Chemical equilibrium active transport

Transport across biological membranes is classified according to the thermodynamics of the process. Passive transport is a thermodynamically downhill process the species move toward the equilibrium. The driving force for the passive transport is the potential difference between the two sides of the membrane. Active transport is a thermodynamically uphill process, it is coupled to a chemical reaction and is driven by it. The following transport mechanisms have been recognized ... 

For a cell membrane in a living animal, a very slight pressure difference will activate transport processes in the membrane, which will effectively eliminate the pressure difference. Introducing this change, there is no longer a state of equilibrium across the membrane, and other transport processes will take place. Such transport often is supported by chemical pumps, which move sodium ions from the protein phase to the aqueous phase. The simple estimation above illustrates that relatively small changes in the concentration are necessary to eliminate the osmotic pressure. In order to force PB — PA = 0, c(Na) in phase B must be reduced by 11 mmol/L, or by less than 10% of the previously determined concentration of 128 mmol/L (Gaiby and Larsen, 1995). 

One of the conventional methods for establishing the existence of active transport is to analyze the effects of metabolic inhibitors. The second is to correlate the level or rate of metabolism with the extent of ion flow or the concentration ratio between the interior and exterior of cells. The third is to measure the current needed in a short-circuited system having similar solutions on each side of the membrane the measured flows contribute to the short-circuited current. Any net flows detected should be due to active transport, since the electrochemical gradients of all ions are zero (Ai// = 0, cD = c,). Experiments indicate that the level of sodium ions within the cells is low in comparison with potassium ions. The generalized force of chemical affinity shows the distance from equilibrium of the /th reaction... 

Derive an equation for the phenomenological description of active transport of a substance through a membrane (Section 2.3.2) for the case of conjugate substance transfer through the membrane and chemical processes far from equilibrium (i.e., at Arij > RT). 

Several chemical reactions, including calcium carbonate and hydroxyapatite precipitation, have been studied to determine their relationship to observed water column and sediment phosphorus contents in hard water regions of New York State. Three separate techniques have been used to Identify reactions important in the distribution of phosphorus between the water column and sediments 1) sediment sample analysis employing a variety of selective extraction procedures 2) chemical equilibrium calculations to determine ion activity products for mineral phases involved in phosphorus transport and 3) seeded calcium carbonate crystallization measurements in the presence and absence of phosphate ion. 

Hence, at rest the neuron is in a state of temporary electrochemical equilibrium in which the resting membrane potential maintains a chemical gradient of ions. The chemical gradient is present due to the diffusion equilibrium potentials for each ion, but also as a result of the interfacial potentials and the electrogenic separation of charges caused by the Na -K" active transport system. Excitability of neurons depends on disequilibrium. 

In the case of the fast binary reaction we could eliminate the reaction term from the reaction-diffusion-advection equation. But in general this is not possible. In this chapter we consider another class of chemical and biological activity for which some explicit analysis is still feasible. We consider the case in which the local-reaction dynamics has a unique stable steady state at every point in space. If this steady state concentration was the same everywhere, then it would be a trivial spatially uniform solution of the full reaction-diffusion-advection problem. However, when the local chemical equilibrium is not uniform in space, due to an imposed external inhomogeneity, the competition between the chemical and transport dynamics may lead to a complex spatial structure of the concentration field. As we will see in this chapter, for this class of chemical or biological systems the dominant processes that determine the main characteristics of the solutions are the advection and the reaction dynamics, while diffusion does not play a major role in the large Peclet number limit considered here. Thus diffusion can be neglected in a first approximation. 

Fig. 11. Active transport using the simple carrier. Formal kinetic schemes for (a) countertransport and (b) co-transport. A and B are the two substrates of the carrier E either of which (in countertramsport) or both which (in co-transport) combine with E to form EA, EB or EAB. Subscripts 1 or 2 refers to substrate at side 1 or 2 of the membrane. The rate constants b, d, f, g, k are defined in the figure. AT" is the equilibrium constant of the chemical reaction /I =4.42 in primary active transport (and is equal to unity in the case of secondary active transport). Af=A /A 2 in co-transport. The square brackets denote concentrations and terms such as /4, =[/l,]/Arj, where is the relevant dissociation constant, here = dj/gi. J is the net flux in the 1 ->2 direction. (Figure taken, with permission, from [30].)...

Kedem ° attempted to circumvent the paradox implicit in the driving of vectorial transport processes with supposedly scalar chemical forces by introducing a vectorial cross coefficient in a non-equilibrium thermodynamic definition of active transport. Jardetzky , however, stated that the direct coupling between a metabolic reaction and a transport process, implied by Kedem s vectorial cross coefficient, was impossible because it would contravene the Curie principle (see also ref. 11). Katchalsky and Kedem, later supported by Moszynski et al, answered the criticism of Jardetzky by saying that Langeland had shown that the principle of Curie applies... 

Under steady-state operation, local mechanical equilibrium prevails at all microscopic and macroscopic interfaces in the membrane. It fixes the stationary distribution of absorbed water. The condition of chemical equilibrium is, however, lifted to allow for the flux of water. Continuity of the net water flux in the PEM and across its interfaces with adjacent media adjusts the gradients in water activity or pressure in the system. Water fluxes occur by diffusion, hydraulic permeation, and electro-osmotic drag. At external interfaces, vaporization and condensation proceed at rates that match the net water flux. These mechanisms apply to PEM operation in a working cell, as well as to ex situ water flux measurements that are conducted in order to investigate the transport properties of PEMs. 

The principle of Le ChStelier asserts that in general a system will react to lessen the effect of a stress on an intensive variable, if it can do so. This effect was illustrated by considering the shift in equilibrium by changing the temperature or the pressure on a system and by adding a reactant or product to the system. The application of the thermodynamics of chemical equilibrium to biological processes was illustrated through a discussion of the coupling of chemical reactions and active transport. 

Depending on the nature of the class, the instructor may wish to spend more time with the basics, such as the mass balance concept, chemical equilibria, and simple transport scenarios more advanced material, such as transient well dynamics, superposition, temperature dependencies, activity coefficients, the thermodynamics of redox reactions, and Monod kinetics, may be omitted. Similarly, by excluding Chapter 4, an instructor can use the text for a course focused only on the water environment. In the case of a more advanced class, the instructor is encomaged to expand on the material suggested additions include more rigorous derivation of the transport equations, discussions of chemical reaction mechanisms, introduction of quantitative models for atmospheric chemical transformations, use of computer software for more complex chemical equilibrium problems and groundwater transport simulations, and inclusion of case studies. References are provided with each chapter to assist the more advanced student in seeking additional material. 

The compulsory energetic coupling of chemical (biochemical) reactions and of diffusive mass-transfers was phenomenologically identified and also introduced in the well-known case for example of the so-called active transport by biologists it was explicited theoretically in several treatments using mostly calculations based on thermodynamics of non-equilibrium processes [7-11]. 

---