Nonlinear elasticity, proteinquakes, and the energy landscapes of functional transitions in proteins

Abstract

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...

Molecular Dynamics of Apo-Adenylate Kinase: A Distance Replica Exchange Method for the Free Energy of Conformational Fluctuations

“…21,20 Both studies conclude that the lid and Amp-bd domains can rearrange without a great (free) energy penalty, while the core is quite stable during this transition. Maragakis and Karplus, 21 starting from the open form, find that first mainly the lid closes and then the Amp-bd domain closes.…”

Protein dynamics and function from solution state NMR spectroscopy

“…the unfolding of localized polypeptide segments in the transition state structure (Hyeon & Onuchic, 2007;Miyashita et al 2003). This postulate builds on a notion from energy landscape theory (Frauenfelder et al 1991(Frauenfelder et al , 2009Onuchic & Wolynes, 1993) that proteins constantly fluctuate between states in a stochastic way.…”

Crystal structure of the zinc-, cobalt-, and iron-containing adenylate kinase from Desulfovibrio gigas: a novel metal-containing adenylate kinase from Gram-negative bacteria

“…2) exhibited good correlation with the experimentally observed changes in conformation [37][38][39][40]. The LID domain and the AMP binding region in the core domain are directly involved in the dynamic event during catalysis, closing over the enzyme's ATP and AMP binding sites.…”

“…The LID domain and the AMP binding region in the core domain are directly involved in the dynamic event during catalysis, closing over the enzyme's ATP and AMP binding sites. Computational pathway analysis of ligand-free E. coli AK [38,39] and the crystal structures of the conformational substates of A. aeolicus along this pathway toward the closed form have shown the changes in these two specified regions along the reaction pathway [41]. The most striking observation was that changing the metal did not influence the directionality of the movement of the LID domain.…”

“…As expected, the LID domain of Zn-AK is in a more open conformation owing to the strong crystal packing interactions and has a different topology owing to the presence of the metal ion. One other structure of AK from Gram-negative bacteria-AK from A. aeolicus [38]-has been reported, as have several structures from Archaea-AK from Methanococcus voltae and Methanococcus thermolithotrophicus [43] (Gram negative) and AK from Methanococcus maripaludis [9,43] and Sulpholobus acidocaldarius (variable response to the Gram stain) [10]-but none of them contain a metal atom in their LID domain. The multiple sequence alignment of AK from D. gigas and these three reported AK is presented in Fig.…”