Hans Frauenfelder

A unified model of protein dynamics

Protein functions require conformational motions. We show here that the dominant conformational motions are slaved by the hydration shell and the bulk solvent. The protein contributes the structure necessary for function. We formulate a model that is based on experiments, insights from the physics of glass-forming liquids, and the concepts of a hierarchically organized energy landscape. To explore the effect of external fluctuations on protein dynamics, we measure the fluctuations in the bulk solvent and the hydration shell with broadband dielectric spectroscopy and compare them with internal fluctuations measured with the Mössbauer effect and neutron scattering. The result is clear. Large-scale protein motions are slaved to the fluctuations in the bulk solvent. They are controlled by the solvent viscosity, and are absent in a solid environment. Internal protein motions are slaved to the beta fluctuations of the hydration shell, are controlled by hydration, and are absent in a dehydrated protein. The model quantitatively predicts the rapid increase of the mean-square displacement above ≈200 K, shows that the external beta fluctuations determine the temperature- and time-dependence of the passage of carbon monoxide through myoglobin, and explains the nonexponential time dependence of the protein relaxation after photodissociation.

The role of structure, energy landscape, dynamics, and allostery in the enzymatic function of myoglobin.

The grail of protein science is the connection between structure and function. For myoglobin (Mb) this goal is close. Described as only a passive dioxygen storage protein in texts, we argue here that Mb is actually an allosteric enzyme that can catalyze reactions among small molecules. Studies of the structural, spectroscopic, and kinetic properties of Mb lead to a model that relates structure, energy landscape, dynamics, and function. Mb functions as a miniature chemical reactor, concentrating and orienting diatomic molecules such as NO, CO, O2, and H2O2 in highly conserved internal cavities. Reactions can be controlled because Mb exists in distinct taxonomic substates with different catalytic properties and connectivities of internal cavities.

Rebinding and relaxation in the myoglobin pocket

The infrared stretching bands of carboxymyoglobin (MbCO) and the rebinding of CO to Mb after photodissociation have been studied in the temperature range 10-300 K in a variety of solvents. Four stretching bands imply that MbCO can exist in four substates, A0-A3. The temperature dependences of the intensities of the four bands yield the relative binding enthalpies and and entropies. The integrated absorbances and pH dependences of the bands permit identification of the substates with the conformations observed in the X-ray data (Kuriyan et al., J. Mol. Biol. 192 (1986) 133). At low pH, A0 is hydrogen-bonded to His E7. The substates A0-A3 interconvert above about 180 K in a 75% glycerol/water solvent and above 270 K in buffered water. No major interconversion is seen at any temperature if MbCO is embedded in a solid polyvinyl alcohol matrix. The dependence of the transition on solvent characteristics is explained as a slaved glass transition. After photodissociation at low temperature the CO is in the heme pocket B. The resulting CO stretching bands which are identified as B substates are blue-shifted from those of the A substates. At 40 K, rebinding after flash photolysis has been studied in the Soret, the near-infrared, and the integrated A and B substates. All data lie on the same rebinding curve and demonstrate that rebinding is nonexponential in time from at least 100 ns to 100 ks. No evidence for discrete exponentials is found. Flash photolysis with monitoring in the infrared region shows four different pathways within the pocket B to the bound substates Ai. Rebinding in each of the four pathways B----A is nonexponential in time to at least 10 ks and the four pathways have different kinetics below 180 K. From the time and temperature dependence of the rebinding, activation enthalpy distributions g(HBA) and preexponentials ABA are extracted. No pumping from one A substate to another, or one B substate to another, is observed below the transition temperature of about 180 K. If MbCO is exposed to intense white light for 10-10(3) s before being fully photolyzed by a laser flash, the amplitude of the long-lived states increases. The effect is explained in terms of a hierarchy of substates and substate symmetry breaking. The characteristics of the CO stretching bands and of the rebinding processes in the heme pocket depend strongly on the external parameters of solvent, pH and pressure. This sensitivity suggests possible control mechanisms for protein reactions.

Biomolecules: Where the Physics of Complexity and Simplicity Meet

Are we moving toward a time when no new and exciting problems appear in physics? Would the vaunted “theory of everything” mean the end of creative physics? A similar scenario was played out at the end of the last century, when some great physicists declared that only minor problems remained to be solved.

Dynamics of carbon monoxide binding to protoheme

Protoheme rebinding of carbon monoxide after photodissociation has been observed at temperatures from 5 to 340 K for times from 2 μs to 1 ks. Below 80 K, binding is nonexponential in time and CO‐concentration independent, above 230 K exponential and the rate is CO‐concentration proportional. A model is proposed in which the carbon monoxide, moving from the solvent to the binding site at the ferrous heme iron, encounters two successive barriers. The outer is formed by the solvent, the inner is a property of the heme and probably connected to the motion of the iron from the spin‐2 deoxy to the spin‐0 carbon monoxide state. The temperature dependence of the two processes yields all activation enthalpies and entropies for the two barriers. The nonexponential rebinding observed at low temperatures implies that the inner barrier possesses distributed activation enthalpy and entropy. The enthalpy spectrum and the entropy spread are determined. The spectrum demonstrates that heme exists in many different conformational states. At low temperatures, these states are frozen; above about 230 K, rapid conformational relaxation renders rebinding exponential. Below 15 K, quantum‐mechanical molecular tunneling dominates. The tunneling rate yields the width of the innermost barrier. Earlier experiments on carbon monoxide binding to myoglobin had provided evidence for four barriers. The present results imply that the innermost barrier in myoglobin is caused by the heme, the outermost by the solvent, and the two intermediate ones by the globin.

Hydration, slaving and protein function

Protein dynamics is crucial for protein function. Proteins in living systems are not isolated, but operate in networks and in a carefully regulated environment. Understanding the external control of protein dynamics is consequently important. Hydration and solvent viscosity are among the salient properties of the environment. Dehydrated proteins and proteins in a rigid environment do not function properly. It is consequently important to understand the effect of hydration and solvent viscosity in detail. We discuss experiments that separate the two effects. These experiments have predominantly been performed with wild-type horse and sperm whale myoglobin, using the binding of carbon monoxide over a broad range of temperatures as a tool. The experiments demonstrate that data taken only in the physiological temperature range are not sufficient to understand the effect of hydration and solvent on protein relaxation and function. While the actual data come from myoglobin, it is expected that the results apply to most or all globular proteins.

THE EFFECT OF VISCOSITY ON THE PHOTOCYCLE OF BACTERIORHODOPSIN

Abstract— We study the effect of solvent viscosity on the kinetics of the photocycle of bacteriorhodopsin (bR) from Halobacterium halobium. Solvent viscosity is altered by changing the glycerol concentration from 20 to 80% glycerol by volume. The kinetics of the photocycle are observed after flash photolysis at four wavelengths at several temperatures between 240 and 315 K. Assuming a sequential model, bR → K ‐→ L → M → O → bR, Arrhenius plots of the rate coefficients determine the activation enthalpies and frequency factors for each step. Kinetic data from all solvents are considered together and studied as a function of temperature for fixed solvent viscosities. The early steps of the cycle are insensitive to solvent viscosity, →; the later steps are retarded with increasing viscosity. Activation enthalpies are independent of viscosity; the frequency factors are proportional to η−K, where the exponent k 0.25 for the transition K → L, 0.0 for L → M, 0.8 for M → O and 0.5 for O → bR.

The energy landscape in non-biological and biological molecules

The concept of energy landscapes promises to connect aspects of biology, chemistry and physics. A recent paper highlights the need for continuous exchange of information between fields to maximize the utility of this idea.

Dynamics of carbon monoxide binding by heme proteins.

Rebinding of carbon monoxide to myoglobin and to cytochrome P-450 after removal by a light flash occurs down to 50�K for myoglobin and 25�K for cytochrome P-450 in glycerol-water solution. Above 240�K the reaction is second order; between 240� and 200�K the rebinding becomes exponential and independent of the carbon monoxide concentration. Below 150�K the reaction follows a power law and is approximately 103 times faster for cytochrome P-450 than for myoglobin.

Time- and temperature dependence of large-scale conformational transitions in myoglobin

Structure, dynamics, and function of proteins are strongly interrelated. We study the structure-function relationship in carbonmonoxy-myoglobin (MbCO) using two techniques: (i) flash photolysis with rebinding monitored in the CO stretch bands over wide ranges in time (≈ 3 μs to 1 s) and temperature (60 to 260 K); (ii) pressure-jump experiments with protein relaxations monitored in the CO stretch bands by FTIR spectroscopy for times between 10 s and 30 ks and temperatures between 155 and 220 K. The three CO stretch bands correspond to three major conformational substates, A0, A1, and A3, with different structures and rebinding kinetics. The flash-photolysis experiments show that the absorbance change of A0 is nonmonotonic in time during rebinding above about 220 K owing to interconversion of A0 with A1 and A3. The P-jump experiments establish that MbCO experiences large-scale motions which are nonexponential in time, non-Arrhenius in temperature, and strongly dependent on solvent viscosity. One of the motions observed in the P-jump experiments corresponds to the large-scale structural transition, A0→A1 + A3, observed during rebinding. These results, together with earlier data, begin to give a detailed picture of the conformational energy landscape of MbCO: it contains many conformational substates which are hierarchically arranged in at least three tiers. Motions in each of the three tiers affect the MbCO rebinding kinetics.