Using a predictive coarse-grained protein force field, we compute and compare the free energy landscapes and relative stabilities of amyloid-β protein (1–42) and amyloid-β protein (1–40) in their monomeric and oligomeric forms up to the octamer. At the same concentration, the aggregation free energy profile of Aβ42 is more downhill, with a computed solubility that is about 10 times smaller than that of Aβ40. At a concentration of 40 μM, the clear free energy barrier between the pre-fibrillar tetramer form and the fibrillar pentamer in the Aβ40 aggregation landscape disappears for Aβ42, suggesting that the Aβ42 tetramer has a more diverse structural range. To further compare the landscapes, we develop a cluster analysis based on the structural similarity between configurations and use it to construct an oligomerization map that captures the paths of easy interconversion between different but structurally similar states of oligomers for both species. A taxonomy of the oligomer species based on β-sheet stacking topologies is proposed. The comparison of the two oligomerization maps highlights several key differences in the landscapes that can be attributed to the two additional C-terminal residues that Aβ40 lacks. In general, the two terminal residues strongly stabilize the oligomeric structures for Aβ42 relative to Aβ40, and greatly facilitate the conversion from pre-fibrillar trimers to fibrillar tetramers.

Energy landscape theory, developed in the context of protein folding, provides, to our knowledge, a new perspective on chromosome architecture. We review what has been learned concerning the topology and structure of both the interphase and mitotic chromosomes from effective energy landscapes constructed using Hi-C data. Energy landscape thinking raises new questions about the nonequilibrium dynamics of the chromosome and gene regulation.

•Conventional fusion experiments start with a very high entropy state.•Molecules provide lower entropy and more initial confinement.•As shown by wavepacket simulations, a coherent control field can enhance collision of nuclei in a field-bound molecule.Quantum-controlled motion of nuclei, starting from the nanometer-size ground state of a molecule, can potentially overcome some of the difficulties of thermonuclear fusion by compression of a fuel pellet or in a bulk plasma. Coherent laser control can manipulate nuclear motion precisely, achieving large phase space densities for the colliding nuclei. We combine quantum wavepacket propagation of D and T nuclei in a field-bound molecule with coherent control by a shaped laser pulse to demonstrate enhancement of nuclear collision rates. Atom-smashers powered by coherent control may become laboratory sources of particle bursts, and even assist muonic fusion.Download high-res image (64KB)Download full-size image

The heterogeneous elastoplastic deformation of structural glasses is explored using the framework of the random first-order transition theory of the glass transition along with an extended mode-coupling theory that includes activated events. The theory involves coupling the continuum elastic theory of strain transport with mobility generation and transport as described in the theory of glass aging and rejuvenation. Fluctuations that arise from the generation and transport of mobility, fictive temperature, and stress are treated explicitly. We examine the nonlinear flow of a glass under deformation at finite strain rate. The interplay among the fluctuating fields leads to the spatially heterogeneous dislocation of the particles in the glass, i.e., the appearance of shear bands of the type observed in metallic glasses deforming under mechanical stress.

Fis protein is a nucleoid-associated protein that plays many roles in transcriptional regulation and DNA site-specific recombination. In contrast to the naïve expectation based on stoichiometry, recent single-molecule studies have shown that the dissociation of Fis protein from DNA is accelerated by increasing the concentration of the Fis protein. Because the detailed molecular mechanism of facilitated dissociation is still not clear, in this study, we employ computational methods to explore the binding landscapes of Fis:DNA complexes with various stoichiometries. When two Fis molecules are present, simulations uncover a ternary complex, where the originally bound Fis protein is partially dissociated from DNA. The simulations support a three-state sequential kinetic model (N ⇄ I → D) for facilitated dissociation, thus explaining the concentration-dependent dissociation.

The nucleosome is the fundamental unit for packaging the genome. A detailed molecular picture for its conformational dynamics is crucial for understanding transcription and gene regulation. We investigate the disassembly of single nucleosomes using a predictive coarse-grained protein DNA model with transferable force fields. This model quantitatively describes the thermodynamic stability of both the histone core complex and the nucleosome and predicts rates of transient nucleosome opening that match experimental measurements. Quantitative characterization of the free-energy landscapes reveals the mechanism of nucleosome unfolding in which DNA unwinding and histone protein disassembly are coupled. The interfaces between H2A-H2B dimers and the (H3-H4)2 tetramer are first lost when the nucleosome opens releasing a large fraction but not all of its bound DNA. For the short strands studied in single molecule experiments, the DNA unwinds asymmetrically from the histone proteins, with only one of its two ends preferentially exposed. The detailed molecular mechanism revealed in this work provides a structural basis for interpreting experimental studies of nucleosome unfolding.

A predictive coarse-grained protein force field [associative memory, water-mediated, structure, and energy model for molecular dynamics (AWSEM)-MD] is used to study the energy landscapes and relative stabilities of amyloid-β protein (1–40) in the monomer and all of its oligomeric forms up to an octamer. We find that an isolated monomer is mainly disordered with a short α-helix formed at the central hydrophobic core region (L17-D23). A less stable hairpin structure, however, becomes increasingly more stable in oligomers, where hydrogen bonds can form between neighboring monomers. We explore the structure and stability of both prefibrillar oligomers that consist of mainly antiparallel β-sheets and fibrillar oligomers with only parallel β-sheets. Prefibrillar oligomers are polymorphic but typically take on a cylindrin-like shape composed of mostly antiparallel β-strands. At the concentration of the simulation, the aggregation free energy landscape is nearly downhill. We use umbrella sampling along a structural progress coordinate for interconversion between prefibrillar and fibrillar forms to identify a conversion pathway between these forms. The fibrillar oligomer only becomes favored over its prefibrillar counterpart in the pentamer where an interconversion bottleneck appears. The structural characterization of the pathway along with statistical mechanical perturbation theory allow us to evaluate the effects of concentration on the free energy landscape of aggregation as well as the effects of the Dutch and Arctic mutations associated with early onset of Alzheimer’s disease.

We recently proposed a model for IκBα-mediated molecular stripping of NFκB from transcription sites. IκBα was shown experimentally to form a transient ternary complex with DNA-bound NFκB, but the mechanism by which the IκBα accelerates dissociation of the NFκB from the DNA was unknown. In this paper we construct and compute free energy profiles for the wild-type IκBα-mediated molecular stripping reaction of NFκB from DNA and compare with that for a mutant of IκBα bearing a charge-neutralized PEST. The differences in the free energy profile for stripping originate from the frustrated electrostatic interactions between the negatively charged PEST and the DNA. The PEST occupies two different conformations in the NFκB–IκBα binary complex, one of which occupies the DNA-binding cavity. Specific interactions with positively charged residues in the N-terminal domains of both p50 and p65 apparently draw the domains closer together hindering reassociation of DNA. Comparison with the charge-neutralized mutant reveals that all of these functional consequences result from the negative charges in the PEST sequence of IκBα.

The associative memory, water mediated, structure and energy model (AWSEM) is a coarse-grained force field with transferable tertiary interactions that incorporates local in sequence energetic biases using bioinformatically derived structural information about peptide fragments with locally similar sequences that we call memories. The memory information from the protein data bank (PDB) database guides proper protein folding. The structural information about available sequences in the database varies in quality and can sometimes lead to frustrated free energy landscapes locally. One way out of this difficulty is to construct the input fragment memory information from all-atom simulations of portions of the complete polypeptide chain. In this paper, we investigate this approach first put forward by Kwac and Wolynes in a more complete way by studying the structure prediction capabilities of this approach for six α-helical proteins. This scheme which we call the atomistic associative memory, water mediated, structure and energy model (AAWSEM) amounts to an ab initio protein structure prediction method that starts from the ground up without using bioinformatic input. The free energy profiles from AAWSEM show that atomistic fragment memories are sufficient to guide the correct folding when tertiary forces are included. AAWSEM combines the efficiency of coarse-grained simulations on the full protein level with the local structural accuracy achievable from all-atom simulations of only parts of a large protein. The results suggest that a hybrid use of atomistic fragment memory and database memory in structural predictions may well be optimal for many practical applications.

Aplysia cytoplasmic polyadenylation element binding (CPEB) protein, a translational regulator that recruits mRNAs and facilitates translation, has been shown to be a key component in the formation of long-term memory. Experimental data show that CPEB exists in at least a low-molecular weight coiled-coil oligomeric form and an amyloid fiber form involving the Q-rich domain (CPEB-Q). Using a coarse-grained energy landscape model, we predict the structures of the low-molecular weight oligomeric form and the dynamics of their transitions to the β-form. Up to the decamer, the oligomeric structures are predicted to be coiled coils. Free energy profiles confirm that the coiled coil is the most stable form for dimers and trimers. The structural transition from α to β is shown to be concentration dependent, with the transition barrier decreasing with increased concentration. We observe that a mechanical pulling force can facilitate the α-helix to β-sheet (α-to-β) transition by lowering the free energy barrier between the two forms. Interactome analysis of the CPEB protein suggests that its interactions with the cytoskeleton could provide the necessary mechanical force. We propose that, by exerting mechanical forces on CPEB oligomers, an active cytoskeleton can facilitate fiber formation. This mechanical catalysis makes possible a positive feedback loop that would help localize the formation of CPEB fibers to active synapse areas and mark those synapses for forming a long-term memory after the prion form is established. The functional role of the CPEB helical oligomers in this mechanism carries with it implications for targeting such species in neurodegenerative diseases.

Genetic switches based on the NF-κB/IκB/DNANF-κB/IκB/DNA system are master regulators of an array of cellular responses. Recent kinetic experiments have shown that IκBIκB can actively remove NF-κB bound to its genetic sites via a process called “molecular stripping.” This allows the NF-κB/IκB/DNANF-κB/IκB/DNA switch to function under kinetic control rather than the thermodynamic control contemplated in the traditional models of gene switches. Using molecular dynamics simulations of coarse-grained predictive energy landscape models for the constituent proteins by themselves and interacting with the DNA we explore the functional motions of the transcription factor NF-κBNF-κB and its various binary and ternary complexes with DNA and the inhibitor IκB. These studies show that the function of the NF-κB/IκB/DNANF-κB/IκB/DNA genetic switch is realized via an allosteric mechanism. Molecular stripping occurs through the activation of a domain twist mode by the binding of IκBIκB that occurs through conformational selection. Free energy calculations for DNA binding show that the binding of IκBIκB not only results in a significant decrease of the affinity of the transcription factor for the DNA but also kinetically speeds DNA release. Projections of the free energy onto various reaction coordinates reveal the structural details of the stripping pathways.

In vivo, the human genome folds into a characteristic ensemble of 3D structures. The mechanism driving the folding process remains unknown. We report a theoretical model for chromatin (Minimal Chromatin Model) that explains the folding of interphase chromosomes and generates chromosome conformations consistent with experimental data. The energy landscape of the model was derived by using the maximum entropy principle and relies on two experimentally derived inputs: a classification of loci into chromatin types and a catalog of the positions of chromatin loops. First, we trained our energy function using the Hi-C contact map of chromosome 10 from human GM12878 lymphoblastoid cells. Then, we used the model to perform molecular dynamics simulations producing an ensemble of 3D structures for all GM12878 autosomes. Finally, we used these 3D structures to generate contact maps. We found that simulated contact maps closely agree with experimental results for all GM12878 autosomes. The ensemble of structures resulting from these simulations exhibited unknotted chromosomes, phase separation of chromatin types, and a tendency for open chromatin to lie at the periphery of chromosome territories.

We investigate the folding of GlpG, an intramembrane protease, using perfectly funneled structure-based models that implicitly account for the absence or presence of the membrane. These two models are used to describe, respectively, folding in detergent micelles and folding within a bilayer, which effectively constrains GlpG's topology in unfolded and partially folded states. Structural free-energy landscape analysis shows that although the presence of multiple folding pathways is an intrinsic property of GlpG’s modular functional architecture, the large entropic cost of organizing helical bundles in the absence of the constraining bilayer leads to pathways that backtrack (i.e., local unfolding of previously folded substructures is required when moving from the unfolded to the folded state along the minimum free-energy pathway). This backtracking explains the experimental observation of thermodynamically destabilizing mutations that accelerate GlpG’s folding in detergent micelles. In contrast, backtracking is absent from the model when folding is constrained within a bilayer, the environment in which GlpG has evolved to fold. We also characterize a near-native state with a highly mobile transmembrane helix 5 (TM5) that is significantly populated under folding conditions when GlpG is embedded in a bilayer. Unbinding of TM5 from the rest of the structure exposes GlpG’s active site, consistent with studies of the catalytic mechanism of GlpG that suggest that TM5 serves as a substrate gate to the active site.

Chromosome conformation capture experiments provide a rich set of data concerning the spatial organization of the genome. We use these data along with a maximum entropy approach to derive a least-biased effective energy landscape for the chromosome. Simulations of the ensemble of chromosome conformations based on the resulting information theoretic landscape not only accurately reproduce experimental contact probabilities, but also provide a picture of chromosome dynamics and topology. The topology of the simulated chromosomes is probed by computing the distribution of their knot invariants. The simulated chromosome structures are largely free of knots. Topologically associating domains are shown to be crucial for establishing these knotless structures. The simulated chromosome conformations exhibit a tendency to form fibril-like structures like those observed via light microscopy. The topologically associating domains of the interphase chromosome exhibit multistability with varying liquid crystalline ordering that may allow discrete unfolding events and the landscape is locally funneled toward “ideal” chromosome structures that represent hierarchical fibrils of fibrils.

Chromosome conformation capture experiments provide a rich set of data concerning the spatial organization of the genome. We use these data along with a maximum entropy approach to derive a least-biased effective energy landscape for the chromosome. Simulations of the ensemble of chromosome conformations based on the resulting information theoretic landscape not only accurately reproduce experimental contact probabilities, but also provide a picture of chromosome dynamics and topology. The topology of the simulated chromosomes is probed by computing the distribution of their knot invariants. The simulated chromosome structures are largely free of knots. Topologically associating domains are shown to be crucial for establishing these knotless structures. The simulated chromosome conformations exhibit a tendency to form fibril-like structures like those observed via light microscopy. The topologically associating domains of the interphase chromosome exhibit multistability with varying liquid crystalline ordering that may allow discrete unfolding events and the landscape is locally funneled toward “ideal” chromosome structures that represent hierarchical fibrils of fibrils.

The temperature–pressure behavior of two proteins, ubiquitin and λ-repressor, is explored using a realistically coarse-grained physicochemical model, the associative memory, water mediated, structure and energy model (AWSEM). The phase diagram across the temperature–pressure plane is obtained by perturbing the water mediated interactions in the Hamiltonian systematically. The phase diagrams calculated with direct simulations along with an extended bridge sampling estimator show the main features found experimentally, including both cold- and pressure-denaturation. The denatured ensembles in different parts of the phase diagram are characterized and found to be structurally distinct. The protein energy landscape is found to be funneled throughout the phase diagram, but modest changes in the entropy and free energy of the water are found to drive both cold and pressure induced denaturation.

We compare dynamical heterogeneities in equilibrated supercooled liquids and in the nonequilibrium glassy state within the framework of the random first order transition theory. Fluctuating mobility generation and transport in the glass are treated by numerically solving stochastic continuum equations for mobility and fictive temperature fields that arise from an extended mode coupling theory containing activated events. Fluctuating spatiotemporal structures in aging and rejuvenating glasses lead to dynamical heterogeneity in glasses with characteristics distinct from those found in the equilibrium supercooled liquid. The non-Gaussian distribution of activation free energies, the stretching exponent β, and the growth of characteristic lengths are studied along with the four-point dynamical correlation function. Asymmetric thermodynamic responses upon heating and cooling are predicted to be the result of the heterogeneity and the out-of-equilibrium behavior of glasses below Tg. Our numerical results agree with experimental calorimetry. We numerically confirm the prediction of Lubchenko and Wolynes in the glass that the dynamical heterogeneity can lead to noticeably bimodal distributions of local fictive temperatures during some histories of preparation which explains in a unified way recent experimental observations that have been interpreted as coming from there being two distinct equilibration mechanisms in glasses.

The energy landscape used by nature over evolutionary timescales to select protein sequences is essentially the same as the one that folds these sequences into functioning proteins, sometimes in microseconds. We show that genomic data, physical coarse-grained free energy functions, and family-specific information theoretic models can be combined to give consistent estimates of energy landscape characteristics of natural proteins. One such characteristic is the effective temperature Tsel at which these foldable sequences have been selected in sequence space by evolution. Tsel quantifies the importance of folded-state energetics and structural specificity for molecular evolution. Across all protein families studied, our estimates for Tsel are well below the experimental folding temperatures, indicating that the energy landscapes of natural foldable proteins are strongly funneled toward the native state.

We explore the hypothesis that the folding landscapes of membrane proteins are funneled once the proteins’ topology within the membrane is established. We extend a protein folding model, the associative memory, water-mediated, structure, and energy model (AWSEM) by adding an implicit membrane potential and reoptimizing the force field to account for the differing nature of the interactions that stabilize proteins within lipid membranes, yielding a model that we call AWSEM-membrane. Once the protein topology is set in the membrane, hydrophobic attractions play a lesser role in finding the native structure, whereas polar–polar attractions are more important than for globular proteins. We examine both the quality of predictions made with AWSEM-membrane when accurate knowledge of the topology and secondary structure is available and the quality of predictions made without such knowledge, instead using bioinformatically inferred topology and secondary structure based on sequence alone. When no major errors are made by the bioinformatic methods used to assign the topology of the transmembrane helices, these two types of structure predictions yield roughly equivalent quality structures. Although the predictive energy landscape is transferable and not structure based, within the correct topological sector we find the landscape is indeed very funneled: Thermodynamic landscape analysis indicates that both the total potential energy and the contact energy decrease as native contacts are formed. Nevertheless the near symmetry of different helical packings with respect to native contact formation can result in multiple packings with nearly equal thermodynamic occupancy, especially at temperatures just below collapse.

Stem cell differentiation has been viewed as coming from transitions between attractors on an epigenetic landscape that governs the dynamics of a regulatory network involving many genes. Rigorous definition of such a landscape is made possible by the realization that gene regulation is stochastic, owing to the small copy number of the transcription factors that regulate gene expression and because of the single-molecule nature of the gene itself. We develop an approximation that allows the quantitative construction of the epigenetic landscape for large realistic model networks. Applying this approach to the network for embryonic stem cell development explains many experimental observations, including the heterogeneous distribution of the transcription factor Nanog and its role in safeguarding the stem cell pluripotency, which can be understood by finding stable steady-state attractors and the most probable transition paths between those attractors. We also demonstrate that the switching rate between attractors can be significantly influenced by the gene expression noise arising from the fluctuations of DNA occupancy when binding to a specific DNA site is slow.

The digital nature of genes combined with the associated low copy numbers of proteins regulating them is a significant source of stochasticity, which affects the phase of biochemical oscillations. We show that unlike ordinary chemical oscillators, the dichotomic molecular noise of gene state switching in gene oscillators affects the stochastic dephasing in a way that may not always be captured by phenomenological limit cycle-based models. Through simulations of a realistic model of the NFκB/IκB network, we also illustrate the dephasing phenomena that are important for reconciling single-cell and population-based experiments on gene oscillators.

Experiments on artificial multidomain protein constructs have probed the early stages of aggregation processes, but structural details of the species that initiate aggregation remain elusive. Using the associative-memory, water-mediated, structure and energy model known as AWSEM, a transferable coarse-grained protein model, we performed simulations of fused constructs composed of up to four copies of the Titin I27 domain or its mutant I27* (I59E). Free energy calculations enable us to quantify the conditions under which such multidomain constructs will spontaneously misfold. Consistent with experimental results, the dimer of I27 is found to be the smallest spontaneously misfolding construct. Our results show how structurally distinct misfolded states can be stabilized under different thermodynamic conditions, and this result provides a plausible link between the single-molecule misfolding experiments under native conditions and aggregation experiments under denaturing conditions. The conditions for spontaneous misfolding are determined by the interplay among temperature, effective local protein concentration, and the strength of the interdomain interactions. Above the folding temperature, fusing additional domains to the monomer destabilizes the native state, and the entropically stabilized amyloid-like state is favored. Because it is primarily energetically stabilized, the domain-swapped state is more likely to be important under native conditions. Both protofibril-like and branching structures are found in annealing simulations starting from extended structures, and these structures suggest a possible connection between the existence of multiple amyloidogenic segments in each domain and the formation of branched, amorphous aggregates as opposed to linear fibrillar structures.

Frustration from strong interdomain interactions can make misfolding a more severe problem in multidomain proteins than in single-domain proteins. On the basis of bioinformatic surveys, it has been suggested that lowering the sequence identity between neighboring domains is one of nature’s solutions to the multidomain misfolding problem. We investigate folding of multidomain proteins using the associative-memory, water-mediated, structure and energy model (AWSEM), a predictive coarse-grained protein force field. We find that reducing sequence identity not only decreases the formation of domain-swapped contacts but also decreases the formation of strong self-recognition contacts between β-strands with high hydrophobic content. The ensembles of misfolded structures that result from forming these amyloid-like interactions are energetically disfavored compared with the native state, but entropically favored. Therefore, these ensembles are more stable than the native ensemble under denaturing conditions, such as high temperature. Domain-swapped contacts compete with self-recognition contacts in forming various trapped states, and point mutations can shift the balance between the two types of interaction. We predict that multidomain proteins that lack these specific strong interdomain interactions should fold reliably.

The remarkable strength of glasses is examined using the random first order transition theory of the glass transition. The theory predicts that strength depends on elastic modulus but also on the configurational energy frozen in when the glass is prepared. The stress catalysis of cooperative rearrangements of the type responsible for the supercooled liquid’s high viscosity account quantitatively for the measured strength of a range of metallic glasses, silica, and a polymer glass.

The associative memory, water mediated, structure and energy model (AWSEM) is a coarse-grained protein force field. AWSEM contains physically motivated terms, such as hydrogen bonding, as well as a bioinformatically based local structure biasing term, which efficiently takes into account many-body effects that are modulated by the local sequence. When combined with appropriate local or global alignments to choose memories, AWSEM can be used to perform de novo protein structure prediction. Herein we present structure prediction results for a particular choice of local sequence alignment method based on short residue sequences called fragments. We demonstrate the model’s structure prediction capabilities for three levels of global homology between the target sequence and those proteins used for local structure biasing, all of which assume that the structure of the target sequence is not known. When there are no homologues in the database of structures used for local structure biasing, AWSEM calculations produce structural predictions that are somewhat improved compared with prior works using related approaches. The inclusion of a small number of structures from homologous sequences improves structure prediction only marginally, but when the fragment search is restricted to only homologous sequences, AWSEM can perform high resolution structure prediction and can be used for kinetics and dynamics studies.

Contractile forces are essential for many developmental processes involving cell shape change and tissue deformation. Recent experiments on reconstituted actomyosin networks, the major component of the contractile machinery, have shown that active contractility occurs above a threshold motor concentration and within a window of cross-link concentration. We present a microscopic dynamic model that incorporates two essential aspects of actomyosin self-organization: the asymmetric load response of individual actin filaments and the correlated motor-driven events mimicking myosin-induced filament sliding. Using computer simulations, we examine how the concentration and susceptibility of motors contribute to their collective behavior and interplay with the network connectivity to regulate macroscopic contractility. Our model is shown to capture the formation and dynamics of contractile structures and agree with the observed dependence of active contractility on microscopic parameters, including the contractility onset. Cooperative action of load-resisting motors in a force-percolating structure integrates local contraction/buckling events into a global contractile state via an active coarsening process, in contrast to the flow transition driven by uncorrelated kicks of susceptible motors.

Contractile forces are essential for many developmental processes involving cell shape change and tissue deformation. Recent experiments on reconstituted actomyosin networks, the major component of the contractile machinery, have shown that active contractility occurs above a threshold motor concentration and within a window of cross-link concentration. We present a microscopic dynamic model that incorporates two essential aspects of actomyosin self-organization: the asymmetric load response of individual actin filaments and the correlated motor-driven events mimicking myosin-induced filament sliding. Using computer simulations, we examine how the concentration and susceptibility of motors contribute to their collective behavior and interplay with the network connectivity to regulate macroscopic contractility. Our model is shown to capture the formation and dynamics of contractile structures and agree with the observed dependence of active contractility on microscopic parameters, including the contractility onset. Cooperative action of load-resisting motors in a force-percolating structure integrates local contraction/buckling events into a global contractile state via an active coarsening process, in contrast to the flow transition driven by uncorrelated kicks of susceptible motors.

We investigate protein–protein association using the associative-memory, water-mediated, structure, and energy model (AWSEM), a coarse-grained protein folding model that has been optimized using energy-landscape theory. The potential was originally parameterized by enforcing a funneled nature for a database of dimeric interfaces but was later further optimized to create funneled folding landscapes for individual monomeric proteins. The ability of the model to predict interfaces was not tested previously. The present results show that simulated annealing of the model indeed is able to predict successfully the native interfaces of eight homodimers and four heterodimers, thus amounting to a flexible docking algorithm. We go on to address the relative importance of monomer geometry, flexibility, and nonnative intermonomeric contacts in the association process for the homodimers. Monomer surface geometry is found to be important in determining the binding interface, but it is insufficient. Using a uniform binding potential rather than the water-mediated potential results in sampling of misbound structures that are geometrically preferred but are nonetheless energetically disfavored by AWSEM, as well as in nature. Depending on the stability of the unbound monomers, nonnative contacts play different roles in the association process. For unstable monomers, thermodynamic states stabilized by nonnative interactions correspond to productive, on-pathway intermediates and can, therefore, catalyze binding through a fly-casting mechanism. For stable monomers, in contrast, states stabilized by nonnative interactions generally correspond to traps that impede binding.

Simulations based on perfectly funneled energy landscapes often capture many of the kinetic features of protein folding. We examined whether simulations based on funneled energy functions can also describe fluctuations in native-state protein ensembles. We quantitatively compared the site-specific local stability determined from structure-based folding simulations, with hydrogen exchange protection factors measured experimentally for ubiquitin, chymotrypsin inhibitor 2, and staphylococcal nuclease. Different structural definitions for the open and closed states based on the number of native contacts for each residue, as well as the hydrogen-bonding state, or a combination of both criteria were evaluated. The predicted exchange patterns agree with the experiments under native conditions, indicating that protein topology indeed has a dominant effect on the exchange kinetics. Insights into the simplest mechanistic interpretation of the amide exchange process were thus obtained.

•Funneled landscapes explain the paradoxes of robust protein folding.•Energy landscape theory leads to structure prediction tools.•Comparing evolution data with landscapes quantifies the frustration of 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.

•We map the unfolding of PR65/A, the HEAT-repeat scaffold subunit of phosphatase PP2A•We reveal a network of intermediate states, formed sequentially and in parallel•Weakly folded central repeats are flanked on both sides by high-stability repeats•PR65/A unfolding has implications for both PP2A assembly and catalytic mechanismHere, we reveal a remarkable complexity in the unfolding of giant HEAT-repeat protein PR65/A, a molecular adaptor for the heterotrimeric PP2A phosphatases. The repeat array ruptures at multiple sites, leading to intermediate states with noncontiguous folded subdomains. There is a dominant sequence of unfolding, which reflects a nonuniform stability distribution across the repeat array and can be rationalized by theoretical models accounting for heterogeneous contact density in the folded structure. Unfolding of certain intermediates is, however, competitive, leading to parallel unfolding pathways. The low-stability, central repeats sample unfolded conformations under physiological conditions, suggesting how folding directs function: certain regions present rigid motifs for molecular recognition, whereas others have the flexibility with which to broaden the search area, as in the fly-casting mechanism. Partial unfolding of PR65/A also impacts catalysis by altering the proximity of bound catalytic subunit and substrate. Thus, the repeat array orchestrates the assembly and activity of PP2A.