PubMed Health⌕ Search

Biomedical subjects

T L Hill

Publications and source records attributed to T L Hill.

17 recordsLinked to original sources
PubMed1979

Coupled enzyme systems in a vesicular membrane: oxidative phosphorylation as an example.

We consider a small vesicle whose membrane transports a ligand L into the vesicle through enzymatic units of type A and transports L out of the vesicle through units of type B. Oxidative phosphorylation in mitochondria provides an example, in which L is H+. The kinetics of the two membrane systems (A and B) are coupled through the concentration of L in the vesicle. This interdependence causes the combined membrane system (A plus B) to simulate a single system whenever the net ligand transport into the vesicle is zero. For example, in oxidative phosphorylation, it was thought for some time that ATP was synthesized by the respiratory chain system (via an "active intermediate"). We give the simplest possible analyses of this kind of coupled system, which is very common, by using two-state enzymes for both A and B above. A numerical example is included that illustrates respiratory control in a qualitative way: although the respiratory chain flux by itself does not depend on ADP concentration, the steady-state flux of the coupled systems (respiratory chain and reverse ATPase) does depend on ADP concentration through the interior ligand (H+) concentration.

Enzymes↗
PubMed1979

Approximate steady-state properties of lattices of interacting three-state enzyme molecules: a novel phase transition.

Previous work on the cooperative behavior of lattices of interacting two-state enzyme molecules at steady state is extended here to interacting three-state enzyme molecules with a one-way cycle. The Bragg-Williams (mean field) approximation is used. A phase-transition example with a bifurcation point is discussed. Compared to conventional phase transitions (with a van der Waals loop), several new and complicated features appear. A second paper on this subject will contain a number of other examples of three-state systems.

Enzymes↗
PubMed1979

Steady-state coupling of four membrane systems in mitochondrial oxidative phosphorylation.

According to Alexandre, Reynafarje, and Lehninger, four different membrane systems are involved, with definite stoichiometry, in the mitochondrial synthesis of ATP by electron transport, via proton transport. We adopt this model and pursue some of its thermodynamic consequences. At steady state, each of the four systems must have the same flux J through the membrane and the overall thermodynamic force X for oxidative phosphorylation is the sum of the four separate forces. From these properties, using an empirical linear flux-force relation for each system, it is easy to obtain J as a function of X. In turn, X depends on the inside [NAD+]/[NADH] and the outside [ATP]/[ADP][Pi] quotients (and on the pH inside). Thus, J is related to these quotients. The relationship we derive is similar to that described by Erecińska and Wilson, as deduced from a quite different model of oxidative phosphorylation. Proton transport is involved explicitly in three of the four systems of the present model. However, because of the steady-state stoichiometric coupling of the four systems, proton transport does not appear in the overall reaction. On the other hand, Erecińska and Wilson use, in their model, a direct connection between electron transport and ATP synthesis. The present paper demonstrates that J can be related to the quotients mentioned above without this direct connection.

Intracellular Membranes↗
PubMed1979

Theoretical methods for study of kinetics of models of the mitochondrial respiratory chain.

In earlier work, Hill and Chance obtained exact steady-state kinetic properties for partial models of the mitochondrial respiratory chain with two isopotential pools and one four-state "site enzyme" between the two pools. That work is extended here to full models of the respiratory chain with four isopotential pools and three four-state site enzymes between pairs of pools. Because of the complexity of the model, exact calculations are no longer possible. Instead, we show, by means of some examples, the feasibility of using Monte Carlo calculations on all cases and numerical solution of thousands of kinetic differential equations in many cases.

Enzymes↗
PubMed1978

Interacting enzyme systems at steady state: further Monte Carlo calculations on two-state molecules.

In this work, Monte Carlo calculations were made on a 10 x 10 lattice of two-state, steady-state enzyme molecules in two special cases for which the Bragg-Williams (mean field) approximation had earlier produced some very interesting phase-transition properties. The Monte Carlo results proved to be similar to Bragg-Williams in some respects but not in others. The discrepancies are attributed primarily to; (i) inadequate treatment by Bragg-Williams of strong negative cooperativity; and (ii) the finite size of the 10 x 10 lattice used in the exact calculations.

Enzymes↗
PubMed1978

Unsymmetrical and concerted examples of the effect of enzyme--enzyme interactions on steady-state enzyme kinetics.

In previous papers of this series, emphasis has been placed on the steady-state phase transition and critical properties of large lattices of interacting, symmetrical, and identical enzyme molecules. The present paper is concerned with a number of examples of enzyme--enzyme interactions that do not belong to the class of models of the earlier papers. These are more biochemically oriented and include heterologous dimers, a linear chain with unsymmetrical interactions, and concerted isologous dimers (half-the-sites reactivity).

Catalysis↗
PubMed1978

Interacting enzyme systems at steady state: location of the phase transition in approximations of the mean field type.

We consider a phase transition "loop," obtained from a mean field type of approximate treatment of a closed steady-state Ising system. Where is the cut (stable path) across the loop located? The general procedure, in answering this question, is to pass to an open version of the same system and use the cut that appears automatically in this case (no loop is possible in an open system). This is equivalent to finding the point at which the two phases have equal total probability in the open system. It is shown here that this procedure, when applied to a system of two-state enzyme molecules, is formally equivalent to well-known thermodynamic methods (Maxwell's theorem, etc.). These can be applied directly to the closed system without considering the open system explicitly. However, for enzyme molecules with more than two states, the "thermodynamic" method generally fails and one must fall back on the open system procedure mentioned above. Practical implementation of this procedure is not easy.

Enzymes↗
PubMed1977

Further study of the effect of enzyme-enzyme interactions on steady-state enzyme kinetics.

This paper continues an earlier one [Hill, T.L. (1977) Proc. Natl . Acad. Sci. USA 74, 3632-3632] and presents further introductory examples. Most attention is devoted to a closed linear chain of two-state enzyme molecules with nearest-neighbor interactions. The one-dimensional Ising theory can be used here. The Bragg-Williams (mean field) approximation is introduced to deal with a one-, two-, or three-dimensional lattice of enzyme molecules, at steady state, with an arbitrary kinetic diagram. The behavior of the flux in a phase transition is noted. Finally, a treatment is given for the first effect (second "viral" coefficient) of interactions on the flux in a dilute solution of two-state enzyme molecules.

Enzymes↗
PubMed1977

"Viral" expansion of enzyme flux and use of quasi-chemical approximation for two-state enzymes with enzyme-enzyme interactions.

Two examples of enzyme systems with interactions, at steady state, are treated here. In both cases, the enzyme cycle has two states and quasi-equilibrium in spatial distributions obtains at steady state (because f alpha + f beta = 1). The first example is a dilute solution of enzyme molecules in a solvent. The flux (turnover) per molecule is expanded in powers of the enzyme concentration (a "viral" expansion). Aggregation of the enzyme molecules in solution is considered as a special case. In the second example, we treat an arbitrary lattice of enzyme molecules, with nearest-neighbor interactions, using the well-known quasi-chemical approximation. The flux per molecule is obtained. Critical behavior and hysteresis are illustrated.

Enzymes↗
PubMed1977

Theoretical study of the effect of enzyme-enzyme interactions on steady-state enzyme kinetics.

Equilibrium statistical mechanics is much concerned with problems involving intermolecularinteractions, either in lattices or in pure fluids or solutions. The possibility of enzyme-enzyme interactions suggests that the same problems might be studied profitably at steady state as well as at equilibrium. In the systems we consider, each of the identical enzyme molecules of the system undergoes steady-state stochastic cycling among states i equal 1,....,n. But the molecules do not cycle independently. Two neghboring molecules, in states i and j, interact with a free energy wij (a function of the distance r in the solution case). The instantaneous transition probabilities between states for a given molecule will depend on the instantaneous interactions between the molecule in question and its neighbors. The primary question of interest is how the enzyme flux is influenced by the interactions. The general problem is outlined here and some simple special cases are treated. The discussion will be continued in a following paper [Hill, T. L. (1977) Proc. Natl. Acad. Sci. USA 74, in press]

Enzymes↗
PubMed1976

Reaction free energy surfaces in myosin-actin-ATP systems.

If we select for consideration any reaction M1 in equilibrium M2 in the myosin-ATPase cycle, the question arises as to the relations between the rate constants for (1) M1 equilibrium M2, (2) AM1 in equilibrium AM2 (A = actin), (3) A + M1 in equilibrium AM1, and (4) A + M2 equilibrium AM2, with actin and myosin either (a) in solution or (b) in the myofilament structure. It is shown here, by means of examples, that a single so-called potential of mean force, W, and structural free energy, Am, suffice to determine the reaction free energy surfaces for all of these transitions (W for the solution case, W + Am for the structured case). In fact, Am is the same for all reactions in the myosin-ATPase cycle. Of course, though indispensable as the starting point and adequate for qualitative understanding, the reaction free energy surface does not provide (without additional theory) the actual values of the rate constants or of the corresponding basic free energy changes in the myosin states involved. These rate constants and free energies are discussed, in a preliminary way, in two other papers.

Actins↗
PubMed1976

Free energy levels and entropy production associated with biochemical kinetic diagrams.

"Basic" and "gross" free energy levels are defined for the discrete states of a macromolecular biochemical kinetic system such as a free energy transducing enzyme (e.g., myosin or Na,K-ATPase). Basic free energy level differences are related to the first-order rate constants for transitions between states while gross free energy differences, along with the corresponding fluxes, determine the rate of entropy production in the system. In muscle contraction the analysis is complicated by the possibility of the system doing external mechanical work. The question of the sign of the flux or of the gross free energy level change in a given transition is examined for both single-cycle and multi-cycle models. More definite statements can be made in single-cycle cases. Some numerical examples are included. The more complicated cases are reserved for a subsequent paper.

Adenosine Triphosphatases↗
PubMed1976

Free energy levels and entropy production in muscle contraction and in related solution systems.

"Basic" and "gross" free energy levels of a macromolecule such as myosin or Na,K-ATPase, defined in a previous publication, are discussed here for two relatively complicated cases: a six-state kinetic diagram of the sort that could be used to describe the actin activation of myosin-ATPase in solution; and muscle contraction, where a similar kinetic diagram is needed for each value of a positional variable X.

Actins↗
PubMed1975

Free energy and the kinetics of biochemical diagrams, including active transport.

In earlier papers on muscle contraction it was found very useful to relate the actual (not standard) free energy levels of the different states in the biochemical diagram of the myosin cross-bridge to the first-order rate constants governing transitions between these states and to the details of the conversion of ATP free energy into mechanical work. This same approach is applied here to other macromolecular biochemical systems, for example, carriers in active transport, and simple enzyme reactions. With the definition of free energy changes between states of diagram used here (and in the muscle papers), the rate constants of the diagram are firat order, the macromolecular transitions are effectively isomeric, the equilibrium constants are dimensionless, the free energy changes are directly related to first-order rate constant ratios, and the ratio of products of forward and backward rate constants around any cycle of the diagram is related to operational free energy changes (e.g. the in vivo free energy of ADP HYDROLYSIS). These general points are illustrated by means of particular arbitrary models, especially transport models. In contrast to the muscle case, the free energy conversion question in other biochemical systems can be handled at the less detailed, complete-cycle level rather than at the elementary transition level. There is a corresponding complete-cycle kinetics, with composite first-order rate constants for the different possible cycles (in both directions). An introductory stochastic treatment of cycle kinetics is included.

Adenosine Triphosphatases↗