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.

It is evident that protein conformational transitions play important roles in biological machinery; however, detailed pictures of these transition processes capable of making kinetic prediction are not yet available. For a full description of these transitions, we first need to describe kinematically movements between stable states. Then, more importantly, a free energy profile associated with the conformational change needs to be obtained. Recently, a new model to describe the energy landscape of protein conformational changes was applied to the conformational transition of adenylate kinase. In this model, the conformational change coupled to the ligand binding is described as a switching between two energy surfaces that correspond to ligand bound and unbound states. The nonlinearity of the protein conformational changes is described through an iterative usage of normal mode calculations. In addition, another kind of nonlinearity enters the dynamics of the conformational transitions due to cracking, or partial unfolding, which may occur during the conformational transitions. The consequences of this theoretical model are explored in greater detail. An improved model for the cracking that includes the cooperativity of the partial unfolding in analogy to nucleation is introduced.

Interprotein electron transfer (ET) reactions play an important role in biological energy conversion processes. One of these reactions, the ET between cytochrome c2 (cyt) and reaction center from photosynthetic bacteria, is the focus of this theoretical study. The changes in the ET rate constant at fixed distances during the association process were calculated as the cyt moved from the electrostatically stabilized encounter complex to the bound state having short range van der Waals contacts in the tunneling region. Multiple conformations of the protein were generated by molecular dynamics simulations including explicit water molecules. For each of these conformations, the ET rate was calculated by using the Pathways model. The ET rate increased smoothly as the cyt approached from the encounter complex to the bound state, with a tunneling decay factor ␤ ‫؍‬ 1.1 Å ؊1 . This relatively efficient coupling between redox centers is due to the ability of interfacial water molecules to form multiple strong hydrogen bonding pathways connecting tunneling pathways on the surfaces of the two proteins. The ET rate determined for the encounter complex ensemble of states is only about a factor of 100 slower than that of the bound state ( ‫؍‬ 100 s, compared with 1 s), because of fluctuations of the cyt within the encounter complex ensemble through configurations having strong tunneling pathways. The ET rate for the encounter complex is in agreement with rates observed in mutant reaction centers modified to remove shortrange hydrophobic interactions, suggesting that in this case, ET occurs within the solvent-separated, electrostatically stabilized encounter complex.encounter complex ͉ protein complex ͉ tunneling pathways E lectron transfer (ET) reactions play vital roles in biological systems. Intraprotein ET through redox cofactors bound within membrane proteins and interprotein ET between cofactors in different protein molecules provide the basis for energy conversion processes such as photosynthesis and respiration. The past few decades has seen tremendous growth in the development of reliable molecular-level theories and models for intramolecular biological ET reactions (for reviews, see refs. 1-7). However, relatively limited attention has been devoted to interprotein ET. These ET reactions are more complex, involving an additional association step needed to bring the two proteins into position for ET to occur.In this article, we investigate the interprotein ET reaction between the photosynthetic reaction center (RC) and the mobile electron carrier protein, cytochrome c 2 (cyt), that are part of the ET cycle in photosynthetic bacteria (1,8). The RC captures light energy by intraprotein ET to form an oxidized primary donor (bacteriochlorophyll dimer, D) and a reduced acceptor quinone (Q). The cyt transfers electrons to the oxidized primary donor in the RC as part of the light-induced ET chain that is coupled to proton pumping and ATP formation. Extensive experimental studies have been performed to understand this ET reacti...

We present a method for reconstructing a 3D structure from a pair distribution function by flexibly fitting known x-ray structures toward a conformation that agrees with the low-resolution data. This method uses a linear combination of low-frequency normal modes from elastic-network description of the molecule in an iterative manner to deform the structure optimally to conform to the target pair distribution function. A simple function, pair distance distribution function between atoms, is chosen as a test model to establish computational algorithms-optimization algorithm and scoring function-that can utilize low-resolution 1D data. To select a correct structural model based on less information, we developed a scoring function that takes into account a characteristic of pair distribution functions. In addition, we employ a new optimization algorithm, the trusted region method, that relies on both first and second derivatives of the scoring function. Illustrative results of our studies on simulated 1D data from five different proteins, for which large conformational changes are known to occur, are presented.