Large-scale motions of biomolecules involve linear elastic deformations along low-frequency normal modes, but for function nonlinearity is essential. In addition, unlike macroscopic machines, biological machines can locally break and then reassemble during function. We present a model for global structural transformations, such as allostery, that involve large-scale motion and possible partial unfolding, illustrating the method with the conformational transition of adenylate kinase. Structural deformation between open and closed states occurs via low-frequency modes on separate reactant and product surfaces, switching from one state to the other when energetically favorable. The switching model is the most straightforward anharmonic interpolation, which allows the barrier for a process to be estimated from a linear normal mode calculation, which by itself cannot be used for activated events. Local unfolding, or cracking, occurs in regions where the elastic stress becomes too high during the transition. Cracking leads to a counterintuitive catalytic effect of added denaturant on allosteric enzyme function. It also leads to unusual relationships between equilibrium constant and rate like those seen recently in singlemolecule experiments of motor proteins.T he regulation of biological machinery through allostery is a dominant theme in our modern molecular understanding of life. Allostery requires a biomolecule to have at least a pair or, more likely, a multiplicity of conformational states of nearly equal free energy. How can we describe movement between such states? When the pair of states exhibits large-scale structural differences, it is tempting to connect the states by routes using the low-frequency collective elastic vibrations around each structure, the normal modes with the smallest restoring forces. Even in its simplest form, the notion of normal modes is remarkably successful for visualizing and predicting the character of the motions. The motions are in reality overdamped, but their structure often parallels the low-frequency normal modes (1). Yet clearly, a linear normal mode description cannot be complete because the very existence of the two low-lying conformations requires us to acknowledge considerable anharmonicity. The normal mode picture strictly describes the excitations about a single minimum. The limited adequacy of a normal mode description becomes even more apparent when we try to embed our picture of the motion between two dominant conformational states in the complete energy landscape of a biomolecule, which is replete with a myriad of local minima, ranging from the more subtle conformational substrates apparent in kinetic experiments (2) to the still more disordered states that are partially unfolded. Our goal in this article is to describe how allosteric conformational switches function by using a theoretical framework that unites an energy landscape description with the elastic model based on normal modes. To do so we need to go beyond the usual approaches that describe only the geometr...

Conformational heterogeneity in proteins is known to often be the key to their function. We present a coarse grained model to explore the interplay between protein structure, folding and function which is applicable to allosteric or non-allosteric proteins. We employ the model to study the detailed mechanism of the reversible conformational transition of Adenylate Kinase (AKE) between the open to the closed conformation, a reaction that is crucial to the protein's catalytic function. We directly observe high strain energy which appears to be correlated with localized unfolding during the functional transition. This work also demonstrates that competing native interactions from the open and closed form can account for the large conformational transitions in AKE. We further characterize the conformational transitions with a new measure Φ Func , and demonstrate that local unfolding may be due, in part, to competing intra-protein interactions.

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Mode coupling in a protein molecule was studied by a molecular dynamics simulation of the intramolecular vibrational energy transfer in myoglobin at near zero temperature. It was found that the vibrational energy is transferred from a given normal mode to a very few number of selective normal modes. These modes are selected by the relation between their frequencies, like Fermi resonance, governed by the third order mode coupling term. It was also confirmed that the coupling coefficients had high correlation with how much the coupled modes geometrically overlapped with each other.