Protein sequence and structure: Is one more fundamental than the other?

We argue that protein native state structures reside in a novel "phase" of matter which confers on proteins their many amazing characteristics. This phase arises from the common features of all globular proteins and is characterized by a sequence-independent free energy landscape with relatively few low energy minima with funnel-like character. The choice of a sequence that fits well into one of these predetermined structures facilitates rapid and cooperative folding. Our model calculations show that this novel phase facilitates the formation of an efficient route for sequence design starting from random peptides.Comment: 7 pages, 4 figures, to appear in J. Stat. Phy

Embedding a Native State into a Random Heteropolymer Model: The Dynamic Approach

We study a random heteropolymer model with Langevin dynamics, in the supersymmetric formulation. Employing a procedure similar to one that has been used in static calculations, we construct an ensemble in which the affinity of the system for a native state is controlled by a "selection temperature" T0. In the limit of high T0, the model reduces to a random heteropolymer, while for T0-->0 the system is forced into the native state. Within the Gaussian variational approach that we employed previously for the random heteropolymer, we explore the phases of the system for large and small T0. For large T0, the system exhibits a (dynamical) spin glass phase, like that found for the random heteropolymer, below a temperature Tg. For small T0, we find an ordered phase, characterized by a nonzero overlap with the native state, below a temperature Tn \propto 1/T0 > Tg. However, the random-globule phase remains locally stable below Tn, down to the dynamical glass transition at Tg. Thus, in this model, folding is rapid for temperatures between Tg and Tn, but below Tg the system can get trapped in conformations uncorrelated with the native state. At a lower temperature, the ordered phase can also undergo a dynamical glass transition, splitting into substates separated by large barriers.Comment: 19 pages, revtex, 6 figure

Small Open Chemical Systems Theory and Its Implications to Darwinian Evolutionary Dynamics, Complex Self-Organization and Beyond

The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time deterministic nonlinear dynamics, and long-time evolutionary behavior with exponentially distributed rare events, discrete jumps among punctuated equilibria, and catastrophe.Comment: 15 page

Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\it exact} quantum analogues of their classical counterparts. The present work is {\it independent} of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (Smoluchowski equation being considered in the overdamped limit).Comment: RevTex, 16 pages, 7 figures, To appear in Physical Review E (minor revision

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe

Protein Folding and structure Prediction from the Ground Up: The Atomistic Associative Memory Structure and Energy Model (AAWSEM)

The associative memory, water mediated, structure and energy model (AWSEM) is a coarse-grained force field with transferable tertiary interactions that incorporates local in sequence energetic biases using bioinformatically derived structural information about peptide fragments with locally similar sequences that we call memories. The memory information from the protein data bank (PDB) database guides proper protein folding. The structural information about available sequences in the database varies in quality and can sometimes lead to frustrated free energy landscapes locally. One way out of this difficulty is to construct the input fragment memory information from all-atom simulations of portions of the complete polypeptide chain. In this paper, we investigate this approach first put forward by Kwac and Wolynes in a more complete way by studying the structure prediction capabilities of this approach for six α-helical proteins. This scheme which we call the atomistic associative memory, water mediated, structure and energy model (AAWSEM) amounts to an ab initio protein structure prediction method that starts from the ground up without using bioinformatic input. The free energy profiles from AAWSEM show that atomistic fragment memories are sufficient to guide the correct folding when tertiary forces are included. AAWSEM combines the efficiency of coarse-grained simulations on the full protein level with the local structural accuracy achievable from all-atom simulations of only parts of a large protein. The results suggest that a hybrid use of atomistic fragment memory and database memory in structural predictions may well be optimal for many practical applications

Binding of NFκB appears to twist the ankyrin repeat domain of IκBα

Total internal reflection fluorescence-based single-molecule Förster resonance energy transfer (FRET) measurements were previously carried out on the ankyrin repeat domain (ARD) of IκBα, the temporally regulated inhibitor of canonical NFκB signaling. Under native conditions, most of the IκBα molecules showed stable, high FRET signals consistent with distances between the fluorophores estimated from the crystal structures of the NFκB(RelA/p50)-IκBα complex. Similar high FRET efficiencies were found when the IκBα molecules were either free or in complex with NFκB(RelA/p50), and were interpreted as being consistent with the crystallographically observed ARD structure. An exception to this was observed when the donor and acceptor fluorophores were attached in AR3 (residue 166) and AR6 (residue 262). Surprisingly, the FRET efficiency was lower for the bound IκBα molecules (0.67) than for the free IκBα molecules (0.74), apparently indicating that binding of NFκB(RelA/p50) stretches the ARD of IκBα. Here, we conducted confocal-based single-molecule FRET studies to investigate this phenomenon in greater detail. The results not only recapitulated the apparent stretching of the ARD but also showed that the effect was more pronounced when the N-terminal domains (NTDs) of both RelA and p50 were present, even though the interface between NFκB(RelA/p50) and IκBα encompasses only the dimerization domains. We also performed mass spectrometry-detected amide hydrogen/deuterium exchange (HDXMS) experiments on IκBα as well as IκBα bound to dimerization-domain-only constructs or full-length NFκB(RelA/p50). Although we expected the stretched IκBα to have regions with increased exchange, instead the HDXMS experiments showed decreases in exchange in AR3 and AR6 that were more pronounced when the NFκB NTDs were present. Simulations of the interaction recapitulated the increased distance between residues 166 and 262, and also provide a plausible mechanism for a twisting of the IκBα ARD induced by interactions of the IκBα proline-glutamate-serine-threonine-rich sequence with positively charged residues in the RelA NTD