Exploring protein energy landscapes

The Journal of Physical Chemistry B, 1997

In this paper we demonstrate how the potential energy surface of a protein, which determines its conformational degrees of freedom, can be constructed from a series of advanced nonlinear optical experiments. The energy landscape of myoglobin was probed by studying its low-temperature structural dynamics, using several spectral hole burning and photon echo techniques. The spectral diffusion of the heme group of the protein was studied on a time scale ranging from nanoseconds to several days while covering a temperature range from 100 mK to 23 K. The spectral line broadening, as measured in three-pulse stimulated photon echo experiments, occurs in a stepwise fashion, while the exact time dependence of the line width is critically dependent on temperature. From these results we obtained the energy barriers between the conformational states of the protein. Aging time dependent hole-burning experiments show that, at 100 mK, it takes several days for the protein to reach thermal equilibrium. When, after this period a spectral hole is burned, the line broadening induced by welldefined temperature cycles is partly reversed over a period of several hours. From this we conclude that a rough structure is superimposed on the overall shape of the potential energy surface of the protein. By combining the hole burning and photon echo results, we construct a detailed image of this energy landscape, supporting the general concept of a structural hierarchy. More specifically, we show that the number of conformational substates in the lower hierarchical tiers is much lower than was previously anticipated and, in fact, is comparable to the number of taxonomic substates.

Physical Biology, 2005

Thermodynamic and dynamic properties of biomolecules can be calculated using a coarse-grained approach based upon sampling stationary points of the underlying potential energy surface. The superposition approximation provides an overall partition function as a sum of contributions from the local minima, and hence functions such as internal energy, entropy, free energy and the heat capacity. To obtain rates we must also sample transition states that link the local minima, and the discrete path sampling method provides a systematic means to achieve this goal. A coarse-grained picture is also helpful in locating the global minimum using the basin-hopping approach. Here we can exploit a fictitious dynamics between the basins of attraction of local minima, since the objective is to find the lowest minimum, rather than to reproduce the thermodynamics or dynamics.

2007

The construction of a realistic theoretical model of proteins is determinant for improving the computational simulations of their structural and functional aspects. Modeling proteins as a network of non-covalent connections between the atoms of amino acid residues has shown valuable insights into these macromolecules. The energyrelated properties of protein structures are known to be very important in molecular dynamics. However, these same properties have been neglected when the protein structures are modeled as networks of atoms and amino acid residues. A new approach for the construction of protein models based on a network of atoms is presented. This method, based Genet. Mol. Res. 6 (4): 799-820 (2007)

1995

Physical Review E, 2005

A method to reconstruct the energy landscape of small peptides is presented with reference to a 2d off-lattice model. The starting point is a statistical analysis of the configurational distances between generic minima and directly connected pairs (DCP). As the mutual distance of DCP is typically much smaller than that of generic pairs, a metric criterion can be established to identify the great majority of DCP. Advantages and limits of this approach are thoroughly analyzed for three different heteropolymeric chains. A funnel-like structure of the energy landscape is found in all of the three cases, but the escape rates clearly reveal that the native configuration is more easily accessible (and is significantly more stable) for the sequence that is expected to behave as a real protein.

Journal of Chemical Theory and Computation, 2019

1990

Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics. C.L. Brooks III, M. Karplus, and B. M. Pettitt.

Nature structural biology, 1995

Using the haem group of myoglobin as a probe in optical experiments makes it possible to study its conformational fluctuations in real time. Results of these experiments can be directly interpreted in terms of the structure of the potential energy surface of the protein. The current view is that proteins have rough energy landscapes comprising a large number of minima which represent conformational substates, and that these substates are hierarchically organized. Here, we show that the energy landscape is characterized by a number of discrete distributions of barrier heights each representing a tier within a hierarchy of conformational substates. Furthermore, we provide evidence that the energy surface is self-similar and offer suggestions for a characterization of the protein fluctuations.

Physical Review E, 2008

Inherent structure theory is used to discover strong connections between simple characteristics of protein structure and the energy landscape of a Gō model. The potential energies and vibrational free energies of inherent structures are highly correlated, and both reflect simple measures of networks of native contacts. These connections have important consequences for models of protein dynamics and thermodynamics.

Biophysical Chemistry, 1987

were performed on the internal motion of Trp 59 of ribonuclease T, (EC 3.1.27.3) in the free enzyme, 2'.GMP-enzyme complex and 3'-GMP-enzyme complex. The Trp 59 motion was also studied in the free enzyme using molecular dynamics simulations. Energetic analysis of activation barriers to the Trp 59 motion was performed using both the transition state theory and Kramers' theory. The activation parameters showed a dependence on solvent viscosity mdlcating the transrtion state approach m aqueous solution to be inadequate.