Theoretical Perspectives on Protein Folding

Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing the folding mechanisms of globular proteins. The experimental data and theoretical methods have revealed the multifaceted character of proteins. Proteins exhibit universal features that can be determined using only the number of amino acid residues (N) and polymer concepts. The sizes of proteins in the denatured and folded states, cooperativity of the folding transition, dispersions in the melting temperatures at the residue level, and time scales of folding are to a large extent determined by N. The consequences of finite N especially on how individual residues order upon folding depends on the topology of the folded states. Such intricate details can be predicted using the Molecular Transfer Model that combines simulations with measured transfer free energies of protein building blocks from water to the desired concentration of the denaturant. By watching one molecule fold at a time, using single molecule methods, the validity of the theoretically anticipated heterogeneity in the folding routes, and the N-dependent time scales for the three stages in the approach to the native state have been established. Despite the successes of theory, of which only a few examples are documented here, we conclude that much remains to be done to solve the "protein folding problem" in the broadest sense.Comment: 48 pages, 9 figure

Protein folding in high-dimensional spaces:hypergutters and the role of non-native interactions

We explore the consequences of very high dimensionality in the dynamical landscape of protein folding. Consideration of both typical range of stabilising interactions, and folding rates themselves, leads to a model of the energy hypersurface that is characterised by the structure of diffusive "hypergutters" as well as the familiar "funnels". Several general predictions result: (1) intermediate subspaces of configurations will always be visited; (2) specific but non-native interactions are important in stabilising these low-dimensional diffusive searches on the folding pathway; (3) sequential barriers will commonly be found, even in "two-state"proteins; (4) very early times will show charactreristic departures from single-exponential kinetics; (5) contributions of non-native interactions to phi-values are calculable, and may be significant. The example of a three-helix bundle is treated in more detail as an illustration. The model also shows that high-dimensional structures provide conceptual relations between the "folding funnel", "diffusion-collision", "nucleation-condensation" and "topomer search" models of protein folding. It suggests that kinetic strategies for fast folding may be encoded rather generally in non-native, rather than native interactions. The predictions are related to very recent findings in experiment and simulation.Comment: Submitted to Biophys.

Single-domain protein folding: a multi-faceted problem

We review theoretical approaches, experiments and numerical simulations that have been recently proposed to investigate the folding problem in single-domain proteins. From a theoretical point of view, we emphasize the energy landscape approach. As far as experiments are concerned, we focus on the recent development of single-molecule techniques. In particular, we compare the results obtained with two main techniques: single protein force measurements with optical tweezers and single-molecule fluorescence in studies on the same protein (RNase H). This allows us to point out some controversial issues such as the nature of the denatured and intermediate states and possible folding pathways. After reviewing the various numerical simulation techniques, we show that on-lattice protein-like models can help to understand many controversial issues.Comment: 26 pages, AIP Conference Proceeding

Human Frataxin Folds Via an Intermediate State. Role of the C-Terminal Region

The aim of this study is to investigate the folding reaction of human frataxin, whose deficiency causes the neurodegenerative disease Friedreich’s Ataxia (FRDA). The characterization of different conformational states would provide knowledge about how frataxin can be stabilized without altering its functionality. Wild-type human frataxin and a set of mutants, including two highly destabilized FRDA-associated variants were studied by urea-induced folding/unfolding in a rapid mixing device and followed by circular dichroism. The analysis clearly indicates the existence of an intermediate state (I) in the folding route with significant secondary structure content but relatively low compactness, compared with the native ensemble. However, at high NaCl concentrations I-state gains substantial compaction, and the unfolding barrier is strongly affected, revealing the importance of electrostatics in the folding mechanism. The role of the C-terminal region (CTR), the key determinant of frataxin stability, was also studied. Simulations consistently with experiments revealed that this stretch is essentially unstructured, in the most compact transition state ensemble (TSE2). The complete truncation of the CTR drastically destabilizes the native state without altering TSE2. Results presented here shed light on the folding mechanism of frataxin, opening the possibility of mutating it to generate hyperstable variants without altering their folding kinetics.Fil: Faraj, Santiago Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Química y Físico-Química Biológicas "Prof. Alejandro C. Paladini". Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Instituto de Química y Físico-Química Biológicas; ArgentinaFil: Gonzalez-Lebrero, Rodolfo Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Química y Físico-Química Biológicas "Prof. Alejandro C. Paladini". Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Instituto de Química y Físico-Química Biológicas; ArgentinaFil: Roman, Ernesto Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Química y Físico-Química Biológicas "Prof. Alejandro C. Paladini". Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Instituto de Química y Físico-Química Biológicas; ArgentinaFil: Santos, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Química y Físico-Química Biológicas "Prof. Alejandro C. Paladini". Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Instituto de Química y Físico-Química Biológicas; Argentin

Statistical Physics of Evolutionary Trajectories on Fitness Landscapes

Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role in evolutionary theory. The topography of fitness landscapes and its effect on evolutionary dynamics have been extensively studied in the literature. We will survey the current research knowledge in this field, focusing on a recently developed systematic approach to characterizing path lengths, mean first-passage times, and other statistics of the path ensemble. This approach, based on general techniques from statistical physics, is applicable to landscapes of arbitrary complexity and structure. It is especially well-suited to quantifying the diversity of stochastic trajectories and repeatability of evolutionary events. We demonstrate this methodology using a biophysical model of protein evolution that describes how proteins maintain stability while evolving new functions

Statics, metastable states and barriers in protein folding: A replica variational approach

Protein folding is analyzed using a replica variational formalism to investigate some free energy landscape characteristics relevant for dynamics. A random contact interaction model that satisfies the minimum frustration principle is used to describe the coil-globule transition (characterized by T_CG), glass transitions (by T_A and T_K) and folding transition (by T_F). Trapping on the free energy landscape is characterized by two characteristic temperatures, one dynamic, T_A the other static, T_K (T_A> T_K), which are similar to those found in mean field theories of the Potts glass. 1)Above T_A, the free energy landscape is monotonous and polymer is melted both dynamically and statically. 2)Between T_A and T_K, the melted phase is still dominant thermodynamically, but frozen metastable states, exponentially large in number, appear. 3)A few lowest minima become thermodynamically dominant below T_K, where the polymer is totally frozen. In the temperature range between T_A and T_K, barriers between metastable states are shown to grow with decreasing temperature suggesting super-Arrhenius behavior in a sufficiently large system. Due to evolutionary constraints on fast folding, the folding temperature T_F is expected to be higher than T_K, but may or may not be higher than T_A. Diverse scenarios of the folding kinetics are discussed based on phase diagrams that take into account the dynamical transition, as well as the static ones.Comment: 41 pages, LaTeX, 9 EPS figure