Factors that affect the folding ability of proteins

Research Progress of Nanomaterial Mechanics for Targeted Treatment of Muscle Strains in Sports Rehabilitation Training

More and more people are beginning to recognize the important role of intelligent rehabilitation training equipment in rehabilitation treatment and continue to carry out related researches. The use of intelligent robot technology for rehabilitation treatment has been rapidly developed, and it has achieved rapid progress on a global scale. Especially in some developed countries, this field has also received corresponding attention in some developed cities in China in recent years. Mesoporous nanomaterials have unique physical, chemical, and biological properties. Mesoporous nanomaterials can be combined with chemotherapy drugs to minimize the harm caused by chemotherapy drugs to the human body and improve the therapeutic effect. As a result, the cure rate has been improved, and it has shown deep potential in breast cancer chemotherapy. Fifty breast cancer patients were selected as the research objects and randomly divided into a control group and an experimental group, each with 25 cases. The control group was treated with conventional chemotherapeutics, and the experimental group was treated with molecular targeted therapy to compare the treatment effects of the two groups. Studies have shown that the recurrence rate and the occurrence probability of complications in the experimental group are significantly lower than those in the control group. Molecular targeted therapy for breast cancer has obvious effects, which reduces the recurrence rate of complications or diseases, and is less toxic.

Receptor binding, immune escape, and protein stability direct the natural selection of SARS-CoV-2 variants

Emergence of new severe acute respiratory syndrome coronavirus 2 variants has raised concerns related to the effectiveness of vaccines and antibody therapeutics developed against the unmutated wildtype virus. Here, we examined the effect of the 12 most commonly occurring mutations in the receptor-binding domain of the spike protein on its expression, stability, activity, and antibody escape potential. Stability was measured using thermal denaturation, and the activity and antibody escape potential were measured using isothermal titration calorimetry in terms of binding to the human angiotensin-converting enzyme 2 and to neutralizing human antibody CC12.1, respectively. Our results show that mutants differ in their expression levels. Of the eight best-expressed mutants, two (N501Y and K417T/E484K/N501Y) showed stronger affinity to angiotensin-converting enzyme 2 compared with the wildtype, whereas four (Y453F, S477N, T478I, and S494P) had similar affinity and two (K417N and E484K) had weaker affinity than the wildtype. Compared with the wildtype, four mutants (K417N, Y453F, N501Y, and K417T/E484K/N501Y) had weaker affinity for the CC12.1 antibody, whereas two (S477N and S494P) had similar affinity, and two (T478I and E484K) had stronger affinity than the wildtype. Mutants also differ in their thermal stability, with the two least stable mutants showing reduced expression. Taken together, these results indicate that multiple factors contribute toward the natural selection of variants, and all these factors need to be considered to understand the evolution of the virus. In addition, since not all variants can escape a given neutralizing antibody, antibodies to treat new variants can be chosen based on the specific mutations in that variant.

Stability of the Influenza Virus Hemagglutinin Protein Correlates with Evolutionary Dynamics

One of the constraints on fast-evolving viruses, such as influenza virus, is protein stability, or how strongly the folded protein holds together. Despite the importance of this protein property, there has been limited investigation of the impact of the stability of the influenza virus hemagglutinin protein—the primary antibody target of the immune system—on its evolution. Using a combination of computational estimates of stability and experiments, our analysis found that viruses with more-stable hemagglutinin proteins were associated with long-term persistence in the population. There are two potential reasons for the observed persistence. One is that more-stable proteins tolerate destabilizing mutations that less-stable proteins could not, thus increasing opportunities for immune escape. The second is that greater stability increases the fitness of the virus through increased production of infectious particles. Further research on the relative importance of these mechanisms could help inform the annual influenza vaccine composition decision process.

Protein thermodynamics are an integral determinant of viral fitness and one of the major drivers of protein evolution. Mutations in the influenza A virus (IAV) hemagglutinin (HA) protein can eliminate neutralizing antibody binding to mediate escape from preexisting antiviral immunity. Prior research on the IAV nucleoprotein suggests that protein stability may constrain seasonal IAV evolution; however, the role of stability in shaping the evolutionary dynamics of the HA protein has not been explored. We used the full coding sequence of 9,797 H1N1pdm09 HA sequences and 16,716 human seasonal H3N2 HA sequences to computationally estimate relative changes in the thermal stability of the HA protein between 2009 and 2016. Phylogenetic methods were used to characterize how stability differences impacted the evolutionary dynamics of the virus. We found that pandemic H1N1 IAV strains split into two lineages that had different relative HA protein stabilities and that later variants were descended from the higher-stability lineage. Analysis of the mutations associated with the selective sweep of the higher-stability lineage found that they were characterized by the early appearance of highly stabilizing mutations, the earliest of which was not located in a known antigenic site. Experimental evidence further suggested that H1N1 HA stability may be correlated with in vitro virus production and infection. A similar analysis of H3N2 strains found that surviving lineages were also largely descended from viruses predicted to encode more-stable HA proteins. Our results suggest that HA protein stability likely plays a significant role in the persistence of different IAV lineages.

IMPORTANCE One of the constraints on fast-evolving viruses, such as influenza virus, is protein stability, or how strongly the folded protein holds together. Despite the importance of this protein property, there has been limited investigation of the impact of the stability of the influenza virus hemagglutinin protein—the primary antibody target of the immune system—on its evolution. Using a combination of computational estimates of stability and experiments, our analysis found that viruses with more-stable hemagglutinin proteins were associated with long-term persistence in the population. There are two potential reasons for the observed persistence. One is that more-stable proteins tolerate destabilizing mutations that less-stable proteins could not, thus increasing opportunities for immune escape. The second is that greater stability increases the fitness of the virus through increased production of infectious particles. Further research on the relative importance of these mechanisms could help inform the annual influenza vaccine composition decision process.

Evolution, energy landscapes and the paradoxes of protein folding

Protein folding has been viewed as a difficult problem of molecular self-organization. The search problem involved in folding however has been simplified through the evolution of folding energy landscapes that are funneled. The funnel hypothesis can be quantified using energy landscape theory based on the minimal frustration principle. Strong quantitative predictions that follow from energy landscape theory have been widely confirmed both through laboratory folding experiments and from detailed simulations. Energy landscape ideas also have allowed successful protein structure prediction algorithms to be developed. The selection constraint of having funneled folding landscapes has left its imprint on the sequences of existing protein structural families. Quantitative analysis of co-evolution patterns allows us to infer the statistical characteristics of the folding landscape. These turn out to be consistent with what has been obtained from laboratory physicochemical folding experiments signaling a beautiful confluence of genomics and chemical physics.

The role of site-directed point mutations in protein misfolding

Mutations inducing higher clashing and lower matching residue pairs lead to misfolding.

A comparison of the folding kinetics of a small, artificially selected DNA aptamer with those of equivalently simple naturally occurring proteins

The folding of larger proteins generally differs from the folding of similarly large nucleic acids in the number and stability of the intermediates involved. To date, however, no similar comparison has been made between the folding of smaller proteins, which typically fold without well-populated intermediates, and the folding of small, simple nucleic acids. In response, in this study, we compare the folding of a 38-base DNA aptamer with the folding of a set of equivalently simple proteins. We find that, as is true for the large majority of simple, single domain proteins, the aptamer folds through a concerted, millisecond-scale process lacking well-populated intermediates. Perhaps surprisingly, the observed folding rate falls within error of a previously described relationship between the folding kinetics of single-domain proteins and their native state topology. Likewise, similarly to single-domain proteins, the aptamer exhibits a relatively low urea-derived Tanford β, suggesting that its folding transition state is modestly ordered. In contrast to this, however, and in contrast to the behavior of proteins, ϕ-value analysis suggests that the aptamer's folding transition state is highly ordered, a discrepancy that presumably reflects the markedly more important role that secondary structure formation plays in the folding of nucleic acids. This difference notwithstanding, the similarities that we observe between the two-state folding of single-domain proteins and the two-state folding of this similarly simple DNA presumably reflect properties that are universal in the folding of all sufficiently cooperative heteropolymers irrespective of their chemical details.

Hydrophobic forces, electrostatic steering, and acid-base bridging between atomically smooth self-assembled monolayers and end-functionalized PEGolated lipid bilayers

A molecular level understanding of interaction forces and dynamics between asymmetric apposing surfaces (including end-functionalized polymers) in water plays a key role in the utilization of molecular structures for smart and functional surfaces in biological, medical, and materials applications. To quantify interaction forces and binding dynamics between asymmetric apposing surfaces in terms of their chemical structure and molecular design we developed a novel surface forces apparatus experiment, using self-assembled monolayers (SAMs) on atomically smooth gold substrates. Varying the SAM head group functionality allowed us to quantitatively identify, rationalize, and therefore control which interaction forces dominated between the SAM surfaces and a surface coated with short-chain, amine end-functionalized polyethylene glycol (PEG) polymers extending from a lipid bilayer. Three different SAM-terminations were chosen for this study: (a) carboxylic acid, (b) alcohol, and (c) methyl head group terminations. These three functionalities allowed for the quantification of (a) specific acid-base bindings, (b) steric effects of PEG chains, and (c) adhesion of hydrophobic segments of the polymer backbone, all as a function of the solution pH. The pH-dependent acid-base binding appears to be a specific and charge mediated hydrogen bonding interaction between oppositely charged carboxylic acid and amine functionalities, at pH values above the acid pK(A) and below the amine pK(A). The long-range electrostatic "steering" of acid and base pairs leads to remarkably rapid binding formation and high binding probability of this specific binding even at distances close to full extension of the PEG tethers, a result which has potentially important implications for protein folding processes and enzymatic catalysis.

Deciphering the hidden informational content of protein sequences: foldability of proinsulin hinges on a flexible arm that is dispensable in the mature hormone

Protein sequences encode both structure and foldability. Whereas the interrelationship of sequence and structure has been extensively investigated, the origins of folding efficiency are enigmatic. We demonstrate that the folding of proinsulin requires a flexible N-terminal hydrophobic residue that is dispensable for the structure, activity, and stability of the mature hormone. This residue (Phe(B1) in placental mammals) is variably positioned within crystal structures and exhibits (1)H NMR motional narrowing in solution. Despite such flexibility, its deletion impaired insulin chain combination and led in cell culture to formation of non-native disulfide isomers with impaired secretion of the variant proinsulin. Cellular folding and secretion were maintained by hydrophobic substitutions at B1 but markedly perturbed by polar or charged side chains. We propose that, during folding, a hydrophobic side chain at B1 anchors transient long-range interactions by a flexible N-terminal arm (residues B1-B8) to mediate kinetic or thermodynamic partitioning among disulfide intermediates. Evidence for the overall contribution of the arm to folding was obtained by alanine scanning mutagenesis. Together, our findings demonstrate that efficient folding of proinsulin requires N-terminal sequences that are dispensable in the native state. Such arm-dependent folding can be abrogated by mutations associated with β-cell dysfunction and neonatal diabetes mellitus.

A structure-centric view of protein evolution, design, and adaptation

Proteins, by virtue of their central role in most biological processes, represent one of the key subjects of the study of molecular evolution. Inherent in the indispensability of proteins for living cells is the fact that a given protein can adopt a specific three-dimensional shape that is specified solely by the protein's sequence of amino acids. Over the past several decades, structural biologists have demonstrated that the array of structures that proteins may adopt is quite astounding, and this has lead to a strong interest in understanding how protein structures change and evolve over time. In this review we consider a large body of recent work that attempts to illuminate this structure-centric picture of protein evolution. Much of this work has focused on the question of how completely new protein structures (i.e., new folds or topologies) are discovered by protein sequences as they evolve. Pursuant to this question of structural innovation has been a desire to describe and understand the observation that certain types of protein structures are far more abundant than others and how this uneven distribution of proteins implicates on the process through which new shapes are discovered. We consider a number of theoretical models that have been successful at explaining this heterogeneity in protein populations and discuss the increasing amount of evidence that indicates that the process of structural evolution involves the divergence of protein sequences and structures from one another. We also consider the topic of protein designability, which concerns itself with understanding how a protein's structure influences the number of sequences that can fold successfully into that structure. Understanding and quantifying the relationship between the physical feature of a structure and its designability has been a long-standing goal of the study of protein structure and evolution, and we discuss a number of recent advances that have yielded a promising answer to this question. Finally, we review the relatively new field of protein structural phylogeny, an area of study in which information about the distribution of protein structures among different organisms is used to reconstruct the evolutionary relationships between them. Taken together, the work that we review presents an increasingly coherent picture of how these unique polymers have evolved over the course of life on Earth.

Crystal structure of a "nonfoldable" insulin: impaired folding efficiency despite native activity

Protein evolution is constrained by folding efficiency ("foldability") and the implicit threat of toxic misfolding. A model is provided by proinsulin, whose misfolding is associated with beta-cell dysfunction and diabetes mellitus. An insulin analogue containing a subtle core substitution (Leu(A16) --> Val) is biologically active, and its crystal structure recapitulates that of the wild-type protein. As a seeming paradox, however, Val(A16) blocks both insulin chain combination and the in vitro refolding of proinsulin. Disulfide pairing in mammalian cell culture is likewise inefficient, leading to misfolding, endoplasmic reticular stress, and proteosome-mediated degradation. Val(A16) destabilizes the native state and so presumably perturbs a partial fold that directs initial disulfide pairing. Substitutions elsewhere in the core similarly destabilize the native state but, unlike Val(A16), preserve folding efficiency. We propose that Leu(A16) stabilizes nonlocal interactions between nascent alpha-helices in the A- and B-domains to facilitate initial pairing of Cys(A20) and Cys(B19), thus surmounting their wide separation in sequence. Although Val(A16) is likely to destabilize this proto-core, its structural effects are mitigated once folding is achieved. Classical studies of insulin chain combination in vitro have illuminated the impact of off-pathway reactions on the efficiency of native disulfide pairing. The capability of a polypeptide sequence to fold within the endoplasmic reticulum may likewise be influenced by kinetic or thermodynamic partitioning among on- and off-pathway disulfide intermediates. The properties of [Val(A16)]insulin and [Val(A16)]proinsulin demonstrate that essential contributions of conserved residues to folding may be inapparent once the native state is achieved.

Uncovering the properties of energy-weighted conformation space networks with a hydrophobic-hydrophilic model

The conformation spaces generated by short hydrophobic-hydrophilic (HP) lattice chains are mapped to conformation space networks (CSNs). The vertices (nodes) of the network are the conformations and the links are the transitions between them. It has been found that these networks have "small-world" properties without considering the interaction energy of the monomers in the chain, i. e. the hydrophobic or hydrophilic amino acids inside the chain. When the weight based on the interaction energy of the monomers in the chain is added to the CSNs, it is found that the weighted networks show the "scale-free" characteristic. In addition, it reveals that there is a connection between the scale-free property of the weighted CSN and the folding dynamics of the chain by investigating the relationship between the scale-free structure of the weighted CSN and the noted parameter Z score. Moreover, the modular (community) structure of weighted CSNs is also studied. These results are helpful to understand the topological properties of the CSN and the underlying free-energy landscapes.

Statistical theory for protein ensembles with designed energy landscapes

Combinatorial protein libraries provide a promising route to investigate the determinants and features of protein folding and to identify novel folding amino acid sequences. A library of sequences based on a pool of different monomer types are screened for folding molecules, consistent with a particular foldability criterion. The number of sequences grows exponentially with the length of the polymer, making both experimental and computational tabulations of sequences infeasible. Herein a statistical theory is extended to specify the properties of sequences having particular values of global energetic quantities that specify their energy landscape. The theory yields the site-specific monomer probabilities. A foldability criterion is derived that characterizes the properties of sequences by quantifying the energetic separation of the target state from low-energy states in the unfolded ensemble and the fluctuations of the energies in the unfolded state ensemble. For a simple lattice model of proteins, excellent agreement is observed between the theory and the results of exact enumeration. The theory may be used to provide a quantitative framework for the design and interpretation of combinatorial experiments.

The emergence of scaling in sequence-based physical models of protein evolution

It has recently been discovered that many biological systems, when represented as graphs, exhibit a scale-free topology. One such system is the set of structural relationships among protein domains. The scale-free nature of this and other systems has previously been explained using network growth models that, although motivated by biological processes, do not explicitly consider the underlying physics or biology. In this work we explore a sequence-based model for the evolution protein structures and demonstrate that this model is able to recapitulate the scale-free nature observed in graphs of real protein structures. We find that this model also reproduces other statistical feature of the protein domain graph. This represents, to our knowledge, the first such microscopic, physics-based evolutionary model for a scale-free network of biological importance and as such has strong implications for our understanding of the evolution of protein structures and of other biological networks.

Comparison of sequence-based and structure-based energy functions for the reversible folding of a peptide

We used computer simulations to compare the reversible folding of a 20-residue peptide, as described by sequence-based and structure-based energy functions. Sequence-based energy functions are transferable and can be used to describe the behavior of different proteins, since interactions are defined between atomic species. Conversely, structure-based energy functions are not transferable, since the interactions are defined relative to the native conformation, which is assumed to correspond to the global minimum of the energy. Our results indicate that the sequence-based and the structure-based descriptions are in qualitative agreement in characterizing the two-state behavior of the peptide that we studied. We also found, however, that several equilibrium properties, including the free-energy landscape, can be significantly different in the various models. These results suggest that the fact that a model describes the native state of a polypeptide chain does not necessarily imply that the thermodynamic and kinetic properties will also be reproduced correctly.

Protein aggregation determinants from a simplified model: cooperative folders resist aggregation

Two-chain aggregation simulations using minimalist models of proteins G, L, and mutants were used to investigate the fundamentals of protein aggregation. Mutations were selected to break up repeats of hydrophobic beads in the sequence while maintaining native topology and folding ability. Data are collected under conditions in which all chain types have similar folded populations and after equilibrating the separated chains to minimize competition between folding and aggregation. Folding cooperativity stands out as the best single-chain determinant under these conditions and for these simple models. It can be experimentally measured by the width of the unfolding transition during thermal denaturation and loosely related to population of intermediate-like states during folding. Additional measures of cooperativity and other properties such as radius of gyration fluctuations and patterning of hydrophobic residues are also examined. Initial contact system states with transition-state characteristics can be identified and are more expanded than average initial contact states. Two-chain minimalist model aggregates are considerably less structured than their native states and have minimal domain-swapping features.

Rapid evolution in conformational space: a study of loop regions in a ubiquitous GTP binding domain

The rapidly evolving subsets of a protein are often evident in multiple sequence alignments as poorly defined, gap-containing regions. We investigated the 3D context of these regions observed in 28 protein structures containing a GTP-binding domain assumed to be homologous to the transforming factor p21-RAS. The phylogenetic depth of this data set is such that it is possible to observe lineages sharing a common protein core that diverged early in the eukaryotic cell history. The sequence variability among these homolog proteins is directly linked to the structural variability of surface loops. We demonstrate that these regions are self-contained and thus mostly free of the evolutionary constraints imposed by the conserved core of the domain. These intraloop interactions have the property to create stem-like structures. Interestingly, these stem-like structures can be observed in loops of varying size, up to the size of small protein domains. We propose a model under which the diversity of protein topologies observed in these loops can be the product of a stochastic sampling of sequence and conformational space in a near-neutral fashion, while the proximity of the functional features of the domain core allows novel beneficial traits to be fixed. Our comparative observations, limited here to the proteins containing the RAS-like GTP-binding domain, suggest that a stochastic process of insertion/deletion analogous to "budding" of loops is a likely mechanism of structural innovation. Such a framework could be experimentally exploited to investigate the folding of increasingly complex model inserts.

Using protein folding rates to test protein folding theories

The fastest simple, kinetically two-state protein folds a million times more rapidly than the slowest. Here we review many recent theories of protein folding kinetics in terms of their ability to qualitatively rationalize, if not quantitatively predict, this fundamental experimental observation.

Comparison of a QM/MM force field and molecular mechanics force fields in simulations of alanine and glycine "dipeptides" (Ace-Ala-Nme and Ace-Gly-Nme) in water in relation to the problem of modeling the unfolded peptide backbone in solution

We compare the conformational distributions of Ace-Ala-Nme and Ace-Gly-Nme sampled in long simulations with several molecular mechanics (MM) force fields and with a fast combined quantum mechanics/molecular mechanics (QM/MM) force field, in which the solute's intramolecular energy and forces are calculated with the self-consistent charge density functional tight binding method (SCCDFTB), and the solvent is represented by either one of the well-known SPC and TIP3P models. All MM force fields give two main states for Ace-Ala-Nme, beta and alpha separated by free energy barriers, but the ratio in which these are sampled varies by a factor of 30, from a high in favor of beta of 6 to a low of 1/5. The frequency of transitions between states is particularly low with the amber and charmm force fields, for which the distributions are noticeably narrower, and the energy barriers between states higher. The lower of the two barriers lies between alpha and beta at values of psi near 0 for all MM simulations except for charmm22. The results of the QM/MM simulations vary less with the choice of MM force field; the ratio beta/alpha varies between 1.5 and 2.2, the easy pass lies at psi near 0, and transitions between states are more frequent than for amber and charmm, but less frequent than for cedar. For Ace-Gly-Nme, all force fields locate a diffuse stable region around phi = pi and psi = pi, whereas the amber force field gives two additional densely sampled states near phi = +/-100 degrees and psi = 0, which are also found with the QM/MM force field. For both solutes, the distribution from the QM/MM simulation shows greater similarity with the distribution in high-resolution protein structures than is the case for any of the MM simulations.

Specific and nonspecific collapse in protein folding funnels

Experiments with fast folding proteins are beginning to address the relationship between collapse and folding. We investigate how different scenarios for folding can arise depending on whether the folding and collapse transitions are concurrent or whether a nonspecific collapse precedes folding. Many earlier studies have focused on the limit in which collapse is fast compared to the folding time; in this work we focus on the opposite limit where, at the folding temperature, collapse and folding occur simultaneously. Real proteins exist in both of these limits. The folding mechanism varies substantially in these two regimes. In the regime of concurrent folding and collapse, nonspecific collapse now occurs at a temperature below the folding temperature (but slightly above the glass transition temperature).

Surface-induced conformational changes in lattice model proteins by Monte Carlo simulation

We present Monte Carlo simulations of thermal, structural, and dynamic properties of a 27-segment lattice model protein adsorbed to a solid surface. The protein consists of a sequence of A and B segments whose order and topological contact energy values are chosen so that a unique (3x3x3 cubic) folded state occurs in the absence of an adsorbing surface [E. I. Shakhnovich and M. Gutin, Proc. Natl. Acad. Sci. USA 90, 7195 (1993)]. The surface consists of a plane of sites that interact either (i) equally with all contacting protein segments (an equal affinity surface) or (ii) more strongly with type A contacting segments (an A affinity surface). For both surfaces, we find the conformational change of an initially folded protein to begin with a continuous transition to a structure where all segments contact the surface. This is followed by a partial refolding to a low energy state; this step is continuous and results in full surface contact for the equal affinity surface and is activated and results in significant loss of surface contact for the A affinity surface. We also observe a lesser (greater) degree of average surface contact in the equal (A) affinity surface with an increase in temperature.

How to guarantee optimal stability for most representative structures in the Protein Data Bank

We proposed recently an optimization method to derive energy parameters for simplified models of protein folding. The method is based on the maximization of the thermodynamic average of the overlap between protein native structures and a Boltzmann ensemble of alternative structures. Such a condition enforces protein models whose ground states are most similar to the corresponding native states. We present here an extensive testing of the method for a simple residue-residue contact energy function and for alternative structures generated by threading. The optimized energy function guarantees high stability and a well-correlated energy landscape to most representative structures in the PDB database. Failures in the recognition of the native structure can be attributed to the neglect of interactions between different chains in oligomeric proteins or with cofactors. When these are taken into account, only very few X-ray structures are not recognized. Most of them are short inhibitors or fragments and one is a structure that presents serious inconsistencies. Finally, we discuss the reasons that make NMR structures more difficult to recognizeCopyright 2001 Wiley-Liss, Inc.

Statistical theory for protein combinatorial libraries. Packing interactions, backbone flexibility, and the sequence variability of a main-chain structure

Combinatorial experiments provide new ways to probe the determinants of protein folding and to identify novel folding amino acid sequences. These types of experiments, however, are complicated both by enormous conformational complexity and by large numbers of possible sequences. Therefore, a quantitative computational theory would be helpful in designing and interpreting these types of experiment. Here, we present and apply a statistically based, computational approach for identifying the properties of sequences compatible with a given main-chain structure. Protein side-chain conformations are included in an atom-based fashion. Calculations are performed for a variety of similar backbone structures to identify sequence properties that are robust with respect to minor changes in main-chain structure. Rather than specific sequences, the method yields the likelihood of each of the amino acids at preselected positions in a given protein structure. The theory may be used to quantify the characteristics of sequence space for a chosen structure without explicitly tabulating sequences. To account for hydrophobic effects, we introduce an environmental energy that it is consistent with other simple hydrophobicity scales and show that it is effective for side-chain modeling. We apply the method to calculate the identity probabilities of selected positions of the immunoglobulin light chain-binding domain of protein L, for which many variant folding sequences are available. The calculations compare favorably with the experimentally observed identity probabilities.

Statistical significance of protein structure prediction by threading

In this study, we estimate the statistical significance of structure prediction by threading. We introduce a single parameter epsilon that serves as a universal measure determining the probability that the best alignment is indeed a native-like analog. Parameter epsilon takes into account both length and composition of the query sequence and the number of decoys in threading simulation. It can be computed directly from the query sequence and potential of interactions, eliminating the need for sequence reshuffling and realignment. Although our theoretical analysis is general, here we compare its predictions with the results of gapless threading. Finally we estimate the number of decoys from which the native structure can be found by existing potentials of interactions. We discuss how this analysis can be extended to determine the optimal gap penalties for any sequence-structure alignment (threading) method, thus optimizing it to maximum possible performance.

Modeling study on the validity of a possibly simplified representation of proteins

The folding characteristics of sequences reduced with a possibly simplified representation of five types of residues are shown to be similar to their original ones with the natural set of residues (20 types or 20 letters). The reduced sequences have a good foldability and fold to the same native structure of their optimized original ones. A large ground state gap for the native structure shows the thermodynamic stability of the reduced sequences. The general validity of such a five-letter reduction is further studied via the correlation between the reduced sequences and the original ones. As a comparison, a reduction with two letters is found not to reproduce the native structure of the original sequences due to its homopolymeric features.

A statistical mechanical method to optimize energy functions for protein folding

We present a method for deriving energy functions for protein folding by maximizing the thermodynamic average of the overlap with the native state. The method has been tested by using the pairwise contact approximation of the energy function and generating alternative structures by threading sequences over a database of 1, 169 structures. With the derived energy function, most native structures: (i) have minimal energy and (ii) are thermodynamically rather stable, and (iii) the corresponding energy landscapes are smooth. Precisely, 92% of the 1,013 x-ray structures are stabilized. Most failures can be attributed to the neglect of interactions between chains forming polychain proteins and of interactions with cofactors. When these are considered, only nine cases remain unexplained. In contrast, 38% of NMR structures are not assigned properly.

Statistical theory of combinatorial libraries of folding proteins: energetic discrimination of a target structure

A self-consistent theory is presented that can be used to estimate the number and composition of sequences satisfying a predetermined set of constraints. The theory is formulated so as to examine the features of sequences having a particular value of Delta=E(f)-<E>(u), where E(f) is the energy of sequences when in a target structure and <E>(u) is an average energy of non-target structures. The theory yields the probabilities w(i)(alpha) that each position i in the sequence is occupied by a particular monomer type alpha. The theory is applied to a simple lattice model of proteins. Excellent agreement is observed between the theory and the results of exact enumerations. The theory provides a quantitative framework for the design and interpretation of combinatorial experiments involving proteins, where a library of amino acid sequences is searched for sequences that fold to a desired structure.

Folding of a model three-helix bundle protein: a thermodynamic and kinetic analysis

The kinetics and thermodynamics of an off-lattice model for a three-helix bundle protein are investigated as a function of a bias gap parameter that determines the energy difference between native and non-native contacts. A simple dihedral potential is used to introduce the tendency to form right-handed helices. For each value of the bias parameter, 100 trajectories of up to one microsecond are performed. Such statistically valid sampling of the kinetics is made possible by the use of the discrete molecular dynamics method with square-well interactions. This permits much faster simulations for off-lattice models than do continuous potentials. It is found that major folding pathways can be defined, although ensembles with considerable structural variation are involved. The large gap models generally fold faster than those with a smaller gap. For the large gap models, the kinetic intermediates are non-obligatory, while both obligatory and non-obligatory intermediates are present for small gap models. Certain large gap intermediates have a two-helix microdomain with one helix extended outward (as in domain-swapped dimers); the small gap intermediates have more diverse structures. The importance of studying the kinetic, as well as the thermodynamics, of folding for an understanding of the mechanism is discussed and the relation between kinetic and equilibrium intermediates is examined. It is found that the behavior of this model system has aspects that encompass both the "new" view and the "old" view of protein folding.

Use of a quantitative structure-property relationship to design larger model proteins that fold rapidly

A quantitative structure-property relationship (QSPR) was used to design model protein sequences that fold repeatedly and relatively rapidly to stable target structures. The specific model was a 125-residue heteropolymer chain subject to Monte Carlo dynamics on a simple cubic lattice. The QSPR was derived from an analysis of a database of 200 sequences by a statistical method that uses a genetic algorithm to select the sequence attributes that are most important for folding and a neural network to determine the corresponding functional dependence of folding ability on the chosen attributes. The QSPR depends on the number of anti-parallel sheet contacts, the energy gap between the native state and quasi-continuous part of the spectrum and the total energy of the contacts between surface residues. Two Monte Carlo procedures were used in series to optimize both the target structures and the sequences. We generated 20 fully optimized sequences and 60 partially optimized control sequences and tested each for its ability to fold in dynamic MC simulations. Although sequences in which either the number of anti-parallel sheet contacts or the energy of the surface residues is non-optimal are capable of folding almost as well as fully optimized ones, sequences in which only the energy gap is optimized fold markedly more slowly. Implications of the results for the design of proteins are discussed.