CHARMM (Chemistry at HARvard Macromolecular Mechanics) is a highly flexible computer program which uses empirical energy functions to model macromolecular systems. The program can read or model build structures, energy minimize them by first- or second-derivative techniques, perform a normal mode or molecular dynamics simulation, and analyze the structural, equilibrium, and dynamic properties determined in these calculations. The operations that CHARMM can perform are described, and some implementation details are given. A set of parameters for the empirical energy function and a sample run are included.

CHARMM: A program for macromolecular energy, minimization, and dynamics calculations

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

Infrared spectroscopy of proteins.

Recent experiments, advances in theory, and analogies to other complex systems such as glasses and spin glasses yield insight into protein dynamics. The basis of the understanding is the observation that the energy landscape is complex: Proteins can assume a large number of nearly isoenergetic conformations (conformational substates). The concepts that emerge from studies of the conformational substates and the motions between them permit a quantitative discussion of one simple reaction, the binding of small ligands such as carbon monoxide to myoglobin.

https://science.sciencemag.org/content/sci/254/5038/1598.full.pdf

The energy landscapes and motions of proteins.

Model for the structure of bacteriorhodopsin based on high-resolution electron cryo-microscopy.

Myoglobin rebinding of carbon monoxide and dioxygen after photodissociation has been observed in the temperature range between 40 and 350 K. A system was constructed that records the change in optical absorption at 436 nm smoothly and without break between 2 musec and 1 ksec. Four different rebinding processes have been found. Between 40 and 160 K, a single process is observed. It is not exponential in time, but approximately given by N(t) = (1 + t/to)-n, where to and n are temperature-dependent, ligand-concentration independent, parameters. At about 170 K, a second and at 200 K, a third concentration-independent process emerge. At 210 K, a concentration-dependent process sets in. If myoglobin is embedded in a solid, only the first three can be seen, and they are all nonexponential. In a liquid glycerol-water solvent, rebinding is exponential. To interpret the data, a model is proposed in which the ligand molecule, on its way from the solvent to the binding site at the ferrous heme iron, encounters four barriers in succession. The barriers are tentatively identified with known features of myoglobin. By computer-solving the differential equation for the motion of a ligand molecule over four barriers, the rates for all important steps are obtained. The temperature dependences of the rates yield enthalpy, entropy, and free-energy changes at all barriers. The free-energy barriers at 310 K indicate how myoglobin achieves specificity and order. For carbon monoxide, the heights of these barriers increase toward the inside; carbon monoxide consequently is partially rejected at each of the four barriers. Dioxygen, in contrast, sees barriers of about equal height and moves smoothly toward the binding site. The entropy increases over the first two barriers, indicating a rupturing of bonds or displacement of residues, and then smoothly decreases, reaching a minimum at the binding site. The magnitude of the decrease over the innermost barrier implies participation of heme and/or protein. The nonexponential rebinding observed at low temperatures and in solid samples implies that the innermost barrier has a spectrum of activation energies. The shape of the spectrum has been determined; its existence can be explained by assuming the presence of many conformational states for myoglobin. In a liquid at temperatures above about 230 K, relaxation among conformational states occurs and rebinding becomes exponential.

Dynamics of ligand binding to myoglobin

Proteins are dynamic systems. Recent evidence demonstrates that they exist in a large number of conformational substates and can continuously move from one substate to another; motion of a small ligand inside a protein may be possible only through these conformational fluctuations. To test this idea, we study with flash photolysis the binding of CO to protoheme and O2 and CO to myoglobin in many different solvents. The standard evaluation of such experiments yields information only about the protein-solvent system. A novel approach is presented which permits conclusions concerning the protein: Data from all solvents are considered together, and the rates for transitions of the ligand over various barriers are studied as a function of temperature for fixed solvent viscosities. Results show that over a wide range in viscosity the transition rates in heme-CO are inversely proportional to the solvent viscosity and can consequently be described by the Kramers equation. The rates of O2 and CO in myoglobin also depend on the solvent viscosity and are most sensitive to the solvent at the lowest viscosity. Viscosity influences protein reactions even in aqueous solutions. The data dan be interpreted by a dynamic model in which transitions into and inside myoglobin are governed by fluctuations between conformational substates corresponding to closed and open pathways. Ligand motion thus is mainly controlled by gates and not by static potential barriers. Some characteristic parameters for the substates are determined, and they agree approximately with similar parameters found in Mossbauer experiments. As expected, the barrier parameters evaluated in the novel approach deviate markedly from the ones obtained by the conventional procedure. Comparison with model calculations or basic theories will be meaningful only with the new evaluation, and the method may be essential for many or possibly all biochemical reactions.

Solvent viscosity and protein dynamics

The recombination after flash photolysis of dioxygen and carbon monoxide with sperm whale myoglobin (Mb), and separated beta chains of human hemoglobin (beta A) and hemoglobin Zurich (beta ZH), has been studied as a function of pH and temperature from 300 to 60 K. At physiological temperatures, a preequilibrium is established between the ligand molecules in the solvent and in the heme pocket. The ligand in the pocket binds to the heme iron by overcoming a barrier at the heme. The association rate is controlled by this final binding step. The association rate of CO to Mb and beta A is modulated by a single titratable group with a pK at 300 K of 5.7. The binding of CO to beta ZH, in which the distal histidine is replaced by arginine, does not depend on pH. Oxygen recombination is independent of pH in all three proteins. Comparison of the binding of CO at 300 K and at low temperatures shows that pH does not affect the preequilibrium but changes the barrier height at the heme. The pH dependence and the difference between O2 and CO binding can be explained by a charge-dipole interaction between the distal histidine and CO.

Control and pH dependence of ligand binding to heme proteins

Fourier transform infrared difference spectroscopy has been used to obtain the vibrational modes in the chromophore and apoprotein that change in intensity or position between light-adapted bacteriorhodopsin and the K and M intermediates in its photocycle and between dark-adapted and light-adapted bacteriorhodopsin. Our infrared measurements provide independent verification of resonance Raman results that in light-adapted bacteriorhodopsin the protein-chromophore linkage is a protonated Schiff base and in the M state the Schiff base is unprotonated. Although we cannot unambiguously identify the Schiff base stretching frequency in the K state, the most likely interpretation of deuterium shifts of the chromophore hydrogen out-of-plane vibrations is that the Schiff base in K is protonated. The intensity of the hydrogen out-of-plane vibrations in the K state compared with the intensities of those in light-adapted and dark-adapted bacteriorhodopsin shows that the conformation of the chromophore in K is considerably distorted. In addition, we find evidence that the conformation of the protein changes during the photocycle.

Fourier transform infrared difference spectroscopy of bacteriorhodopsin and its photoproducts.

We have studied the infrared spectra of the bound and photodissociated states of Mb-12CO and Mb-13CO from 5.2 to 300 K. The absorbance peaks seen between 1800 and 2200 cm-1 correspond to CO stretching vibrations. In the bound state of Mb-12CO, the known lines A0 at 1969, A1 at 1945, and A2 at 1927 cm-1, have center frequencies, widths, and absorbances that are independent of temperature between 5.2 and 160 K. Above 160 K, A2 gradually shifts to 1933 cm-1. The low-temperature photodissociated state (Mb) shows three lines (B0, B1, B2) at 2144, 2131, and 2119 cm-1 for 12CO. The absorbances of the three lines depend on temperature. B0 is tentatively assigned to free CO in the heme pocket and B1 and B2, to CO weakly bound to the heme or heme pocket wall. The data are consistent with a model in which photodissociation of MbCO leads to B1 and B2. B2 decays thermally to B1 above 13 K; rebinding to A occurs from B1. The barriers between B2 and B1 and between B1 and A are described by activation enthalpy spectra. Heme and the central metal atom in state Mb have near-infrared, EPR, and Mossbauer spectra that differ slightly from those of deoxyMb. The observation of essentially free CO in state B implies that the difference between Mb and deoxyMb is not due to an interaction of the flashed-off ligand with the protein but is caused by an incomplete relaxation of the protein structure at low temperatures.

L. Eisenstein

Papers

Dynamics of ligand binding to myoglobin

Solvent viscosity and protein dynamics

Control and pH dependence of ligand binding to heme proteins

Fourier transform infrared difference spectroscopy of bacteriorhodopsin and its photoproducts.

Infrared spectroscopy of photodissociated carboxymyoglobin at low temperatures