Entropy and barrier-controlled fluctuations determine conformational viscoelasticity of single biomolecules

Biological macromolecules have complex and nontrivial energy landscapes, endowing them with a unique conformational adaptability and diversity in function. Hence, understanding the processes of elasticity and dissipation at the nanoscale is important to molecular biology and emerging fields such as nanotechnology. Here we analyze single molecule fluctuations in an atomic force microscope, using a generic model of biopolymer viscoelasticity that includes local "internal" conformational dissipation. Comparing two biopolymers, dextran and cellulose (polysaccharides with and without local bistable transitions), demonstrates that signatures of simple conformational change are minima in both the elastic and internal friction constants around a characteristic force. A novel analysis of dynamics on a bistable energy landscape provides a simple explanation: an elasticity driven by the entropy, and friction by a barrier-controlled hopping time of populations between states, which is surprisingly distinct to the well-known relaxation time. This nonequilibrium microscopic analysis thus provides a means of quantifying new dynamical features of the energy landscape of the glucopyranose ring, revealing an unexpected underlying roughness and information on the shape of the barrier of the chair-boat transition in dextran. The results presented herein provide a basis toward probing the viscoelasticity of macromolecular conformational transitions on more complex energy landscapes, such as during protein folding.     

Folding of the SAM-I riboswitch: A tale with a twist

Riboswitches are ligand-dependent RNA genetic regulators that control gene expression by altering their structures. The elucidation of riboswitch conformational changes before and after ligand recognition is crucial to understand how riboswitches can achieve high ligand binding affinity and discrimination against cellular analogs. The detailed characterization of riboswitch folding pathways suggest that they may use their intrinsic conformational dynamics to sample a large array of structures, some of which being nearly identical to ligand-bound molecules. Some of these structural conformers can be "captured" upon ligand binding, which is crucial for the outcome of gene regulation. Recent studies about the SAM-I riboswitch have revealed unexpected and previously unknown RNA folding mechanisms. For instance, the observed helical twist of the P1 stem upon ligand binding to the SAM-I aptamer adds a new element in the repertoire of RNA strategies for recognition of small metabolites. From an RNA folding perspective, these findings also strongly indicate that the SAM-I riboswitch could achieve ligand recognition by using an optimized combination of conformational capture and induced-fit approaches, a feature that may be shared by other RNA regulatory sequences.     

Single-molecule studies of riboswitch folding

The folding dynamics of riboswitches are central to their ability to modulate gene expression in response to environmental cues. In most cases, a structural competition between the formation of a ligand-binding aptamer and an expression platform (or some other competing off-state) determines the regulatory outcome. Here, we review single-molecule studies of riboswitch folding and function, predominantly carried out using single-molecule FRET or optical trapping approaches. Recent results have supplied new insights into riboswitch folding energy landscapes, the mechanisms of ligand binding, the roles played by divalent ions, the applicability of hierarchical folding models, and kinetic vs. thermodynamic control schemes. We anticipate that future work, based on improved data sets and potentially combining multiple experimental techniques, will enable the development of more complete models for complex RNA folding processes. This article is part of a Special Issue entitled: Riboswitches.     

All-atom replica exchange molecular simulation of protein BBL

Downhill folding is one of the most important predictions of energy landscape theory. Recently, the Escherichia coli 2-oxoglutarate dehydrogenase PSBD was described as a first example of global downhill folding (Garcia-Mira et al., Science 2002;298:2191), classification that has been later subject of significant controversy. To help resolve this problem, by using intensive all-atom simulation with explicit water model and the replica exchange method, we sample the phase space of protein BBL and depict the free energy landscape. We give an estimate of the free energy barrier height of 1-2 k(B)T, dependent on the way the energy landscape is projected. We also study the conformational distribution of the transition region and find that the three helices generally take the similar positions as that in the native states whereas their spatial orientations show large variability. We further detect the inconsistency between different signals by individually fitting the thermal denaturation curves of five structural features using two-state model, which gives a wide spread melting temperature of 19 K. All of these features are consistent with a picture of folding with very low cooperativities. Compared with the experimental data (Sadqi et al., Nature 2006; 442:317), our results indicate that the Naf-BBL (pH5.3) may have an even lower barrier height and cooperativity.     

From mutations to mechanisms and dysfunction via computation and mining of protein energy landscapes

Background

The protein energy landscape underscores the inherent nature of proteins as dynamic molecules interconverting between structures with varying energies. Reconstructing a protein’s energy landscape holds the key to characterizing a protein’s equilibrium conformational dynamics and its relationship to function. Many pathogenic mutations in protein sequences alter the equilibrium dynamics that regulates molecular interactions and thus protein function. In principle, reconstructing energy landscapes of a protein’s healthy and diseased variants is a central step to understanding how mutations impact dynamics, biological mechanisms, and function.

Results

Recent computational advances are yielding detailed, sample-based representations of protein energy landscapes. In this paper, we propose and describe two novel methods that leverage computed, sample-based representations of landscapes to reconstruct them and extract from them informative local structures that reveal the underlying organization of an energy landscape. Such structures constitute landscape features that, as we demonstrate here, can be utilized to detect alterations of landscapes upon mutation.

Conclusions

The proposed methods detect altered protein energy landscape features in response to sequence mutations. By doing so, the methods allow formulating hypotheses on the impact of mutations on specific biological activities of a protein. This work demonstrates that the availability of energy landscapes of healthy and diseased variants of a protein opens up new avenues to harness the quantitative information embedded in landscapes to summarize mechanisms via which mutations alter protein dynamics to percolate to dysfunction.

     

Role of unfolded state heterogeneity and en-route ruggedness in protein folding kinetics

In order to improve our understanding of the physical bases of protein folding, there is a compelling need for better connections between experimental and computational approaches. This work addresses the role of unfolded state conformational heterogeneity and en-route intermediates, as an aid for planning and interpreting protein folding experiments. The expected kinetics were modeled for different types of energy landscapes, including multiple parallel folding routes, preferential paths dominated by one primary folding route, and distributed paths with a wide spectrum of microscopic folding rate constants. In the presence of one or more preferential routes, conformational exchange among unfolded state populations slows down the observed rates for native protein formation. We find this to be a general phenomenon, taking place even when unfolded conformations interconvert much faster than the "escape" rate constants to folding. Dramatic kinetic deceleration is expected in the presence of an increasing number of folding-incompetent unfolded conformations. This argues for the existence of parallel folding paths involving several folding-competent unfolded conformations, during the early stages of protein folding. Deviations from single-exponential behavior are observed for unfolded conformations exchanging at comparable rates or more slowly than folding events. Analysis of the effect of en-route (on-path) intermediate formation and landscape ruggedness on folding kinetics leads to the following unexpected conclusions: (1) intermediates, which often retard native state formation, may in some cases accelerate folding, and (2) rugged landscapes, usually associated with stretched exponentials, display single-exponential behavior in the presence of late high-friction paths.     

The importance of explicit chain representation in protein folding models: an examination of Ising-like models

A class of models that represents a protein chain as a sequence of "folded" and "unfolded" residues has recently been used to correlate rates and mechanisms of protein folding with the protein native structure. In order to better understand the conditions under which these "Ising-like" models apply, we compare results from this model to those obtained from an off-lattice model which uses the same potential function. We find that Ising-like models by construction impose folding via a highly sequential nucleation-condensation mechanism, which in turn leads to more rugged energy landscapes, fewer "pathways" to the native state, and in the specific case examined here, the cold shock protein A from Escherichia coli, a qualitative difference in the most likely order of events in folding.     

Protein folding in the landscape perspective: Chevron plots and non-arrhenius kinetics

We use two simple models and the energy landscape perspective to study protein folding kinetics. A major challenge has been to use the landscape perspective to interpret experimental data, which requires ensemble averaging over the microscopic trajectories usually observed in such models. Here, because of the simplicity of the model, this can be achieved. The kinetics of protein folding falls into two classes: multiple-exponential and two-state (single-exponential) kinetics. Experiments show that two-state relaxation times have “chevron plot” dependences on denaturant and non-Arrhenius dependences on temperature. We find that HP and HP+ models can account for these behaviors. The HP model often gives bumpy landscapes with many kinetic traps and multiple-exponental behavior, whereas the HP+ model gives more smooth funnels and two-state behavior. Multiple-exponential kinetics often involves fast collapse into kinetic traps and slower barrier climbing out of the traps. Two-state kinetics often involves entropic barriers where conformational searching limits the folding speed. Transition states and activation barriers need not define a single conformation; they can involve a broad ensemble of the conformations searched on the way to the native state. We find that unfolding is not always a direct reversal of the folding process. Proteins 30:2–33, 1998. © 1998 Wiley-Liss, Inc.     

Conformational capture of the SAM-II riboswitch

Riboswitches are gene regulation elements in mRNA that function by specifically responding to metabolites. Although the metabolite-bound states of riboswitches have proven amenable to structure determination efforts, knowledge of the structural features of riboswitches in their ligand-free forms and their ligand-response mechanisms giving rise to regulatory control is lacking. Here we explore the ligand-induced folding process of the S-adenosylmethionine type II (SAM-II) riboswitch using chemical and biophysical methods, including NMR and fluorescence spectroscopy, and single-molecule fluorescence imaging. The data reveal that the unliganded SAM-II riboswitch is dynamic in nature, in that its stem-loop element becomes engaged in a pseudoknot fold through base-pairing with nucleosides in the 3' overhang containing the Shine-Dalgarno sequence. Although the pseudoknot structure is highly transient in the absence of its ligand, S-adenosylmethionine (SAM), it becomes conformationally restrained upon ligand recognition, through a conformational capture mechanism. These insights provide a molecular understanding of riboswitch dynamics that shed new light on the mechanism of riboswitch-mediated translational regulation.     

Engineering strand-specific DNA nicking enzymes from the type IIS restriction endonucleases BsaI, BsmBI, and BsmAI

To determine the extent to which protein folding rates and free energy landscapes have been shaped by natural selection, we have examined the folding kinetics of five proteins generated using computational design methods and, hence, never exposed to natural selection. Four of these proteins are complete computer-generated redesigns of naturally occurring structures and the fifth protein, called Top7, has a computer-generated fold not yet observed in nature. We find that three of the four redesigned proteins fold much faster than their naturally occurring counterparts. While natural selection thus does not appear to operate on protein folding rates, the majority of the designed proteins unfold considerably faster than their naturally occurring counterparts, suggesting possible selection for a high free energy barrier to unfolding. In contrast to almost all naturally occurring proteins of less than 100 residues but consistent with simple computational models, the folding energy landscape for Top7 appears to be quite complex, suggesting the smooth energy landscapes and highly cooperative folding transitions observed for small naturally occurring proteins may also reflect the workings of natural selection.     

Coevolution of function and the folding landscape: correlation with density of native contacts

The relationship between the folding landscape and function of evolved proteins is explored by comparison of the folding mechanisms for members of the flavodoxin fold. CheY, Spo0F, and NtrC have unrelated functions and low sequence homology but share an identical topology. Recent coarse-grained simulations show that their folding landscapes are uniquely tuned to properly suit their respective biological functions. Enhanced packing in Spo0F and its limited conformational dynamics compared to CheY or NtrC lead to frustration in its folding landscape. Simulation as well as experimental results correlate with the local density of native contacts for these and a sample of other proteins. In particular, protein regions of low contact density are observed to become structured late in folding; concomitantly, these dynamic regions are often involved in binding or conformational rearrangements of functional importance. These observations help to explain the widespread success of Gomacr;-like coarse-grained models in reproducing protein dynamics.     

Energy landscape and dynamics of the beta-hairpin G peptide and its isomers: Topology and sequences

We have investigated free energy landscape [MM/PBSA + normal modes entropy] of permutations in the G peptide (41-56) from the protein G B1 domain by studying six isomers corresponding to moving the hydrophobic cluster along the beta-strands (toward the turn: T1, AGEWTYDDKTFTVTET; T2, GEDTWDYATFTVTKTE; T3, GEDDWTYATFTVTKTE; toward the end: E1, WTYDDAGETKTFTVT; E2, WEYTGDDATKTETFTV; E3, WTYEGDDATKTETFTV). The free energy terms include molecular mechanics energy, Poisson-Boltzmann electrostatic solvation energy, surface area solvation energy, and conformational entropy estimated by using normal mode analysis. From the wild type to T1, then T3, and finally T2, we see a progressively changing energy landscape, toward a less stable beta-hairpin structure. Moving the hydrophobic cluster outside toward the end region causes a greater change in the energy landscape. alpha-Helical instead of a beta-hairpin structure was the most stable form for the E2 isomer. However, no matter how much the sequence changes, for all variants studied, ideal "native" beta-hairpin topologies remain as minima (regardless of whether global or local) in the energy landscape. In general, we find that the energy landscape is dependent on the hydrophobic cluster topology and on the sequence. Our present study indicates that the key is the relative conformational energies of the different conformations. Changes in the sequence strongly modulate the relative stabilities of topologically similar regions in the energy landscape, rather than redefine the topology space. This finding is consistent with a population redistribution in the process of protein folding. The limited variation of topological space, compared with the number of possible sequence changes, may relate to the observation that the number of known protein folds are far less than the sequential allowance.     

Context-dependence of T-loop Mediated Long-range RNA Tertiary Interactions

The architecture and folding of complex RNAs is governed by a limited set of highly recurrent structural motifs that form long-range tertiary interactions. One of these motifs is the T-loop, which was first identified in tRNA but is broadly distributed across biological RNAs. While the T-loop has been examined in detail in different biological contexts, the various receptors that it interacts with are not as well defined. In this study, we use a cell-based genetic screen in concert with bioinformatic analysis to examine three different, but related, T-loop receptor motifs found in the flavin mononucleotide (FMN) and cobalamin (Cbl) riboswitches. As a host for different T-loop receptors, we employed the env8 class-II Cbl riboswitch, an RNA that uses two T-loop motifs for both folding and supporting the ligand binding pocket. A set of libraries was created in which select nucleotides that participate in the T-loop/T-loop receptor (TL/TLR) interaction were fully randomized. Library members were screened for their ability to support Cbl-dependent expression of a reporter gene. While T-loops appear to be variable in sequence, we find that the functional sequence space is more restricted in the Cbl riboswitch, suggesting that TL/TLR interactions are context dependent. Our data reveal clear sequence signatures for the different types of receptor motifs that align with phylogenic analysis of these motifs in the FMN and Cbl riboswitches. Finally, our data suggest the functional contribution of various nucleobase-mediated long-range interactions within the riboswitch subclass of TL/TLR interactions that are distinct from those found in other RNAs.     

A Structural Basis for the Recognition of 2′-Deoxyguanosine by the Purine Riboswitch

Riboswitches are noncoding RNA elements that are commonly found in the 5′-untranslated region of bacterial mRNA. Binding of a small-molecule metabolite to the riboswitch aptamer domain guides the folding of the downstream sequence into one of two mutually exclusive secondary structures that directs gene expression. The purine riboswitch family, which regulates aspects of purine biosynthesis and transport, contains three distinct classes that specifically recognize guanine/hypoxanthine, adenine, or 2′-deoxyguanosine (dG). Structural analysis of the guanine and adenine classes revealed a binding pocket that almost completely buries the nucleobase within the core of the folded RNA. Thus, it is somewhat surprising that this family of RNA elements also recognizes dG. We have used a combination of structural and biochemical techniques to understand how the guanine riboswitch could be converted into a dG binder and the structural basis for dG recognition. These studies reveal that a limited number of sequence changes to a guanine-sensing RNA are required to cause a specificity switch from guanine to 2′-deoxyguanosine, and to impart an altered structure for accommodating the additional deoxyribose sugar moiety.     

The Topology of the Energy Landscapes of Macromolecules in the Torsion Angle Space and the Principle of the Minimum Energy Dissipation Rate in Conformational Relaxation

This article discusses some basic problems of structural biology and molecular dynamics simulation methods that need to be taken into account when considering, the protein folding problem, and prediction of 3D-structures for biopolymers. A multidimensional Fourier series expansions were formulated for the energy landscapes of the systems with conformational mobility, These energy landscape representations are correct from the viewpoint of the topology of the macromolecule configuration spaces. The problem of the single global minimum on the energy landscape for proteins is discussed and is formulated in tems of phase rules for the component of Fourier expansions. This rule is formally similar to the problem of diffraction on a multidimensional cubic lattice. The calibration of biopolymer force fields and their correspondence to topologically correct energy landscapes are discussed. Equations of motion were obtained in a matrix form for the relaxation of a representative point position on a multidimensional potential energy surface. The solutions of the equations for conformational relaxation were shown to obey the principle of the minimum energy dissipation rate at a given relaxation rate of potential energy (or folding rate).     

Effects of Topology and Sequence in Protein Folding Linked via Conformational Fluctuations

Experiments have compared the folding of proteins with different amino acid sequences but the same basic structure, or fold. Results indicate that folding is robust to sequence variations for proteins with some nonlocal folds, such as all-β, whereas the folding of more local, all-α proteins typically exhibits a stronger sequence dependence. Here, we use a coarse-grained model to systematically study how variations in sequence perturb the folding energy landscapes of three model sequences with 3α, 4β + α, and β-barrel folds, respectively. These three proteins exhibit folding features in line with experiments, including expected rank order in the cooperativity of the folding transition and stability-dependent shifts in the location of the free-energy barrier to folding. Using a generalized-ensemble simulation approach, we determine the thermodynamics of around 2000 sequence variants representing all possible hydrophobic or polar single- and double-point mutations. From an analysis of the subset of stability-neutral mutations, we find that folding is perturbed in a topology-dependent manner, with the β-barrel protein being the most robust. Our analysis shows, in particular, that the magnitude of mutational perturbations of the transition state is controlled in part by the size or “width” of the underlying conformational ensemble. This result suggests that the mutational robustness of the folding of the β-barrel protein is underpinned by its conformationally restricted transition state ensemble, revealing a link between sequence and topological effects in protein folding.