Characterization of the folding landscape of monomeric lactose repressor: quantitative comparison of theory and experiment

Investigating the folding mechanism of the N-terminal domain of ribosomal protein L9

Protein folding is a popular topic in the life science. However, due to the limited sampling ability of experiments and simulations, the general folding mechanism is not yet clear to us. In this work, we study the folding of the N-terminal domain of ribosomal protein L9 (NTL9) in detail by a mixing replica exchange molecular dynamics method. The simulation results are close to previous experimental observations. According to the Markov state model, the folding of the protein follows a nucleation-condensation path. Moreover, after the comparison to its 39-residue β-α-β motif, we find that the helix at the C-terminal has a great influence on the folding process of the intact protein, including the nucleation of the key residues in the transition state ensemble and the packing of the hydrophobic residues in the native state.

Exploring the role of hydrophilic amino acids in unfolding of protein in aqueous ethanol solution

Hydrophobic association is the key contributor behind the formation of well packed core of a protein which is often believed to be an important step for folding from an unfolded chain to its compact functional form. While most of the protein folding/unfolding studies have evaluated the changes in the hydrophobic interactions during chemical denaturation, the role of hydrophilic amino acids in such processes are not discussed in detail. Here we report the role of the hydrophilic amino acids behind ethanol induced unfolding of protein. Using free energy simulations, we show that chicken villin head piece (HP-36) protein unfolds gradually in presence of water-ethanol binary mixture with increasing composition of ethanol. However, upon mutation of hydrophilic amino acids by glycine while keeping the hydrophobic amino acids intact, the compact state of the protein is found to be stable at all compositions with gradual flattening of the free energy landscape upon increasing compositions. The local environment around the protein in terms of ethanol/water number significantly differs in wild type protein compared to the mutated protein. The calculated Wyman-Tanford preferential binding coefficient of ethanol for wild type protein reveals that a greater number of cosolutes (here ethanol) bind to the unfolded state compared to its folded state. However, no significant increase in binding coefficient of ethanol at the unfolded state is found for mutated protein. Local-bulk partition coefficient calculation also suggests similar scenarios. Our results reveal that the weakening of hydrophobic interactions in aqueous ethanol solution along with larger preferential binding of ethanol to the unfolded state mediated by hydrophilic amino acids combinedly helps unfolding of protein in aqueous ethanol solution.

Biomolecular Assemblies: Moving from Observation to Predictive Design

Biomolecular assembly is a key driving force in nearly all life processes, providing structure, information storage, and communication within cells and at the whole organism level. These assembly processes rely on precise interactions between functional groups on nucleic acids, proteins, carbohydrates, and small molecules, and can be fine-tuned to span a range of time, length, and complexity scales. Recognizing the power of these motifs, researchers have sought to emulate and engineer biomolecular assemblies in the laboratory, with goals ranging from modulating cellular function to the creation of new polymeric materials. In most cases, engineering efforts are inspired or informed by understanding the structure and properties of naturally occurring assemblies, which has in turn fueled the development of predictive models that enable computational design of novel assemblies. This Review will focus on selected examples of protein assemblies, highlighting the story arc from initial discovery of an assembly, through initial engineering attempts, toward the ultimate goal of predictive design. The aim of this Review is to highlight areas where significant progress has been made, as well as to outline remaining challenges, as solving these challenges will be the key that unlocks the full power of biomolecules for advances in technology and medicine.

Solution NMR investigation of the response of the lactose repressor core domain dimer to hydrostatic pressure

Previous investigations of the sensitivity of the lac repressor to high-hydrostatic pressure have led to varying conclusions. Here high-pressure solution NMR spectroscopy is used to provide an atomic level view of the pressure induced structural transition of the lactose repressor regulatory domain (LacI* RD) bound to the ligand IPTG. As the pressure is raised from ambient to 3kbar the native state of the protein is converted to a partially unfolded form. Estimates of rotational correlation times using transverse optimized relaxation indicates that a monomeric state is never reached and that the predominate form of the LacI* RD is dimeric throughout this pressure change. Spectral analysis suggests that the pressure-induced transition is localized and is associated with a volume change of approximately -115mlmol^-1 and an average pressure dependent change in compressibility of approximately 30mlmol^-1kbar^-1. In addition, a subset of resonances emerge at high-pressures indicating the presence of a non-native but folded alternate state.

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.

Coarse-grained molecular simulation of epidermal growth factor receptor protein tyrosine kinase multi-site self-phosphorylation

Upon the ligand-dependent dimerization of the epidermal growth factor receptor (EGFR), the intrinsic protein tyrosine kinase (PTK) activity of one receptor monomer is activated, and the dimeric receptor undergoes self-phosphorylation at any of eight candidate phosphorylation sites (P-sites) in either of the two C-terminal (CT) domains. While the structures of the extracellular ligand binding and intracellular PTK domains are known, that of the ∼225-amino acid CT domain is not, presumably because it is disordered. Receptor phosphorylation on CT domain P-sites is critical in signaling because of the binding of specific signaling effector molecules to individual phosphorylated P-sites. To investigate how the combination of conventional substrate recognition and the unique topological factors involved in the CT domain self-phosphorylation reaction lead to selectivity in P-site phosphorylation, we performed coarse-grained molecular simulations of the P-site/catalytic site binding reactions that precede EGFR self-phosphorylation events. Our results indicate that self-phosphorylation of the dimeric EGFR, although generally believed to occur in trans, may well occur with a similar efficiency in cis, with the P-sites of both receptor monomers being phosphorylated to a similar extent. An exception was the case of the most kinase-proximal P-site-992, the catalytic site binding of which occurred exclusively in cis via an intramolecular reaction. We discovered that the in cis interaction of P-site-992 with the catalytic site was facilitated by a cleft between the N-terminal and C-terminal lobes of the PTK domain that allows the short CT domain sequence tethering P-site-992 to the PTK core to reach the catalytic site. Our work provides several new mechanistic insights into the EGFR self-phosphorylation reaction, and demonstrates the potential of coarse-grained molecular simulation approaches for investigating the complexities of self-phosphorylation in molecules such as EGFR (HER/ErbB) family receptors and growth factor receptor PTKs in general.

The epidermal growth factor receptor (EGFR) is one of a large group of cell surface receptors that allow cells to respond to growth-stimulating signals in their environment. Upon sensing of growth factor, the EGFR is activated, which triggers a signaling cascade leading to the cell nucleus and ultimately initiating cell division. The first event following receptor activation is an intramolecular kinase reaction that results in the introduction of phosphate groups onto several specific amino acids (phosphorylation sites or P-sites) in the tail of the EGFR protein. Thus, the tail of the receptor undergoes self-phosphorylation, which involves conformational motions enabling the various P-sites to access the catalytic site. The structure of the tail of the receptor is unknown, and hence the mechanism of the self-phosphorylation reaction is not well understood. To investigate this mechanism, we generated a structural model of the EGFR protein and performed computer simulations of EGFR P-site/catalytic site binding reactions. These simulations indicated how the distribution of P-sites along the tail of the receptor and restrictions in molecular movements of the tail lead to selectivity in the phosphorylation of the different P-sites. Our simulations yielded unique insights into the mechanism of EGFR self-phosphorylation that have important biological implications.

Multidomain protein solves the folding problem by multifunnel combined landscape: theoretical investigation of a Y-family DNA polymerase

Approximately three-fourths of eukaryotic proteins are composed of multiple independently folded domains. However, much of our understanding is based on single domain proteins or isolated domains whose studies directly lead to well-known energy landscape theory in which proteins fold by navigating through a funneled energy landscape toward native structure ensembles. The degrees of freedom for proteins with multiple domains are many orders of magnitude larger than that for single domain proteins. Now, the question arises: How do the multidomain proteins solve the "protein folding problem"? Here, we specifically address this issue by exploring the structure folding relationship of Sulfolobus solfataricus DNA polymerase IV (DPO4), a prototype Y-family DNA polymerase which contains a polymerase core consisting of a palm (P domain), a finger (F domain), and a thumb domain (T domain) in addition to a little finger domain (LF domain). The theoretical results are in good agreement with the experimental data and lead to several theoretical predictions. Finally, we propose that for rapid folding into well-defined conformations which carry out the biological functions, four-domain DPO4 employs a divide-and-conquer strategy, that is, combining multiple individual folding funnels into a single funnel (domains fold independently and then coalesce). In this way, the degrees of freedom for multidomain proteins are polynomial rather than exponential, and the conformational search process can be reduced effectively from a large to a smaller time scale.

αC helix as a switch in the conformational transition of Src/CDK-like kinase domains

One mechanism of regulating the catalytic activity of protein kinases is through conformational transitions. Despite great diversity in the structural changes involved in the transitions, a certain set of changes within the kinase domain (KD) has been observed for many kinases including Src and CDK2. We investigated this conformational transition computationally to identify the topological features that are energetically critical to the transition. Results from both molecular dynamics sampling and transition path optimization highlight the displacement of the αC helix as the major energy barrier, mediating the switch of the KD between the active and down-regulated states. The critical role of the αC helix is noteworthy by providing a rationale for a number of activation and deactivation mechanisms known to occur in cells. We find that kinases with the αC helix displacement exist throughout the kinome, suggesting that this feature may have emerged early in evolution.

Coarse-grained model for protein folding based on structural profiles

We study a coarse-grained protein model whose primary characteristics are (i) a tubelike geometry to describe the self-avoidance effects of the polypeptide chain and (ii) an energy function based on a one-dimensional structural representation. The latter specifies the connectivity of a sequence in a given conformation, so that the energy function, rather than favoring the formation of specific native pairwise contacts, promotes the establishment of a specific target connectivity for each amino acid. We show that the resulting dynamics is in good agreement with both experimental observations and the results of all-atoms simulations. In contrast to the latter, our coarse-grained approach provides the possibility to explore longer time scales and thus enables one to access, albeit in less detail, larger regions of the conformational space. We illustrate our approach by its application to the villin headpiece domain, a three-helix protein, by studying its folding behavior and determining heat capacities and free-energy landscapes in various reaction coordinates.

Aggregation of γ-crystallins associated with human cataracts via domain swapping at the C-terminal β-strands

The prevalent eye disease age-onset cataract is associated with aggregation of human γD-crystallins, one of the longest-lived proteins. Identification of the γ-crystallin precursors to aggregates is crucial for developing strategies to prevent and reverse cataract. Our microseconds of atomistic molecular dynamics simulations uncover the molecular structure of the experimentally detected aggregation-prone folding intermediate species of monomeric native γD-crystallin with a largely folded C-terminal domain and a mostly unfolded N-terminal domain. About 30 residues including a, b, and c strands from the Greek Key motif 4 of the C-terminal domain experience strong solvent exposure of hydrophobic residues as well as partial unstructuring upon N-terminal domain unfolding. Those strands comprise the domain-domain interface crucial for unusually high stability of γD-crystallin. We further simulate the intermolecular linkage of these monomeric aggregation precursors, which reveals domain-swapped dimeric structures. In the simulated dimeric structures, the N-terminal domain of one monomer is frequently found in contact with residues 135-164 encompassing the a, b, and c strands of the Greek Key motif 4 of the second molecule. The present results suggest that γD-crystallin may polymerize through successive domain swapping of those three C-terminal β-strands leading to age-onset cataract, as an evolutionary cost of its very high stability. Alanine substitutions of the hydrophobic residues in those aggregation-prone β-strands, such as L145 and M147, hinder domain swapping as a pathway toward dimerization. These findings thus provide critical molecular insights onto the initial stages of age-onset cataract, which is important for understanding protein aggregation diseases.

Application of nonlinear dimensionality reduction to characterize the conformational landscape of small peptides

The automatic classification of the wealth of molecular configurations gathered in simulation in the form of a few coordinates that help to explain the main states and transitions of the system is a recurring problem in computational molecular biophysics. We use the recently proposed ScIMAP algorithm to automatically extract motion parameters from simulation data. The procedure uses only molecular shape similarity and topology information inferred directly from the simulated conformations, and is not biased by a priori known information. The automatically recovered coordinates prove as excellent reaction coordinates for the molecules studied and can be used to identify stable states and transitions, and as a basis to build free-energy surfaces. The coordinates provide a better description of the free energy landscape when compared with coordinates computed using principal components analysis, the most popular linear dimensionality reduction technique. The method is first validated on the analysis of the dynamics of an all-atom model of alanine dipeptide, where it successfully recover all previously known metastable states. When applied to characterize the simulated folding of a coarse-grained model of beta-hairpin, in addition to the folded and unfolded states, two symmetric misfolding crossings of the hairpin strands are observed, together with the most likely transitions from one to the other.

Universal distribution of protein evolution rates as a consequence of protein folding physics

The hypothesis that folding robustness is the primary determinant of the evolution rate of proteins is explored using a coarse-grained off-lattice model. The simplicity of the model allows rapid computation of the folding probability of a sequence to any folded conformation. For each robust folder, the network of sequences that share its native structure is identified. The fitness of a sequence is postulated to be a simple function of the number of misfolded molecules that have to be produced to reach a characteristic protein abundance. After fixation probabilities of mutants are computed under a simple population dynamics model, a Markov chain on the fold network is constructed, and the fold-averaged evolution rate is computed. The distribution of the logarithm of the evolution rates across distinct networks exhibits a peak with a long tail on the low rate side and resembles the universal empirical distribution of the evolutionary rates more closely than either distribution resembles the log-normal distribution. The results suggest that the universal distribution of the evolutionary rates of protein-coding genes is a direct consequence of the basic physics of protein folding.

Analysis of the free-energy surface of proteins from reversible folding simulations

Computer generated trajectories can, in principle, reveal the folding pathways of a protein at atomic resolution and possibly suggest general and simple rules for predicting the folded structure of a given sequence. While such reversible folding trajectories can only be determined ab initio using all-atom transferable force-fields for a few small proteins, they can be determined for a large number of proteins using coarse-grained and structure-based force-fields, in which a known folded structure is by construction the absolute energy and free-energy minimum. Here we use a model of the fast folding helical λ-repressor protein to generate trajectories in which native and non-native states are in equilibrium and transitions are accurately sampled. Yet, representation of the free-energy surface, which underlies the thermodynamic and dynamic properties of the protein model, from such a trajectory remains a challenge. Projections over one or a small number of arbitrarily chosen progress variables often hide the most important features of such surfaces. The results unequivocally show that an unprojected representation of the free-energy surface provides important and unbiased information and allows a simple and meaningful description of many-dimensional, heterogeneous trajectories, providing new insight into the possible mechanisms of fast-folding proteins.

The process of protein folding is a complex transition from a disordered to an ordered state. Here, we simulate a specific fast-folding protein at the point at which the native and denatured states are at equilibrium and show that obtaining an accurate description of the mechanisms of folding and unfolding is far from trivial. Using simple quantities which quantify the degree of native order is, in the case of this protein, clearly misleading. We show that an unbiased representation of the free-energy surface can be obtained; using such a representation we are able to redesign the landscape and thus modify, upon site-specific “mutations”, the folding and unfolding rates. This leads us to formulate a hypothesis to explain the very fast folding of many proteins.

Quantitative approaches to the study of bistability in the lac operon of Escherichia coli

In this paper, the history and importance of the lac operon in the development of molecular and systems biology are briefly reviewed. We start by presenting a description of the regulatory mechanisms in this operon, taking into account the most recent discoveries. Then we offer a survey of the history of the lac operon, including the discovery of its main elements and the subsequent influence on the development of molecular and systems biology. Next the bistable behaviour of the operon is discussed, both with respect to its discovery and its molecular origin. A review of the literature in which this bistable phenomenon has been studied from a mathematical modelling viewpoint is then given. We conclude with some brief remarks.

Coarse-grained models reveal functional dynamics--II. Molecular dynamics simulation at the coarse-grained level--theories and biological applications

Molecular dynamics (MD) simulation has remained the most indispensable tool in studying equilibrium/non-equilibrium conformational dynamics since its advent 30 years ago. With advances in spectroscopy accompanying solved biocomplexes in growing sizes, sampling their dynamics that occur at biologically interesting spatial/temporal scales becomes computationally intractable; this motivated the use of coarse-grained (CG) approaches. CG-MD models are used to study folding and conformational transitions in reduced resolution and can employ enlarged time steps due to the absence of some of the fastest motions in the system. The Boltzmann-Inversion technique, heavily used in parameterizing these models, provides a smoothed-out effective potential on which molecular conformation evolves at a faster pace thus stretching simulations into tens of microseconds. As a result, a complete catalytic cycle of HIV-1 protease or the assembly of lipid-protein mixtures could be investigated by CG-MD to gain biological insights. In this review, we survey the theories developed in recent years, which are categorized into Folding-based and Molecular-Mechanics-based. In addition, physical bases in the selection of CG beads/time-step, the choice of effective potentials, representation of solvent, and restoration of molecular representations back to their atomic details are systematically discussed.

Folding domain B of protein A on a dynamically partitioned free energy landscape

The B domain of staphylococcal protein A (BdpA) is a small helical protein that has been studied intensively in kinetics experiments and detailed computer simulations that include explicit water. The simulations indicate that BdpA needs to reorganize in crossing the transition barrier to facilitate folding its C-terminal helix (H3) onto the nucleus formed from helices H1 and H2. This process suggests frustration between two partially ordered forms of the protein, but recent varphi value measurements indicate that the transition structure is relatively constant over a broad range of temperatures. Here we develop a simplistic model to investigate the folding transition in which properties of the free energy landscape can be quantitatively compared with experimental data. The model is a continuation of the Muñoz-Eaton model to include the intermittency of contacts between structured parts of the protein, and the results compare variations in the landscape with denaturant and temperature to varphi value measurements and chevron plots of the kinetic rates. The topography of the model landscape (in particular, the feature of frustration) is consistent with detailed simulations even though variations in the varphi values are close to measured values. The transition barrier is smaller than indicated by the chevron data, but it agrees in order of magnitude with a similar alpha-carbon type of model. Discrepancies with the chevron plots are investigated from the point of view of solvent effects, and an approach is suggested to account for solvent participation in the model.

Mapping folding energy landscapes with theory and experiment

The detailed characterization of the overall free energy landscape associated with the folding process of a protein is the ultimate goal in protein folding studies. Modern experimental techniques and all-atom simulations provide a way to obtain accurate thermodynamic and kinetic measurements, but they are oftentimes restricted to probe limited regions of a protein landscape. Although simplified protein models can access larger regions of the landscape, they are built on assumptions and approximations that can affect the accuracy of the results. We review here recent promising approaches that allow to combine the complementary strengths of theory and experiment for a more complete characterization of a protein folding landscape at multiple resolutions. Recent results and possible applications are discussed.

Coarse-grained models of protein folding: toy models or predictive tools?

Coarse-grained models are emerging as a practical alternative to all-atom simulations for the characterization of protein folding mechanisms over long time scales. While a decade ago minimalist toy models were mainly designed to test general hypotheses on the principles regulating protein folding, the latest coarse-grained models are increasingly realistic and can be used to characterize quantitatively the detailed folding mechanism of specific proteins. The ability of such models to reproduce the essential features of folding dynamics suggests that each single atomic degree of freedom is not by itself particularly relevant to folding and supports a statistical mechanical approach to characterize folding transitions. When combined with more refined models and with experimental studies, the systematic investigation of protein systems and complexes using coarse-grained models can advance our theoretical understanding of the actual organizing principles that emerge from the complex network of interactions among protein atomic constituents.

Consequences of localized frustration for the folding mechanism of the IM7 protein

In the laboratory, IM7 has been found to have an unusual folding mechanism in which an "on-pathway" intermediate with nonnative interactions is formed. We show that this intermediate is a consequence of an unusual cluster of highly frustrated interactions in the native structure. This cluster is involved in the binding of IM7 to its target, Colicin E7. Redesign of residues in this cluster to eliminate frustration is predicted by simulations to lead to faster folding without the population of an intermediate ensemble.

Kinetics analysis methods for approximate folding landscapes

MOTIVATION

Protein motions play an essential role in many biochemical processes. Lab studies often quantify these motions in terms of their kinetics such as the speed at which a protein folds or the population of certain interesting states like the native state. Kinetic metrics give quantifiable measurements of the folding process that can be compared across a group of proteins such as a wild-type protein and its mutants.

RESULTS

We present two new techniques, map-based master equation solution and map-based Monte Carlo simulation, to study protein kinetics through folding rates and population kinetics from approximate folding landscapes, models called maps. From these two new techniques, interesting metrics that describe the folding process, such as reaction coordinates, can also be studied. In this article we focus on two metrics, formation of helices and structure formation around tryptophan residues. These two metrics are often studied in the lab through circular dichroism (CD) spectra analysis and tryptophan fluorescence experiments, respectively. The approximated landscape models we use here are the maps of protein conformations and their associated transitions that we have presented and validated previously. In contrast to other methods such as the traditional master equation and Monte Carlo simulation, our techniques are both fast and can easily be computed for full-length detailed protein models. We validate our map-based kinetics techniques by comparing folding rates to known experimental results. We also look in depth at the population kinetics, helix formation and structure near tryptophan residues for a variety of proteins.

AVAILABILITY

We invite the community to help us enrich our publicly available database of motions and kinetics analysis by submitting to our server: http://parasol.tamu.edu/foldingserver/.

Supersymmetric Langevin equation to explore free-energy landscapes

The recently discovered supersymmetric generalizations of the Langevin dynamics and Kramers equation can be utilized for the exploration of free-energy landscapes of systems whose large time-scale separation hampers the usefulness of standard molecular dynamics techniques. The first realistic application is here presented. The system chosen is a minimalist model for a short alanine peptide exhibiting a helix-coil transition.

Guanylate kinase, induced fit, and the allosteric spring probe

Since the introduction of the induced-fit theory by D. E. Koshland Jr., it has been established that conformational motion invariably accompanies the execution of protein function. The catalytic activity of kinases, specifically, is associated with large conformational changes ( approximately 1 nm amplitude). In the case of guanylate kinase, upon substrate binding, the LID and nucleotide-monophosphate-binding domains are brought together and toward the CORE with large concerted movements about the alpha3 (helix 3) axis. However, whether the change in conformation mostly affects the catalytic rate or mostly increases binding affinities for one or the other substrate is unclear. We investigate this question using a nanotechnology approach based on mechanical stress. Using an "allosteric spring probe", we bias conformational states in favor of the "open" (substrate-free) conformation of the enzyme; the result is that the binding constant for the substrate guanosine monophosphate (GMP) is reduced by up to a factor of 10, whereas the binding constant for adenosine triphosphate (ATP) and the catalytic rate are essentially unaffected. The results show that the GMP-induced conformational change, which promotes catalysis, does not promote ATP binding, consistent with previous mutagenesis studies. Furthermore, they show that this conformational change is of the induced-fit type with respect to GMP binding (but not ATP binding). We elaborate on this point by proposing a quantitative criterion for the classification of conformational changes with respect to the induced-fit theory. More generally, these results show that the allosteric spring probe can be used to affect enzymatic activity in a continuously controlled manner, and also to affect specific steps of the reaction mechanism while leaving others unaffected. It is presumed that this will enable informative comparisons with the results of future molecular dynamics or statistical mechanics computations.

Hamiltonian dynamics of homopolymer chain models

The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of observables numerically computed along dynamical trajectories are found to reproduce results given by the statistical mechanics of homopolymer models. The dynamical treatment, however, indicates a nontrivial transition between regimes of slow and fast phase space mixing. Such a transition is inaccessible to a statistical mechanical treatment and reflects a bimodality in the relaxation of time averages to corresponding ensemble averages. It is also found that a change in the energy dependence of the largest Lyapunov exponent indicates the Theta transition between filamentary and globular polymer configurations, clearly detecting the transition even for a finite number of particles.

Minimalist protein model as a diagnostic tool for misfolding and aggregation

We propose a realistic coarse-grained protein model and a technique to "anchor" the model to available experimental data. We apply this procedure to characterize the effect of multiple mutations on the folding mechanism of protein S6. We show that the mutation of a few "gatekeeper" residues triggers significant changes on the folding landscape of S6. These results suggest that gatekeeper residues control the flexibility of critical regions of S6, that in turn regulates the delicate balance between folding and aggregation. Although obtained with a minimalist protein model, these results are fully consistent with experimental evidence and offer a clue to understand the interplay between folding and aggregation in protein S6.

Molecular simulations of cotranslational protein folding: fragment stabilities, folding cooperativity, and trapping in the ribosome

Although molecular simulation methods have yielded valuable insights into mechanistic aspects of protein refolding in vitro, they have up to now not been used to model the folding of proteins as they are actually synthesized by the ribosome. To address this issue, we report here simulation studies of three model proteins: chymotrypsin inhibitor 2 (CI2), barnase, and Semliki forest virus protein (SFVP), and directly compare their folding during ribosome-mediated synthesis with their refolding from random, denatured conformations. To calibrate the methodology, simulations are first compared with in vitro data on the folding stabilities of N-terminal fragments of CI2 and barnase; the simulations reproduce the fact that both the stability and thermal folding cooperativity increase as fragments increase in length. Coupled simulations of synthesis and folding for the same two proteins are then described, showing that both fold essentially post-translationally, with mechanisms effectively identical to those for refolding. In both cases, confinement of the nascent polypeptide chain within the ribosome tunnel does not appear to promote significant formation of native structure during synthesis; there are however clear indications that the formation of structure within the nascent chain is sensitive to location within the ribosome tunnel, being subject to both gain and loss as the chain lengthens. Interestingly, simulations in which CI2 is artificially stabilized show a pronounced tendency to become trapped within the tunnel in partially folded conformations: non-cooperative folding, therefore, appears in the simulations to exert a detrimental effect on the rate at which fully folded conformations are formed. Finally, simulations of the two-domain protease module of SFVP, which experimentally folds cotranslationally, indicate that for multi-domain proteins, ribosome-mediated folding may follow different pathways from those taken during refolding. Taken together, these studies provide a first step toward developing more realistic methods for simulating protein folding as it occurs in vivo.

Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction

The definition of reaction coordinates for the characterization of a protein-folding reaction has long been a controversial issue, even for the "simple" case in which one single free-energy barrier separates the folded and unfolded ensemble. We propose a general approach to this problem to obtain a few collective coordinates by using nonlinear dimensionality reduction. We validate the usefulness of this method by characterizing the folding landscape associated with a coarse-grained protein model of src homology 3 as sampled by molecular dynamics simulations. The folding free-energy landscape projected on the few relevant coordinates emerging from the dimensionality reduction can correctly identify the transition-state ensemble of the reaction. The first embedding dimension efficiently captures the evolution of the folding process along the main folding route. These results clearly show that the proposed method can efficiently find a low-dimensional representation of a complex process such as protein folding.

Molecular simulations of cotranslational protein folding: fragment stabilities, folding cooperativity, and trapping in the ribosome

Although molecular simulation methods have yielded valuable insights into mechanistic aspects of protein refolding in vitro, they have up to now not been used to model the folding of proteins as they are actually synthesized by the ribosome. To address this issue, we report here simulation studies of three model proteins: chymotrypsin inhibitor 2 (CI2), barnase, and Semliki forest virus protein (SFVP), and directly compare their folding during ribosome-mediated synthesis with their refolding from random, denatured conformations. To calibrate the methodology, simulations are first compared with in vitro data on the folding stabilities of N-terminal fragments of CI2 and barnase; the simulations reproduce the fact that both the stability and thermal folding cooperativity increase as fragments increase in length. Coupled simulations of synthesis and folding for the same two proteins are then described, showing that both fold essentially post-translationally, with mechanisms effectively identical to those for refolding. In both cases, confinement of the nascent polypeptide chain within the ribosome tunnel does not appear to promote significant formation of native structure during synthesis; there are however clear indications that the formation of structure within the nascent chain is sensitive to location within the ribosome tunnel, being subject to both gain and loss as the chain lengthens. Interestingly, simulations in which CI2 is artificially stabilized show a pronounced tendency to become trapped within the tunnel in partially folded conformations: non-cooperative folding, therefore, appears in the simulations to exert a detrimental effect on the rate at which fully folded conformations are formed. Finally, simulations of the two-domain protease module of SFVP, which experimentally folds cotranslationally, indicate that for multi-domain proteins, ribosome-mediated folding may follow different pathways from those taken during refolding. Taken together, these studies provide a first step toward developing more realistic methods for simulating protein folding as it occurs in vivo.

Scaling approach to the folding kinetics of large proteins

We study a nucleation-growth model of protein folding and extend it to describe larger proteins with multiple folding units. The model is of one of an extremely simple type in which amino acids are allowed just two states--either folded (frozen) or unfolded. Its energetics are heterogeneous and Gō-like, the energy being defined in terms of the number of atom-to-atom contacts that would occur between frozen amino acids in the native crystal structure of the protein. Each collective state of the amino acids is intended to represent a small free energy microensemble consisting of the possible configurations of unfolded loops, open segments, and free ends constrained by the cross-links that form between folded parts of the molecule. We approximate protein free energy landscapes by an infinite subset of these microensemble topologies in which loops and open unfolded segments can be viewed roughly as independent objects for the purpose of calculating their entropy, and we develop a means to implement this approximation in Monte Carlo simulations. We show that this approach describes transition state structures (phi values) more accurately and identifies folding intermediates that were unavailable to previous versions of the model that restricted the number of loops and nuclei.

The experimental folding landscape of monomeric lactose repressor, a large two-domain protein, involves two kinetic intermediates

To probe the experimental folding behavior of a large protein with complex topology, we created a monomeric variant of the lactose repressor protein (MLAc), a well characterized tetrameric protein that regulates transcription of the lac operon. Purified MLAc is folded, fully functional, and binds the inducer isopropyl beta-d-thiogalactoside with the same affinity as wild-type LacI. Equilibrium unfolding of MLAc induced by the chemical denaturant urea is a reversible, apparent two-state process (pH 7.5, 20 degrees C). However, time-resolved experiments demonstrate that unfolding is single-exponential, whereas refolding data indicate two transient intermediates. The data reveal the initial formation of a burst-phase (tau < ms) intermediate that corresponds to approximately 50% of the total secondary-structure content. This step is followed by a rearrangement reaction that is rate-limited by an unfolding process (tau approximately 3 s; pH 7.5, 20 degrees C) and results in a second intermediate. This MLAc intermediate converts to the native structure (tau approximately 30 s; pH 7.5, 20 degrees C). Remarkably, the experimental folding-energy landscape for MLAc is in excellent agreement with theoretical predictions using a simple topology-based C(alpha)-model as presented in a companion article in this issue.