Thermodynamics and bioenergetics

Bioenergetics is concerned with the energy conservation and conversion processes in a living cell, particularly in the inner membrane of the mitochondrion. This review summarizes the role of thermodynamics in understanding the coupling between the chemical reactions and the transport of substances in bioenergetics. Thermodynamics has the advantages of identifying possible pathways, providing a measure of the efficiency of energy conversion, and of the coupling between various processes without requiring a detailed knowledge of the underlying mechanisms. In the last five decades, various new approaches in thermodynamics, non-equilibrium thermodynamics and network thermodynamics have been developed to understand the transport and rate processes in physical and biological systems. For systems not far from equilibrium the theory of linear non-equilibrium thermodynamics is used, while extended non-equilibrium thermodynamics is used for systems far away from equilibrium. All these approaches are based on the irreversible character of flows and forces of an open system. Here, linear non-equilibrium thermodynamics is mostly discussed as it is the most advanced. We also review attempts to incorporate the mechanisms of a process into some formulations of non-equilibrium thermodynamics. The formulation of linear non-equilibrium thermodynamics for facilitated transport and active transport, which represent the key processes of coupled phenomena of transport and chemical reactions, is also presented. The purpose of this review is to present an overview of the application of non-equilibrium thermodynamics to bioenergetics, and introduce the basic methods and equations that are used. However, the reader will have to consult the literature reference to see the details of the specific applications.     

May active solute flux control the cell volume in the steady state?

The dynamics of a bioreactor with a variable volume and an active solute flux based on the thermodynamics of irreversible processes and stability analysis was studied. The active solute flux may control both the bioreactor volume and the hydrostatic pressure as well as the concentration of the solute inside the cell in the steady state. The range of the active solute flux is limited by amplitudes (j1(0), J2(0] of the active transport depending on the membrane transport parameters. The dynamic system is stable for j0 greater than jth0.     

Electrical potential differences across salt transporting membranes

The electrical potential differences across membranes where active transport of ions occurs has been examined using the formalism of linear non-equilibrium thermodynamics, and can be represented as the arithmetic sum of a resistive term, a term directly dependent on metabolism (i.e. electrogenic) and terms appropriate for describing a diffusion potential. The Hittorf transport number for each ion in the latter terms is the ratio of the partial conductances of the membrane to that ion to the total membrane conductance, and the conductance to an ion consists of the arithmetic sum of conductance of active and passive pathways providing these are independent. The conductances of active transport mechanisms arise from variation of the rate of transport with the electrochemical potentials against which they operate. The electrogenic term arises from imbalance between anion and cation transport. If an ion is transported by an obligatorily electrically neutral exchange for some other ion such transport gives rise to no electrogenic effect. A membrane will transport salt most efficiently if there is no imbalance between anion and cation transport, when it will not be electrogenic, but modest deviations from this condition will not degrade the efficiency of active transport markedly.     

Sodium transport and oxygen consumption in toad bladder. A thermodynamic approach.

The relationship between active sodium transport and oxygen consumption was investigated in toad urinary bladder exposed to identical sodium-Ringer's solution at each surface, while controlling the transepithelial electrical potential difference delta phi. Rates of sodium transport and oxygen consumption were measured simultaneously, both in the short-circuited state (delta phi = 0) and when delta phi was varied. Under short-circuit conditions, when the rates of active sodium transport changed spontaneously or were depressed with amiloride, the ratio of active sodium transport to the estimated suprabasal oxygen consumption Na/O2 was constant for each tissue, but varied among different tissues. Only when delta phi was varied did the ratio Na+/O2 change with the rate of active sodium transport; under these circumstances dNa+/dO2 was constant but exceeded the ratio measured at short-circuit [(Na+/O2)delta phi = 0[. This suggests that coupling between transport and metabolism is incomplete. The results are analyzed according to the principles of nonequilibrium thermodynamics, and intepreted in terms of a simple model of the transepithelial sodium transport system.     

Steady-state diffusion and the cell resting potential

The steady-state diffusion of ions through separate, selective channels is described according to irreversible thermodynamics. Ion fluxes thus obtained are the same as those in the parallel conductance model. The equivalent electric circuit set up to describe the system has its electromotive forces expressed by the chemical potentials of the diffusing ions. The expression obtained for the potential differs from the Goldman-Hodgkin-Katz formula, and is reputed to be more accurate. In order for the passive diffusion flows to remain steady, active transport mechanisms must pump the ions up their electrochemical potentials. Such pumps have been incorporated into the equivalent circuit. They supply energy lost in the dissipation caused by preexisting passive forces without affecting the potential, which can thus hardly be called passive diffusion potential. Ion pumps can also create an electric potential in excess of that by passive forces, especially when secondary active transport is involved. The same equivalent circuit is, however, able to describe the whole range of seemingly different situations – from passive diffusion of an electrolyte to active extrusion of anions from the living cell. It has been applied to explain the measured plasma membrane potential of cells, especially those whose potential does not behave as the potassium electrode. Received: 6 July 1998 / Revised version: 7 November 1998 / Accepted: 10 November 1998     

Sodium transport and oxygen consumption in toad bladder: A thermodynamic approach

The relationship between active sodium transport and oxygen consumption was investigated in toad urinary bladder exposed to identical sodium-Ringer's solution at each surface, while controlling the transepithelial electrical potential difference Δψ. Rates of sodium transport and oxygen consumption were measured simultaneously, both in the short-circuited state (Δψ = 0) and when Δψ was varied. Under short-circuit conditions, when the rates of active sodium transport changed spontaneously or were depressed with amiloride, the ratio of active sodium transport to the estimated suprabasal oxygen consumption Na⁺/O₂ was constant for each tissue, but varied among different tissues. Only when Δψ was varied did the ratio Na⁺/dO₂ change with the rate of active sodium transport; under these circumstances dNa⁺/dO₂ was constant but exceeded the ratio measured at short-circuit [(Na⁺/O₂)_Δψ=0]. This suggests that coupling between transport and metabolism is incomplete. The results are analyzed according to the principles of nonequilibrium thermodynamics, and interpreted in terms of a simple model of the transepithelial sodium transport system.     

Maltotriose fermentation by Saccharomyces cerevisiae

Maltotriose, the second most abundant sugar of brewer's wort, is not fermented but is respired by several industrial yeast strains. We have isolated a strain capable of growing on a medium containing maltotriose and the respiratory inhibitor, antimycin A. This strain produced equivalent amounts of ethanol from 20 g l⁻¹ glucose, maltose, or maltotriose. We performed a detailed analysis of the rates of active transport and intracellular hydrolysis of maltotriose by this strain, and by a strain that does not ferment this sugar. The kinetics of sugar hydrolysis by both strains was similar, and our results also indicated that yeast cells do not synthesize a maltotriose-specific α-glucosidase. However, when considering active sugar transport, a different pattern was observed. The maltotriose-fermenting strain showed the same rate of active maltose or maltotriose transport, while the strain that could not ferment maltotriose showed a lower rate of maltotriose transport when compared with the rates of active maltose transport. Thus, our results revealed that transport across the plasma membrane, and not intracellular hydrolysis, is the rate-limiting step for the fermentation of maltotriose by these Saccharomyces cerevisiae cells. Journal of Industrial Microbiology & Biotechnology (2001) 27, 34–38. Received 13 January 2001/ Accepted in revised form 29 May 2001     

Tissue specificity of assimilation and transport of nitrogen in the root ofZea mays L. seedlings. II. Radial transport of14C-amino acids

The radial transport of organic nitrogen compounds was studied in maize seedling roots in relation to the metabolism of uniformly labelled¹⁴C-amino acids (alanine, arginine, dicarboxylic amino acids and their amides) in the cortex zone. Most active metabolism accompanying transport to the stele was observed for¹⁴C-glutamic acid of “primary” amino acids and for¹⁴C-glutamine of “reserve” nitrogen sources. The transport of¹⁴C-asparagine and¹⁴C-arginine to the conducting bundles is accompanied by weak metabolism. A distinguishing feature of nitrogen metabolism in the stele is intensive decarboxylation of glutamic acid, formed in the course of radial transport and metabolism, to gamma-amino butyric acid. This process is assisted by a highly active glutamate decarboxylase present in the conducting bundles.     

Evidence for the Transport of Maltose by the Sucrose Permease,CscB, of <Emphasis Type="Italic">Escherichia coli</Emphasis>

The purpose of this study was to examine the sugar recognition and transport properties of the sucrose permease (CscB), a secondary active transporter from Escherichia coli. We tested the hypothesis that maltose transport is conferred by the wild-type CscB transporter. Cells of E. coli HS4006 harboring pSP72/cscB were red on maltose MacConkey agar indicator plates. We were able to measure “downhill” maltose transport and establish definitive kinetic behavior for maltose entry in such cells. Maltose was an effective competitor of sucrose transport in cells with CscB, suggesting that the respective maltose and sucrose binding sites and translocation pathways through the CscB channel overlap. Accumulation (“uphill” transport) of maltose by cells with CscB was profound, demonstrating active transport of maltose by CscB. Sequencing of cscB encoded on plasmid pSP72/cscB used in cells for transport studies indicate an unaltered primary CscB structure, ruling out the possibility that mutation conferred maltose transport by CscB. We conclude that maltose is a bona fide substrate for the sucrose permease of E. coli. Thus, future studies of sugar binding, transport, and permease structure should consider maltose, as well as sucrose. Yang Peng and Sanath Kumar contributed equally to this paper.     

Oxygen diffusion and consumption in active aerobic granules of heterogeneous structure

The interior structure of aerobic granules is highly heterogeneous, hence, affecting the transport and reaction processes in the granules. The granule structure and the dissolved oxygen profiles were probed at the same granule in the current work for possible estimation of transport and kinetic parameters in the granule. With the tested granules fed by phenol or acetate as carbon source, most inflow oxygen was consumed by an active layer thickness of less than 125 μm on the granule surface. The confocal laser scanning microscopy scans also revealed a surface layer thickness of approximately 100 μm consisting of cells. The diffusivities of oxygen transport and the kinetic constant of oxygen consumption in the active layers only were evaluated. The theoretical models adopted in literature that ignored the contributions of the layered structure of aerobic granule could have overlooked the possible limitations on oxygen transport.     

The Nature of Water Transport across Frog Skin

A method has been developed for determining simultaneously shortcircuit currents and net water fluxes across frog skin. The basis of the water flux measurement is the determination of changes in weight of a plastic chamber containing the skin and external solution. The accuracy of this method permits net water flows larger than 0.5 mg cm^-2hr.^-1 to be detected, and the apparatus has been used to investigate the relationship between active Na transport and non-osmotic water flow across the skin. Measurement of Na transport and net water influx across completely short-circuited skins provides no good correlation between the two flows. However, skins exhibiting no net water movement in sulfate Ringer displayed an apparent electroosmotic flow of about 40 water molecules per Na ion when depolarizing current densities of 50 and 100 μA cm^-2 are used. It is concluded from this and other evidence that the net water influx across frog skin may be partially electroosmotic in character and that there remains another component of water flow unrelated to active Na transport. A theoretical model, based on irreversible thermodynamics, has been developed to explain the non-osmotic water flow across frog skin.     

Transport kinetics of 6-deoxy-D-glucose inCandida parapsilosis

The strictly aerobic yeastCandida parapsilosis transports the nonmetabolizable monosaccharide 6-deoxy-D-glucose by an active process (inhibition by 2.4-dinitrophenol and other uncouplers but not by iodoacetamide), the accumulation ratio decreasing with increasing substrate concentration. Measured accumulation ratios are in agreement with those predicted from kinetic constants for influx and efflux. Energy for transport is probably required in the translocation step. The maximum rate is temperature-dependent with a transition point at 21 °C. the accumulation ratio is not, The uptake is most active at pH 4.5–8.5. It appears not to involve stoichiometric proton symport. The transport system is shared by D-glucose, D-mannose, D-galactose and possibly maltose but not by fructose, sucrose or pentoses. The apparent half-life of the transport system was 3.5–4 h.     

Model of Active Transport of Ions in Archaea Cells

A mathematical model of the active transport of main ions in cells of archaebacteria has been constructed. A set of equations has been developed and solved for ion fluxes through the bacterium membrane. The model is based on the principle “one ion—one transport system.” Considering experimental data, the major transport mechanism was determined for each ion and the balance equation was written on the basis of this mechanism in the stationary state. This allowed calculating values of the membrane potential and intracellular concentrations of the ions independently. The calculated values of the intracellular concentrations and resting potential are in qualitative agreement with the corresponding experimental values for cells of extremely halophilic archaea.     

Dual Pattern of Potassium Transport in Plant Cells: A Physical Artifact of a Single Uptake Mechanism

Analysis of potassium transport in plant root cells shows tworate-influencing regions: an unstirred boundary layer adjacentto the cell wall acts as a rate-limiting region and the negativelycharged cell wall acts as a rate-enhancing region. The rate-enhancingregion gives rise to a pseudo ‘dual mechanism’.These two regions act in concert to influence significantlythe characteristics of the concentration-dependent potassiumuptake process. The anomalous ion uptake behaviour found inthe literature is explained on the basis of a single activeuptake mechanism operating under the influence of these tworegions. The most critical property in support of the conceptof a ‘dual mechanism’ for cation uptake in plantroots is explained on this basis. It is unnecessary to invokeseparate groups of enzymes, each one of which is active overdifferent concentration ranges. One mechanism operating overthe entire concentration range is sufficient. Key words: Potassium transport, Rate-limiting region, Rate-enhancing region     

Energetics of active transport processes.

Active sodium transport across epithelial membranes has been analyzed by means of linear nonequilibirium thermodynamics. In this formulation the rates of active sodium transport JNa and the associated metabolic reaction Jr are postulated to be linear functions of both the electrochemical potential difference of sodium--XNa and the affinity A (negative free energy) of the metabolic reaction of driving transport. Experimental studies in various epithelia demonstrate that both JNa and Jr (oxygen consumption) are indeed linear functions of XNa. Theoretical considerations and experimental studies in other systems suggest that likelihood of linearity in A as well. If so, A may be evaluated. Several observations indicate that the quantity A evaluated from the thermodynamic formalism does in fact reflect the substrate-product ratio of the metabolic reaction which supports transport. This is in contrast to measurements of mean cellular concentrations, which may not reflect conditions at the site of transport. Associated studies of isotope kinetics permit the distinction between effects on the permeability of the active and passive transport pathways. With these combined approaches, it may prove possible to characterize both the energetic and permeability factors which regulate transport. The formulation has been applied to an analysis of the mechanism of action of the hormone aldosterone.     

A case of apparent active transport. I

When an experimenter determines the “internal concentration” of a substance in a cell (or cell suspension) it is in general the average concentration (quantity of substance divided by cell volume or volume of cell water) which is measured. When this concentration is less than that in the ambient medium but there is either no flow into the cell or flow from the cell into the medium, then (under the usually tacit assumption of spatial uniformity in the cell) the possibility of active transport is considered. The possibility that lack of spatial uniformity could lead to apparent active transport was early proposed by A. Bierman and later examined quantitatively by N. Rashevsky for a special case. In this paper spherical cells are treated but under quite general conditions regarding the metabolic aspects of the problem. It is shown that apparent active transport can result for a metabolite which is a reactant in one set of reactions and a product in another provided the sites of these sets of reactions are spatially separated in the cell.     

Mechanism of L-Lysine Transport by Pea Protoplasts

Dureja, I., Guha-Mukherjee, S. and Prasad, R. 1986. Mechanismof L-lysine transport by pea protoplasts.—J. exp. Bot.37: 549–555. L-Lysine uptake was studied in pea protoplasts to characterizethe transport process. The uptake was pH dependent with optimumat pH 5?8. A kinetic analysis of uptake showed that L-lyslneuptake was biphasic. The respiratory inhibitors, sodium arsenate,azide, iodoacetate and 2, 4, dinitrophenol, inhibited the uptakeof L-lysine at a final concentration of 0?1 mol m^–3 suggestingit to be mediated in part by an active process. Competitiveinhibition of L-lysine uptake by only L-arglnine and of L-leucineand glycine uptake by several amino acids indicated that L-lysineuptake occurs via a specific system whereas the uptake of L-leucineand glycine was mediated through a relatively non-specific permease. Key words: Pea protoplasts, L-lysine transport, active transport, specific system