The physical aspects of enzyme functioning

On the beneficent thickness of water

In the 1930s, Lars Onsager published his famous 'reciprocal relations' describing free energy conversion processes. Importantly, these relations were derived on the assumption that the fluxes of the processes involved in the conversion were proportional to the forces (free energy gradients) driving them. For chemical reactions, however, this condition holds only for systems operating close to equilibrium-indeed very close; nominally requiring driving forces to be smaller than k B T. Fairly soon thereafter, however, it was quite inexplicably observed that in at least some biological conversions both the reciprocal relations and linear flux-force dependency appeared to be obeyed no matter how far from equilibrium the system was being driven. No successful explanation of how this 'paradoxical' behaviour could occur has emerged and it has remained a mystery. We here argue, however, that this anomalous behaviour is simply a gift of water, of its viscosity in particular; a gift, moreover, without which life almost certainly could not have emerged. And a gift whose appreciation we primarily owe to recent work by Prof. R. Dean Astumian who, as providence has kindly seen to it, was led to the relevant insights by the later work of Onsager himself.

The chemical properties of out-of-equilibrium states of proteins and the role of these states in protein functioning

The out-of-equilibrium states of several iron-containing proteins (cytochromes c of different origin, haemoglobin, myoglobin, ferredoxin and other non-haem iron proteins, cytochrome c oxidase, horseradish peroxidase) were recorded after fast changes in the active centre (electron reduction of iron, ligand dissociation). Strained states result in which the active centre has already been changed and undergone vibrational relaxation but the main part of protein globule is in the 'old', now out-of-equilibrium, state. Protein structure and chemical properties in these states differ considerably from those in equilibrium states. As a rule, the rate constants of protein-specific chemical reactions increase in out-of-equilibrium states by 1--3 orders of magnitude in comparison with those in equilibrium states. Spectra and reactivity of these proteins change in the course of slow (up to 10(-1) s) conformational relaxation, continuously approaching the equilibrium values. It seems that this conformational relaxation is essentially the elementary act of many enzymic reactions for which the rate of substrate-product transformation is determined by the rate of this conformational change.

Regulation of CFTR ion channel gating by MgATP

Single channel currents of wild-type CFTR reconstituted in lipid bilayers were recorded to study the temperature dependence of channel gating between +20 degrees C and +40 degrees C. The opening of the channel was highly temperature dependent and required an activation energy of about 100 kJ/mol. Closing of the channel was only weakly temperature dependent with an activation energy close to that of diffusion in water. We found no significant difference in the free energy between the open and closed states. Most of the excess energy needed to activate channel opening is used to diminish the entropy of the open state. This structural reorganization is initiated by ATP binding followed by interconversion to the open channel structure as the CFTR-ATP-Mg complex passes to the transition state for hydrolysis. The energy of the CFTR-ATP-Mg interaction in the transition state is responsible for the CFTR ion channel opening rather than the energy of ATP hydrolysis. Channel closing is a diffusion limited process and does not require additional ATP binding.

Evidence for a low temperature transition state binding preference in bovine adenosine deaminase

Arrhenius plots of the interactions of bovine adenosine deaminase (ADA) and of coformycin-inhibited ADA with adenosine are non-linear and reveal that coformycin significantly increases the activation energy for reaction only at temperatures well below the normal operating temperature of the enzyme (38.3 degrees C). This apparent enhanced affinity of the enzyme for the transition state analog at low temperature is confirmed from determinations of coformycin binding at 38.3 degrees C (KI = 5.3 x 10(-11) M) and at 21 degrees C (KI = 1.1 x 10(-11) M). It is suggested that these data are inconsistent with a model for general enzyme catalysis that requires an initial transition state complementary active site. Instead, it is suggested that an initial active site transition state complementarity is undesirable and the tendency of the enzyme to exist in this conformer at low temperatures is responsible for its inefficient interaction with adenosine substrate.

Distinct affinity and effector residues in the binding site for a regulatory ligand. The mitochondrial uncoupling protein as a model

A hypothesis concerning two distinct classes of amino acid residues in some regulatory binding sites is proposed. The "affinity residues" are those that are unable to transduce the ligand information signal but are responsible for overcoming the barrier for the attachment of a ligand to its binding site while the "effector residues" transfer the binding signal to the other functional part of the protein, which then undergoes a non-equilibrium energetic cycle induced by interaction with the ligand. As an example, the purine nucleotide inhibition of H+ transport through the uncoupling protein of brown adipose tissue mitochondria is discussed; there is a concentration range in which the nucleotide is bound but does not inhibit H+ transport. This is interpreted in terms of inaccessibility of the effector residues inducing H+ transport inhibition below a certain threshold concentration.

Comparison of the kinetics and thermodynamics of the carrier systems for glucose and leucine in human red blood cells

Kinetic data for the transport of glucose and leucine in human red blood cells are fitted to the conventional carrier model and the thermodynamics of the two carrier mechanisms are compared. In the absence of the carried molecule both carriers exist mainly in the inward-facing conformation at low temperatures and the outward-facing conformation at physiological or supra-physiological temperatures, this finding reflecting the strongly endothermic process involved in changing from the inward- to outward-facing forms. Reorientations from inward- to outward-conformations also involve substantial increases in entropy for both carriers. In contrast, substrate binding to the glucose carrier involves little change in enthalpy and an increase in entropy, while leucine binding is strongly exothermic and associated with a decrease in entropy. Application of transition state theory to glucose carrier kinetics reveals that the entropy of formation of the transition state of the carrier is much greater than that for the transition state of the carrier-glucose complex.

The exponential model for a regulatory enzyme. An interpretation of the linear free-energy relationship

A physical mechanism is suggested to explain the linear free-energy relationship employed in the exponential model for a regulatory enzyme [Ainsworth (1977) J. Theor. Biol. 68, 391-413]. The interpretation depends on the assumption that the structure of the enzyme changes in proportion to its saturation by substrate but at a rate that is low compared with the rates of the association-dissociation reactions of the enzyme-substrate system.

Protein dynamics investigated by neutron diffraction

The most correct model of the molecular structure of a protein molecule is one which describes it as having a number of variable conformational states. These states differ in degree over a large spectrum of structural variation ranging from individual atomic vibrational motion to significant tertiary denaturation. The application of the neutron diffraction techniques discussed above dealt with two classes of conformational fluctuation, "protein breathing" and "regional melting." The utility of the neutron technique stems from the ability to locate hydrogen atoms and to discriminate between hydrogens and deuteriums. This latter attribute allows for performing H/D exchange experiments by identifying individual sites of exchange. With this information it has been possible to discern which regions of the protein molecule undergo regional melting. Protein breathing was explored by analyzing the rotational properties of side chain methyl groups. Such information clearly suggested that most of these groups reside in "staggered" (low energy) conformation in the time averaged structure and are not greatly affected by local structural packing. Together these two classes of conformational fluctuation span nearly the full range of all motions that might play a role in biological activity. Information about such motions can be obtained from other types of physicochemical methods, but in most cases the interpretation of the data is considerably less definitive than that which can be obtained from a neutron analysis.

Dynamical theory of activated processes in globular proteins

A method is described for calculating the reaction rate in globular proteins of activated processes such as ligand binding or enzymatic catalysis. The method is based on the determination of the probability that the system is in the transition state and of the magnitude of the reactive flux for transition-state systems. An "umbrella sampling" simulation procedure is outlined for evaluating the transition-state probability. The reactive flux is obtained from an approach described previously for calculating the dynamics of transition-state trajectories. An application to the rotational isomerization of an aromatic ring in the bovine pancreatic trypsin inhibitor is presented. The results demonstrate the feasibility of calculating rate constants for reactions in proteins and point to the importance of solvent effects for reactions that occur near the protein surface.

Protein dynamics investigated by the neutron diffraction-hydrogen exchange technique

A new approach, using neutron diffraction and the hydrogen exchange (H/D) technique, has been used to study the extent and nature of the inherent conformational fluctuations in the protein, trypsin. The observed pattern of exchange was used to investigate systematic relationships between exchangeable sites and structural and chemical properties of the molecule. Results of this analysis indicate that hydrogen-bonding structure is the dominant factor governing rates of exchange. The model of conformational mobility which best explains the experimental findings involves a localized disruption of the secondary structure within different regions of the protein molecule, each limited in extent to the breaking of a small number of hydrogen bonds.

Dynamics of proton transfer and enzymatic activity

The rate-determining elementary reaction step, i.e. proton transfer from the chymotrypsin active centre to the scissile substrate bond had been studied in the present work. On the basis of our theoretical results a hypothesis was formulated to explain chymotrypsin enzymatic efficiency. After ES complex formation excited vibrational states are populated in the enzyme molecule. In the rate-determining elementary reaction step, the proton transfer takes place from the first excited vibrational state of the N-H bond in the imidazole group of His57. This proton transfer is realised by quantum mechanical tunneling mechanism.

Crystallographic studies of the dynamic properties of lysozyme

The patterns of atomic displacements in the crystals of hen and human lysozyme derived from independent crystallographic refinement are broadly similar. Analysis of the pattern indicates a close correlation with molecular structure, strongly suggestive of intramolecular motion. The active site of lysozyme is located in a region of high displacement. It is concluded that protein mobility may play a significant part in biological activity and that X-ray crystallography can contribute to its analysis.

A molecular mechanism of the energetic coupling of a sequence of electron transfer reactions to endergonic reactions

A molecular mechanism of the energetic coupling of a sequence of electron transfer reactions to endergonic reactions is proposed and discussed from a physical point of view. The scheme represents a synthesis of concepts of electron transfer by tunneling and the conformational and chemiosmotic aspects of energy coupling processes. Its relation to existing experimental information and theoretical models is discussed, and further experimental tests are suggested.

The physical aspects of energy transduction in biological systems

The primary energy sources for all the organisms living on the Earth are either sunlight or the energy liberated during chemical transformations (mainly, oxidation) of certain substances – food. Within the cell this energy is transformed, accumulated, and then utilized to ensure a multitude of processes (synthesis of new low- and high-molecular compounds, muscle contraction, luminescence, transfer of ions counter to their concentration gradients, etc.).

The role of universal ‘energy keeper’, of the, as it were, ‘energy small change’ in biology is played by the molecules of adenosine tri- phosphate (ATP) whose hydrolytic dissociation in water solutions with the formation of adenosine diphosphate (ADP) and inorganic phosphate (P1) is accompanied by a rather strong decrease of system energy.†