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FAST Predictions for Protein Flexibility and Stability Dennis R. Livesay and Donald J. Jacobs The University of North Carolina at Charlotte Linking Protein Flexibility to Thermodynamic Stability Computer-aided Protein Engineering and Design MECHANICS Globally Rigid Globally Flexible What is the motivation? Computational design of proteins with specific stability and flexibility relationships would significantly advance the pharmaceutical and biotechnology industries. Yet, many pitfalls continue to limit the success of computer-aided molecular design. -TS Why focus on conformational flexibility? A critical link between structure, stability and biological function is conformational flexibility, which is characterized by an ensemble of accessible states. Conformational flexibility regulates specificity in mechanical response as manifested in dynamics. For example, enzymes must be flexible enough to mediate a reaction pathway, yet rigid enough to achieve molecular recognition. Conformational flexibility regulates protein stability through conformational entropy as an enthalpy-entropy compensation mechanism. For example, the binding affinity of a ligand at a receptor site in a protein can be altered by the binding of a different molecule at a distant site, leading to allostery. H H -TS -TS H STABLE representing the native state (NS) UNSTABLE representing the transition state (TS) STABLE representing the unfolded state (US) THERMODYNAMICS QSFR: Quantitative Stability & Flexibility Relationships What is the challenge? The challenge is to develop a physical model to accurately predict protein flexibility and stability for specified thermodynamic and solvent conditions in fast computing times for high throughput applications. Simulation, Models and Fundamental Science Assuming a perfect model, simulations will generally miss important mechanisms because of incomplete exploration of the ensemble of accessible states. To overcome this problem it is common to employ the simplest possible model that retains all essential elements of interest. However, simulations based on a flawed model will predict events that are impossible to occur. That is, an oversimplified model will misrepresent the underlying Physics, Chemistry and/or Biology. (a) Free energy landscapes for E. coli & T. thermophilius orthologs at their respective Tm. (b) Rigid cluster size susceptibility. (c) Probability metric for backbone flexibility. Comparative QSFR Across Protein Families A Mechanical Model for Protein Thermodynamics A protein consist of many types of competing weak interactions that determine its structure and thermodynamic stability. The most fundamental aspect of any model is to identify all relevant degrees of freedom and constraints. In statistical physics, global constraints such as fixed total energy or temperature, or fixed total volume or pressure, play an essential role in defining the relevant thermodynamic ensemble to calculate equilibrium properties. Likewise, chemical bonding and weaker contact interactions act as mechanical constraints. Applying constraint theory allows the ensemble of accessible states to be partitioned in terms of mechanical characteristics. A Radically Different Computational Method (Top) Sequence alignment of 9 oxidized thioredoxin (TRX) structures. (Red, blue) indicates the backbone is (flexible, rigid). (Right) A dendrogram describing the clustering of 9 TRX cooperativity correlation. Mapping out allosteric response in Calmodulin (CaM) What is the big picture? A free energy functional is derived by applying constraint theory to a free energy decomposition scheme. Each interaction type is modeled by a molecular partition function (MPF). Free energy reconstitution is the process of solving the functional using graph rigidity to account for nonadditivity in conformational entropy. Bare parameters in a MPF describe an interaction within a reference environment. The MPF parameters renormalize to reflect a modified environment that is determined heat self-consistently. Consequently, the actual enthalpy/entropy contributions depend resistor on many-body effects and the thermodynamic/solvent conditions. Order parameters describing solvation and conformational flexibility define a free energy landscape from which thermodynamic properties are calculated. Mechanical properties are obtained from graph rigidity calculations that are appropriately ensemble averaged. What is the significance? Thermodynamic and mechanical properties are calculated in matter of minutes using FAST software that provides a Flexibility And Stability Test on aqueous proteins. Quantitative Stability and Flexibility Relationships (QSFR) are calculated with great precision and can be employed in high throughput applications. (Top) Response in conformational flexibility to a mechanical perturbation at Ile136 (shown in orange). (Red, blue) indicates a (degrease, increase) in flexibility. (Right) The complete perturbation/response characteristics. FAST is now in Development: Expected Release is 2010 The extended DCM includes solvation effects, and will be able to accurately decompose the changes in free energy due to different mechanisms. In the new model, pressure, pH and solute concentrations are accounted for, and mobility information will be added to the QSFR descriptions. This work is supported by: NIH R01 GM070382 Contact information: [email protected] or [email protected]