Topography of funneled landscapes determines the thermodynamics and kinetics of protein folding

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Folding thermodynamics of a model three-helix-bundle protein

The calculated folding thermodynamics of a simple off-lattice three-helix-bundle protein model under equilibrium conditions shows the experimentally observed protein transitions: a collapse transition, a disordered-to-ordered globule transition, a globule to native-state transition, and the transition from the active native state to a frozen inactive state. The cooperativity and physical origin of the various transitions are explored with a single “optimization” parameter and characterized with the Lindemann criterion for liquid versus solid-state dynamics. Below the folding temperature, the model has a simple free energy surface with a single basin near the native state; the surface is similar to that calculated from a simulation of the same three-helix-bundle protein with an all-atom representation [Boczko, E. M. & Brooks III, C. L. (1995) Science 269, 393–396].

The thermodynamics and statistical mechanics of protein folding

The physics of self-organization and complexity is manifested on a variety of biological scales, from large ecosystems to the molecular level. Protein molecules exhibit characteristics of complex systems in terms of their structure, dynamics, and function. Proteins have the extraordinary ability to fold to a specific functional three-dimensional shape, starting from a random coil, in a biologically relevant time. How they accomplish this is one of the secrets of life. In this work, theoretical research into understanding this remarkable behavior is discussed. Thermodynamic and statistical mechanical tools are used in order to investigate the protein folding dynamics and stability. Theoretical analyses of the results from computer simulation of the dynamics of a four-helix bundle show that the excluded volume entropic effects are very important in protein dynamics and crucial for protein stability. The dramatic effects of changing the size of sidechains imply that a strategic placement of amino acid residues with a particular size may be an important consideration in protein engineering. Another investigation deals with modeling protein structural transitions as a phase transition. Using finite size scaling theory, the nature of unfolding transition of a four-helix bundle protein was investigated and critical exponents for the transition were calculated for various hydrophobic strengths in the core. It is found that the order of the transition changes from first to higher order as the strength of the hydrophobic interaction in the core region is significantly increased. Finally, a detailed kinetic and thermodynamic analysis was carried out in a model two-helix bundle. The connection between the structural free-energy landscape and folding kinetics was quantified. I show how simple protein engineering, by changing the hydropathy of a small number of amino acids, can enhance protein folding by significantly changing the free energy landscape so that kinetic traps are removed. The results have general applicability in protein engineering as well as understanding the underlying physical mechanisms of protein folding. ^

Electrostatic Contributions to the Thermodynamics of Ribonuclease P Protein Folding

Electrostatic interactions are of fundamental importance in determining the structure and stability of macromolecules. For example, charge-charge interactions modulate the folding and binding of proteins and influence protein solubility. Electrostatic interactions are highly variable and can be both favorable and unfavorable. The ability to quantify these interactions is challenging but vital to understanding the detailed balance and major roles that they have in different proteins and biological processes. Measuring pKa values of ionizable groups provides a sensitive method for experimentally probing the electrostatic properties of a protein.

pKa values report the free energy of site-specific proton binding and provide a direct means of studying protein folding and pH-dependent stability. Using a combination of NMR, circular dichroism, and fluorescence spectroscopy along with singular value decomposition, we investigated the contributions of electrostatic interactions to the thermodynamic stability and folding of the protein subunit of Bacillus subtilis ribonuclease P, P protein. Taken together, the results suggest that unfavorable electrostatics alone do not account for the fact that P protein is intrinsically unfolded in the absence of ligand because the pKa differences observed between the folded and unfolded state are small. Presumably, multiple factors encoded in the P protein sequence account for its IUP property, which may play an important role in its function.

Interpreting the effects of small uncharged solutes on protein-folding equilibria

Proteins are designed to function in environments crowded by cosolutes, but most studies of protein equilibria are conducted in dilute solution. While there is no doubt that crowding changes protein equilibria, interpretations of the changes remain controversial. This review combines experimental observations on the effect of small uncharged cosolutes (mostly sugars) on protein stability with a discussion of the thermodynamics of cosolute-induced nonideality and critical assessments of the most commonly applied interpretations. Despite the controversy surrounding the most appropriate manner for interpreting these effects of thermodynamic nonideality arising from the presence of small cosolutes, experimental advantage may still be taken of the ability of the cosolute effect to promote not only protein stabilization but also protein self-association and complex formation between dissimilar reactants. This phenomenon clearly has potential ramifications in the cell, where the crowded environment could well induce the same effects.

Protein Folding Simulations: Confinement, External Fields and Sequence Design

The present Thesis looks at the problem of protein folding using Monte Carlo and Langevin simulations, three topics in protein folding have been studied: 1) the effect of confining potential barriers, 2) the effect of a static external field and 3) the design of amino acid sequences which fold in a short time and which have a stable native state (global minimum). Regarding the first topic, we studied the confinement of a small protein of 16 amino acids known as 1NJ0 (PDB code) which has a beta-sheet structure as a native state. The confinement of proteins occurs frequently in the cell environment. Some molecules called Chaperones, present in the cytoplasm, capture the unfolded proteins in their interior and avoid the formation of aggregates and misfolded proteins. This mechanism of confinement mediated by Chaperones is not yet well understood. In the present work we considered two kinds of potential barriers which try to mimic the confinement induced by a Chaperon molecule. The first kind of potential was a purely repulsive barrier whose only effect is to create a cavity where the protein folds up correctly. The second kind of potential was a barrier which includes both attractive and repulsive effects. We performed Wang-Landau simulations to calculate the thermodynamical properties of 1NJ0. From the free energy landscape plot we found that 1NJ0 has two intermediate states in the bulk (without confinement) which are clearly separated from the native and the unfolded states. For the case of the purely repulsive barrier we found that the intermediate states get closer to each other in the free energy landscape plot and eventually they collapse into a single intermediate state. The unfolded state is more compact, compared to that in the bulk, as the size of the barrier decreases. For an attractive barrier modifications of the states (native, unfolded and intermediates) are observed depending on the degree of attraction between the protein and the walls of the barrier. The strength of the attraction is measured by the parameter $\epsilon$. A purely repulsive barrier is obtained for $\epsilon=0$ and a purely attractive barrier for $\epsilon=1$. The states are changed slightly for magnitudes of the attraction up to $\epsilon=0.4$. The disappearance of the intermediate states of 1NJ0 is already observed for $\epsilon =0.6$. A very high attractive barrier ($\epsilon \sim 1.0$) produces a completely denatured state. In the second topic of this Thesis we dealt with the interaction of a protein with an external electric field. We demonstrated by means of computer simulations, specifically by using the Wang-Landau algorithm, that the folded, unfolded, and intermediate states can be modified by means of a field. We have found that an external field can induce several modifications in the thermodynamics of these states: for relatively low magnitudes of the field ($<2.06 \times 10^8$ V/m) no major changes in the states are observed. However, for higher magnitudes than ($6.19 \times 10^8$ V/m) one observes the appearance of a new native state which exhibits a helix-like structure. In contrast, the original native state is a $\beta$-sheet structure. In the new native state all the dipoles in the backbone structure are aligned parallel to the field. The design of amino acid sequences constitutes the third topic of the present work. We have tested the Rate of Convergence criterion proposed by D. Gridnev and M. Garcia ({\it work unpublished}). We applied it to the study of off-lattice models. The Rate of Convergence criterion is used to decide if a certain sequence will fold up correctly within a relatively short time. Before the present work, the common way to decide if a certain sequence was a good/bad folder was by performing the whole dynamics until the sequence got its native state (if it existed), or by studying the curvature of the potential energy surface. There are some difficulties in the last two approaches. In the first approach, performing the complete dynamics for hundreds of sequences is a rather challenging task because of the CPU time needed. In the second approach, calculating the curvature of the potential energy surface is possible only for very smooth surfaces. The Rate of Convergence criterion seems to avoid the previous difficulties. With this criterion one does not need to perform the complete dynamics to find the good and bad sequences. Also, the criterion does not depend on the kind of force field used and therefore it can be used even for very rugged energy surfaces.

The water factor in the protein-folding problem

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Analyzing the effect of homogeneous frustration in protein folding

The energy landscape theory has been an invaluable theoretical framework in the understanding of biological processes such as protein folding, oligomerization, and functional transitions. According to the theory, the energy landscape of protein folding is funneled toward the native state, a conformational state that is consistent with the principle of minimal frustration. It has been accepted that real proteins are selected through natural evolution, satisfying the minimum frustration criterion. However, there is evidence that a low degree of frustration accelerates folding. We examined the interplay between topological and energetic protein frustration. We employed a Cα structure-based model for simulations with a controlled nonspecific energetic frustration added to the potential energy function. Thermodynamics and kinetics of a group of 19 proteins are completely characterized as a function of increasing level of energetic frustration. We observed two well-separated groups of proteins: one group where a little frustration enhances folding rates to an optimal value and another where any energetic frustration slows down folding. Protein energetic frustration regimes and their mechanisms are explained by the role of non-native contact interactions in different folding scenarios. These findings strongly correlate with the protein free-energy folding barrier and the absolute contact order parameters. These computational results are corroborated by principal component analysis and partial least square techniques. One simple theoretical model is proposed as a useful tool for experimentalists to predict the limits of improvements in real proteins. © 2013 Wiley Periodicals, Inc.

Quantifying protein folding pathways

A deep understanding of the proteins folding dynamics can be get quantifying folding landscape by calculating how the number of microscopic configurations (entropy) varies with the energy of the chain, Ω=Ω(E). Because of the incredibly large number of microstates available to a protein, direct enumeration of Ω(E) is not possible on realistic computer simulations. An estimate of Ω(E) can be obtained by use of a combination of statistical mechanics and thermodynamics. By combining different definitions of entropy that are valid for a system whose probability for occupying a state is given by the canonical Boltzmann probability, computers allow the determination of Ω(E). ^ The energy landscapes of two similar, but not identical model proteins were studied. One protein contains no kinetic tracks. Results show a smooth funnel for the folding landscape. That allows the contour determination of the folding funnel. Also it was presented results for the folding landscape for a modified protein with kinetic traps. Final results show that the computational approach is able to distinguish and explore regions of the folding landscape that are due to kinetic traps from the native state folding funnel.^

Structure of TcpG, the DsbA protein folding catalyst from Vibrio cholerae

The efficient and correct folding of bacterial disulfide bonded proteins in vivo is dependent upon a class of periplasmic oxidoreductase proteins called DsbA, after the Escherichia coli enzyme. In the pathogenic bacterium Vibrio cholerae, the DsbA homolog (TcpG) is responsible for the folding, maturation and secretion of virulence factors. Mutants in which the tcpg gene has been inactivated are avirulent; they no longer produce functional colonisation pill and they no longer secrete cholera toxin. TcpG is thus a suitable target for inhibitors that could counteract the virulence of this organism, thereby preventing the symptoms of cholera. The crystal structure of oxidized TcpG (refined at a resolution of 2.1 Angstrom) serves as a starting point for the rational design of such inhibitors. As expected, TcpG has the same fold as E. coli DsbA, with which it shares similar to 40% sequence identity. Ln addition, the characteristic surface features of DsbA are present in TcpG, supporting the notion that these features play a functional role. While the overall architecture of TcpG and DsbA is similar and the surface features are retained in TcpG, there are significant differences. For example, the kinked active site helix results from a three-residue loop in DsbA, but is caused by a proline in TcpG (making TcpG more similar to thioredoxin in this respect). Furthermore, the proposed peptide binding groove of TcpG is substantially shortened compared with that of DsbA due to a six-residue deletion. Also, the hydrophobic pocket of TcpG is more shallow and the acidic patch is much less extensive than that of E. coli DsbA. The identification of the structural and surface features that are retained or are divergent in TcpG provides a useful assessment of their functional importance in these protein folding catalysts and is an important prerequisite for the design of TcpG inhibitors. (C) 1997 Academic Press Limited.

Translation termination and protein folding pathway genes are not correlated in gastric cancer

Background: The eukaryotic release factor 3 (eRF3) has been shown to affect both tubulin and actin cytoskeleton, suggesting a role in cytoskeleton assembly, mitotic spindle formation and chromosome segregation. Also, direct interactions between eRF3 and subunits of the cytosolic chaperonin CCT have been described. Moreover, both eRF3a and CCT subunits have been described to be up-regulated in cancer tissues. Our aim was to evaluate the hypothesis that eRF3 expression levels are correlated with the expression of genes encoding proteins involved in the tubulin folding pathways. Methods: Relative expression levels of eRF1, eRF3a/GSPT1, PFDN4, CCT2, CCT4, and TBCA genes in tumour samples relative to their adjacent normal tissues were investigated using real time-polymerase chain reaction in 20 gastric cancer patients. Results: The expression levels of eRF3a/GSPT1 were not correlated with the expression levels of the other genes studied. However, significant correlations were detected between the other genes, both within intestinal and diffuse type tumours. Conclusions: eRF3a/GSPT1 expression at the mRNA level is independent from both cell translation rates and from the expression of the genes involved in tubulin-folding pathways. The differences in the patterns of expression of the genes studied support the hypothesis of genetically independent pathways in the origin of intestinal and diffuse type gastric tumours.

Protein folding, metal ions and conformational states: the case of a di-cluster ferredoxin

Dissertation presented to obtain the PhD degree in Biochemistry at the Instituto de Tecnologia Química e Biológica, Universidade Nova de Lisboa

Defective protein folding and function in metabolic disorders: studies on the mitochondrial flavoenzyme ETF

Dissertation presented to obtain the PhD degree in Biochemistry at the Instituto de Tecnologia Química e Biológica, Universidade Nova de Lisboa

Metal ions and protein folding: conformational and functional interplay

Dissertation presented to obtain a PhD degree in Biochemistry at Instituto de Tecnologia Química e Biológica, Universidade Nova de Lisboa

PROTEIN FOLDING AND DISEASE THE MITOCHONDRIAL PROTEIN FRATAXIN

This dissertation focuses on the study of frataxin, a small mitochondrial protein whose deficiency is associated with the neurodegenerative disease Friedreich's ataxia (FRDA). Aiming at a better understanding of frataxin conformational and functional properties, two lines of research were followed: first, the effect of FRDA-related mutations in human frataxin (FXN) were studied and the role of oxidative stress related modification addressed; second, yeast frataxin (Yfh1) orthologue was used to explore the conformational and functional properties of the protein.(...)