it with a comparable decrease in theK _m for AIB efflux. 3T3 vesicles display little overshoot, and this finding can be explained mostly by a lower carrier affinity for Na⁺.     

A mathematical description of metabolizing systems I

An integral equation is established applicable to many types of metabolizing systems. The equation is applied to first order chemical reactions and to some biological systems.     

A new mathematical continuum theory of axoplasmic transport.

The hypothesis is advanced that successive waves of apparent contraction-relaxation (due perhaps to filament sliding) propagate along the filamentous proteins that pierce axoplasm oriented parallel to the axon length. A mathematical continuum model is developed to characterize the flow that could result in the viscous fluid bathing the moving filamentous proteins. This flow is complicated and oscillatory in time and space, but, on the average, it yields a bi-directional drift of fluid. It would transport various substances riding in the fluid, soluble and particulate, at various distinct speeds both up and down the axon. The model can thus account qualitatively for many observed features of axoplasmic transport.     

Kinetics of leucine transport in brush border membrane vesicles from lepidopteran larvae midgut.

The kinetics of K(+)-leucine cotransport in the midgut of lepidopteran larvae was investigated using brush border membrane vesicles. Initial rate (3 s) of leucine uptake was determined under experimental conditions similar to those occurring in vivo, i.e. in the presence of delta psi much greater than 0 (inside negative) and a delta pH of 1.4 units (7.4in/8.8out). Leucine and K+ bind to the carrier according to a sequential mechanism, and the binding of one substrate changed the dissociation constant for the other substrate by a factor of 0.15. Both trans-K+ and trans-leucine were mixed-type inhibitors of leucine uptake. Moreover, a portion of total leucine uptake was K+ independent, and it was competitively inhibited by trans-leucine. We interpret the trans inhibitory effects to mean that the partially loaded K+ only form is virtually unable to translocate across the membrane, whereas the binary complex carrier, leucine, can isomerize from the trans to the cis side of the membrane. However, the K(+)-independent leucine uptake occurs with a Keq greater than 1, i.e. the efflux route through the partially loaded leucine only form is slower than the rate of isomerization of the unloaded carrier from trans to cis side. Taken together, these results suggest a model in which transport occurs by an iso-random Bi Bi system. Since K+ does not act as a pure competitive activator, this model is different from that proposed for most of the Na(+)-linked solutes transport agencies and may be related to the broadening of the cation specificity of the amino acid transporters in lepidopteran larvae.     

Phenomenological description of active transport of salt and water

The phenomenological definition of active transport by Kedem and the methods of Kedem and Katchalsky have been used to obtain practical equations describing active transport in the single salt and bi-ionic systems. Procedures were devised to evaluate the required set of 10 coefficients for the single salt case and 15 for the bi-ionic. Three of these coefficients are unusual. They express the effects of active transport, i.e. of entrainment between metabolism and the conventional transport flows: active salt transport coefficient, a volume pump coefficient, and an electrogenicity coefficient. In the bi-ionic case a new passive coefficient, lambda, was used to express the linkage between the fluxes of the two salts. However, if primary active transport involves only one ion, for example in the bi-ionic case, 12 coefficients suffice and certain relations can be predicted between the practical coefficients. Particular types of primary active transport could be identified by this means. The relation of active transport to membrane electrogenesis was also examined and the flux ratio equation was rederived in terms of the practical coefficients. Applications to specific parallel and series membrane systems have been analyzed.     

Characterization of passive ion transport in plasma membrane vesicles of oat roots

The passive influx and efflux of inorganic ions across plasma membrane vesicles purified from extracts of Avena sativa roots were investigated. Uptake was measured by incubating the vesicles in a radioisotope for various times. The “loaded” vesicles were separated from the external solution by gel filtration. Efflux was measured by dialyzing the preloaded vesicles.     

A mathematical model of the functional state of the oxygen transport system

Based on the principle of minimum power, a mathematical model of the functional state of the oxygen transport system is presented. The optimization model minimizes the power expenditure of the heart, bone marrow, lung and other tissues. The model is used to determine the functional parameters of the oxygen transport system in man under both normal and varying barometric pressures. Theoretical results are compared with experimental data.     

A mathematical description of metabolizing systems: II

Some of the laboratory procedures available for determining the functions in the integral equation established in part I are discussed. The tracer or tagged molecule technique is shown to be especially promising including the use of “double tracer” molecules. Conversely, the integral equation may be a convenient device for correlating and integrating some of the work now being done with tracer molecules in biological systems.