Funnel-shaped Energy Landscapes Research Articles

Consistency Principle for Protein Design

Protein design holds promise for applications such as the control of cells, therapeutics, new enzymes and protein-based materials. Recently, there has been progress in rational design of protein molecules, and a lot of attempts have been made to create proteins with functions of our interests. The key to the progress is the development of methods for controlling desired protein tertiary structures with atomic-level accuracy. A theory for protein folding, the consistency principle, proposed by Nobuhiro Go in 1983, was a compass for the development. Anfinsen hypothesized that proteins fold into the free energy minimum structures, but Go further considered that local and non-local interactions in the free energy minimum structures are consistent with each other. Guided by the principle, we proposed a set of rules for designing ideal protein structures stabilized by consistent local and non-local interactions. The rules made possible designs of amino acid sequences with funnel-shaped energy landscapes toward our desired target structures. So far, various protein structures have been created using the rules, which demonstrates significance of our rules as intended. In this review, we briefly describe how the consistency principle impacts on our efforts for developing the design technology.

Delineating the conformational dynamics of intermediate structures on the unfolding pathway of β-lactoglobulin in aqueous urea and dimethyl sulfoxide

The funnel shaped energy landscape model of the protein folding suggests that progression of folding proceeds through multiple pathways, having the multiple intermediates which leads to multidimensional free-energy surface. Herein, we applied all-atom MD simulation to conduct a comparative study on the structure of β-lactoglobulin (β-LgA) in aqueous mixture of 8 M urea and 8 M dimethyl sulfoxide (DMSO), at different temperatures. The cumulative results of multiple simulations suggest a common unfolding pathway of β-LgA, occurred through the stable and meta-stable intermediates (I), in both urea and DMSO. However, the free-energy landscape (FEL) analyses show that the structural transitions of I-states are energetically different. In urea, FEL shows distinct ensemble of intermediates, I1 and I2, separated by the energy barrier of ∼3.0 kcal mol−1. Similarly, we find the population of two distinct I1 and I2 states in DMSO, however, the I1 appeared transiently around ∼30–35 ns and is short-lived. But, the I2 ensemble is observed structurally compact and long-lived (∼50–150 ns) as compared to unfolding in urea. Furthermore, the I1 and I2 are separated through a high energy barrier of ∼6.0 kcal mol−1. Thus, our results provide the structural insights of intermediates which essentially bear the signature of a different unfolding pathway of β-LgA in urea and DMSO.Abbreviationsβ-LgAβ-lactoglobulinDMSOdimethyl sulfoxideFELfree-energy landscapeGdmClguanidinium chlorideIintermediate stateMGmolten globule statePMEparticle mesh EwaldQfraction of native contactsRMSDroot mean square deviationRMSFroot mean square fluctuationRgradius of gyrationSASAsolvent Accessible Surface AreascSASAthe side chain SASATrptryptophanCommunicated by Ramaswamy H. Sarma

Consistency principle for protein design.

Protein design holds promise for applications such as the control of cells, therapeutics, new enzymes and protein-based materials. Recently, there has been progress in rational design of protein molecules, and a lot of attempts have been made to create proteins with functions of our interests. The key to the progress is the development of methods for controlling desired protein tertiary structures with atomic-level accuracy. A theory for protein folding, the consistency principle, proposed by Nobuhiro Go in 1983, was a compass for the development. Anfinsen hypothesized that proteins fold into the free energy minimum structures, but Go further considered that local and non-local interactions in the free energy minimum structures are consistent with each other. Guided by the principle, we proposed a set of rules for designing ideal protein structures stabilized by consistent local and non-local interactions. The rules made possible designs of amino acid sequences with funnel-shaped energy landscapes toward our desired target structures. So far, various protein structures have been created using the rules, which demonstrates significance of our rules as intended. In this review, we briefly describe how the consistency principle impacts on our efforts for developing the design technology.

Investigating Characteristics of Folding Cores from Analyses of Folding Mechaniams on Multi-Transition Proteins by Means of a Coarse-Grained Go Model

Though it has become clear that small and fast folding proteins have funnel shaped energy landscape, we have not know explicitly what and when happens in folding process. The knowledge of precise picture in each transition in the folding process of multi state proteins should provide the hints to elucidate the detailed folding processes.However, many hypotheses that try to explain the mechanisms of multi-state folding have been proposed (such as hypotheses regarding the packing of side chains after searching the protein's topology, those regarding a number of subdomains that form a distinct barrier, those regarding discrete two-dimensional and three-dimensional structure formation, and others) and we have not yet gained a precise understanding.To understand the mechanisms of multi-state folding, thermodynamic contributions of each component of the system, such as a main-chain, a side-chain and water, should be specified. It can be accomplished by comparing the simulation results of some models which has different resolution such as Ca-Go model, full-atom Go model and all-atom with explicit water.In the precedent study, as a first step, we showed that the difference in the shape of the free energy profiles could be interpreted by the number of the regions that folds cooperatively and degree of coupling of the regions by means of modified Ca-Go model.In this study, we apply the same method with previous work to other proteins which are suggested to fold into the native structures through multiple transitions and affirm the number of the barrier and stability of the intermediate states. We also investigate that the characteristics of the regions to contribute to barrier constructions.

The Protein-Folding Problem, 50 Years On

The protein-folding problem was first posed about one half-century ago. The term refers to three broad questions: (i) What is the physical code by which an amino acid sequence dictates a protein's native structure? (ii) How can proteins fold so fast? (iii) Can we devise a computer algorithm to predict protein structures from their sequences? We review progress on these problems. In a few cases, computer simulations of the physical forces in chemically detailed models have now achieved the accurate folding of small proteins. We have learned that proteins fold rapidly because random thermal motions cause conformational changes leading energetically downhill toward the native structure, a principle that is captured in funnel-shaped energy landscapes. And thanks in part to the large Protein Data Bank of known structures, predicting protein structures is now far more successful than was thought possible in the early days. What began as three questions of basic science one half-century ago has now grown into the full-fledged research field of protein physical science.

Energy landscape of the small protein Ace-(Ala)10-NMe

The energy landscape of the polyalanine Ace-(Ala)10-NMe, one of the standard models for the study of α-helix folding, is investigated using conformational space annealing (CSA) and the all-atom CHARMM force field (param22). The native α-helical conformation is obtained for all 100 CSA runs. Gathering all conformations in the final banks of 100 independent CSA runs, we collect a total of 1933 distinct local minima, enabling us to investigate the energy landscape. Our results clearly indicate a funnel-shaped energy landscape leading to the native helical conformation. To the best of our knowledge, this kind of funnel-shaped landscape for Ace-(Ala)10-NMe is obtained for the first time. Also, we find that the conformations of low-energy local minima are classified approximately into five groups according to their secondary structures: native-like α-helix conformations, partially α-helical conformations, conformations with an α-helix and a β-sheet, β-sheet conformations, and coil conformations.

Profile of Ken A. Dill

A protein is a chain of amino acids that has been folded into a precise shape, explains statistical physicist Ken Dill, a recently elected member of the National Academy of Sciences and director of the Laufer Center for Physical and Quantitative Biology at Stony Brook University in New York. A protein with 100 amino acids can ball up in a staggering number of ways: roughly 3200 (1). Yet each protein molecule balls up into the exact shape needed to perform its desired role in the body. Even more impressive–the folding often occurs within milliseconds. Ken A. Dill. How, researchers like Dill have long wondered, does the protein know just what to do? More than answer a grand challenge in biology, predicting the secrets behind how a protein folds could pave the way for pharmaceutical drugs that target errant proteins. From the 1980s to the 1990s, Dill devised a theory to explain protein folding in terms of funnel-shaped energy landscapes. Today, that theory, which shows how amino acids in a protein chain can glom together in different ways and still arrive at the same protein shape, has emerged as the accepted view of how proteins fold (1, 3). In his recent inaugural article, Dill (4) expanded from looking at the physics of a single protein to looking at all of the proteins inside a cell—a collection known as the proteome. Dill has found that proteomes have evolved to optimize performance inside their host cell. For instance, he says, his models show that cells are packed with the perfect number of proteins, a situation that he likens to a good party. Too few guests (or proteins) and the party fizzles out, he says. Too many guests and it becomes too crowded for one guest to travel across the room …

Direct visualization reveals dynamics of a transient intermediate during protein assembly

Interactions between proteins underlie numerous biological functions. Theoretical work suggests that protein interactions initiate with formation of transient intermediates that subsequently relax to specific, stable complexes. However, the nature and roles of these transient intermediates have remained elusive. Here, we characterized the global structure, dynamics, and stability of a transient, on-pathway intermediate during complex assembly between the Signal Recognition Particle (SRP) and its receptor. We show that this intermediate has overlapping but distinct interaction interfaces from that of the final complex, and it is stabilized by long-range electrostatic interactions. A wide distribution of conformations is explored by the intermediate; this distribution becomes more restricted in the final complex and is further regulated by the cargo of SRP. These results suggest a funnel-shaped energy landscape for protein interactions, and they provide a framework for understanding the role of transient intermediates in protein assembly and biological regulation.

Cyclic Conformational Modification of an Enzyme: Serial Engagement, Energy Relay, Hysteretic Enzyme, and Fischer’s Hypothesis

Reversible chemical modification of enzymes is one of the most important mechanisms in cellular signaling. We generalize this concept to include cyclic modification of enzyme conformations. The mechanism is fundamentally different from the ligand induced conformational change: It only requires a catalytic amount of ligand to activate an enzyme, but it does require an active chemical energy driving a "futile cycle" akin to the phosphorylation-dephosphorylation cycle. The mechanism covers several previously proposed models that include serial engagement for T-cell receptor activation, energy relay for proofreading in DNA replication and protein biosynthesis, the hysteretic enzyme, and Fischer's hypothesis on protein tyrosine phosphatase action. While for small proteins operating under a funnel-shaped energy landscape, multiple conformations with sufficiently long dwell times are not common, recent experiments suggest that for larger, multidomain proteins, cyclic conformational modification (CCM) is much more likely and evolution presumably finds a way to capitalize on this mode of regulation. CCM can be difficult to identify in cells; however, it is potentially an important, and yet overlooked, regulatory mechanism in cellular signal transduction. We suggest the serial engagement mechanism in T-cell activation to be a possible testing case for the CCM mechanism.

Graph-theoretical identification of dissociation pathways on free energy landscapes of biomolecular interaction

Biomolecular association and dissociation reactions take place on complicated interaction free energy landscapes that are still very hard to characterize computationally. For large enough distances, though, it often suffices to consider the six relative translational and rotational degrees of freedom of the two particles treated as rigid bodies. Here, we computed the six-dimensional free energy surface of a dimer of water-soluble alpha-helices by scanning these six degrees of freedom in about one million grid points. In each point, the relative free energy difference was computed as the sum of the polar and nonpolar solvation free energies of the helix dimer and of the intermolecular coulombic interaction energy. The Dijkstra graph algorithm was then applied to search for the lowest cost dissociation pathways based on a weighted, directed graph, where the vertices represent the grid points, the edges connect the grid points and their neighbors, and the weights are the reaction costs between adjacent pairs of grid points. As an example, the configuration of the bound state was chosen as the source node, and the eight corners of the translational cube were chosen as the destination nodes. With the strong electrostatic interaction of the two helices giving rise to a clearly funnel-shaped energy landscape, the eight lowest-energy cost pathways coming from different orientations converge into a well-defined pathway for association. We believe that the methodology presented here will prove useful for identifying low-energy association and dissociation pathways in future studies of complicated free energy landscapes for biomolecular interaction.

Replica exchange simulations of transient encounter complexes in protein–protein association

Recent paramagnetic relaxation enhancement (PRE) studies on several weakly interacting protein complexes have unequivocally demonstrated the existence of transient encounter complexes. Here, we present a computational method to study protein-protein binding by creating equilibrium ensembles that include both specific and nonspecific protein complexes. In a joint analysis of simulation and experiment we explore the physical nature and underlying physicochemical characteristics of encounter complexes involving three protein-protein interactions of the bacterial phosphotransferase system. Replica exchange Monte Carlo simulations using a coarse-grained energy function recover the structures of the specific complexes and produce binding affinities in good agreement with experiment. Together with the specific complex, a relatively small number of distinct nonspecific complexes largely accounts for the measured PRE data. The combined relative population of the latter is less than approximately 10%. The binding interfaces of the specific and nonspecific complexes differ primarily in size but exhibit similar amino acid compositions. We find that the overall funnel-shaped energy landscape of complex formation is dominated by the specific complex, a small number of structured nonspecific complexes, and a diffuse cloud of loosely bound complexes connecting the specific and nonspecific binding sites with each other and the unbound state. Nonspecific complexes may not only accelerate the binding kinetics by enhancing the rate of success of random diffusional encounters but also play a role in protein function as alternative binding modes.

Protein model refinement using an optimized physics-based all-atom force field

One of the greatest challenges in protein structure prediction is the refinement of low-resolution predicted models to high-resolution structures that are close to the native state. Although contemporary structure prediction methods can assemble the correct topology for a large fraction of protein domains, such approximate models are often not of the resolution required for many important applications, including studies of reaction mechanisms and virtual ligand screening. Thus, the development of a method that could bring those structures closer to the native state is of great importance. We recently optimized the relative weights of the components of the Amber ff03 potential on a large set of decoy structures to create a funnel-shaped energy landscape with the native structure at the global minimum. Such an energy function might be able to drive proteins toward their native structure. In this work, for a test set of 47 proteins, with 100 decoy structures per protein that have a range of structural similarities to the native state, we demonstrate that our optimized potential can drive protein models closer to their native structure. Comparing the lowest-energy structure from each trajectory with the starting decoy, structural improvement is seen for 70% of the models on average. The ability to do such systematic structural refinements by using a physics-based all-atom potential represents a promising approach to high-resolution structure prediction.

Substructural cooperativity and parallel versus sequential events during protein unfolding

According to the "old view," proteins fold along well-defined sequential pathways, whereas the "new view" sees protein folding as a highly parallel stochastic process on funnel-shaped energy landscapes. We have analyzed parallel and sequential processes on a large number of molecular dynamics unfolding trajectories of the protein CI2 at high temperatures. Using rigorous statistical measures, we quantify the degree of sequentiality on two structural levels. The unfolding process is highly parallel on the microstructural level of individual contacts. On a coarser, macrostructural level of contact clusters, characteristic parallel and sequential events emerge. These characteristic events can be understood from loop-closure dependencies between the contact clusters. A correlation analysis of the unfolding times of the contacts reveals a high degree of substructural cooperativity within the contact clusters.

Computing the transition state populations in simple protein models.

We describe the master equation method for computing the kinetics of protein folding. We illustrate the method using a simple Go model. Presently most models of two-state fast-folding protein folding kinetics invoke the classical idea of a transition state to explain why there is a single exponential decay in time. However, if proteins fold via funnel-shaped energy landscapes, as predicted by many theoretical studies, then it raises the question of what is the transition state. Is it a specific structure, or a small ensemble of structures, as is expected from classical transition state theory? Or is it more like the denatured states of proteins, a very broad ensemble? The answer that is usually obtained depends on the assumptions made about the transition state. The present method is a rigorous way to find transition states, without assumptions or approximations, even for very nonclassical shapes of energy landscapes. We illustrate the method here, showing how the transition states in two-state protein folding can be very broad ensembles.

Transition states and the meaning of Phi-values in protein folding kinetics.

What is the mechanism of two-state protein folding? The rate-limiting step is typically explored through a Phi-value, which is the mutation-induced change in the transition state free energy divided by the change in the equilibrium free energy of folding. Phi-values ranging from 0 to 1 have been interpreted as meaning the transition state is denatured-like (0), native-like (1) or in-between. But there is no classical interpretation for the experimental Phi-values that are negative or >1. Using a rigorous method to identity transition states via an exact lattice model, we find that nonclassical Phi-values can arise from parallel microscopic flow processes, such as those in funnel-shaped energy landscapes. Phi < 0 results when a mutation destabilizes a slow flow channel, causing a backflow into a faster flow channel. Phi > 1 implies the reverse: a backflow from a fast channel into a slow one. Using a 'landscape mapping' method, we find that Phi correlates with the acceleration/deceleration of folding induced by mutations, rather than with the degree of nativeness of the transition state.

Comparing search strategies for finding global optima on energy landscapes

We provide some tests of the convex global underestimator (CGU) algorithm, which aims to find global minima on funnel-shaped energy landscapes. We use two different potential functions—the reduced Lennard–Jones cluster potential, and the modified Sun protein folding potential, to compare the CGU algorithm with the simplest versions of the traditional trajectory-based search methods, simulated annealing (SA), and Monte Carlo (MC). For both potentials, the CGU reaches energies lower on the landscapes than both SA and MC, even when SA and MC are given the same number of starting points as in a full CGU run or when all methods are given the same amount of computer time. The CGU consistently finds the global minima of the Lennard–Jones potential for all cases with up to at least n=30 degrees of freedom. Finding the global or near-global minimum in the CGU method requires polynomial time [scaling between O(n3) and O(n4)], on average. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1527–1532, 1999