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.     

Cooperativity,smooth energy landscapes and the origins of topology-dependent protein folding rates

The relative folding rates of simple, single-domain proteins, proteins whose folding energy landscapes are smooth, are highly dispersed and strongly correlated with native-state topology. In contrast, the relative folding rates of small, Gō-potential lattice polymers, which also exhibit smooth energy landscapes, are poorly dispersed and insignificantly correlated with native-state topology. Here, we investigate this discrepancy in light of a recent, quantitative theory of two-state folding kinetics, the topomer search model. This model stipulates that the topology-dependence of two-state folding rates is a direct consequence of the extraordinarily cooperative equilibrium folding of simple proteins. We demonstrate that traditional Gō polymers lack the extreme cooperativity that characterizes the folding of naturally occurring, two-state proteins and confirm that the folding rates of a diverse set of Gō 27-mers are poorly dispersed and effectively uncorrelated with native state topology. Upon modestly increasing the cooperativity of the Gō-potential, however, significantly increased dispersion and strongly topology-dependent kinetics are observed. These results support previous arguments that the cooperative folding of simple, single-domain proteins gives rise to their topology-dependent folding rates. We speculate that this cooperativity, and thus, indirectly, the topology-rate relationship, may have arisen in order to generate the smooth energetic landscapes upon which rapid folding can occur.     

Exploring folding free energy landscapes using computational protein design

Recent advances in computational protein design have allowed exciting new insights into the sequence dependence of protein folding free energy landscapes. Whereas most previous studies have examined the sequence dependence of protein stability and folding kinetics by characterizing naturally occurring proteins and variants of these proteins that contain a small number of mutations, it is now possible to generate and characterize computationally designed proteins that differ significantly from naturally occurring proteins in sequence and/or structure. These computer-generated proteins provide insights into the determinants of protein structure, stability and folding, and make it possible to disentangle the properties of proteins that are the consequence of natural selection from those that reflect the fundamental physical chemistry of polypeptide chains.     

Designing cooperativity into the designed protein Top7

The topology of the designed protein Top7 is not found in natural proteins. Top7 shows signatures of non‐cooperative folding in both experimental studies and computer simulations. In particular, molecular dynamics of coarse‐grained structure‐based models of Top7 show a well‐populated C‐terminal folding‐intermediate. Since most similarly sized globular proteins are cooperative folders, the non‐natural topology of Top7 has been suggested as a reason for its non‐cooperative folding. Here, we computationally examine the folding of Top7 with the intent of making it cooperative. We find that its folding cooperativity can be increased in two ways: (a) Optimization of packing interactions in the N‐terminal half of the protein enables further folding of the C‐terminal intermediate. (b) Reduction in the packing density of the C‐terminal region destabilizes the intermediate. In practice, these strategies are implemented in our Top7 model through modifications to the contact‐map. These modifications do not alter the topology of Top7 but result in cooperative folding. Amino‐acid mutations that mimic these modifications also lead to a significant increase in folding cooperativity. Finally, we devise a method to randomize the sizes of amino‐acids within the same topology, and confirm that the structure of Top7 makes its folding sensitive to packing interactions. In contrast, the ribosomal protein S6, which has secondary structure similar to Top7, has folding which is much less sensitive to packing perturbations. Thus, it should be possible to make a sequence fold cooperatively to the structure of Top7, but to do so its side‐chain packing needs to be carefully designed. Proteins 2014; 82:364–374. © 2013 Wiley Periodicals, Inc.     

Cooperativity and the origins of rapid, single-exponential kinetics in protein folding

The folding of naturally occurring, single-domain proteins is usually well described as a simple, single-exponential process lacking significant trapped states. Here we further explore the hypothesis that the smooth energy landscape this implies, and the rapid kinetics it engenders, arises due to the extraordinary thermodynamic cooperativity of protein folding. Studying Miyazawa-Jernigan lattice polymers, we find that, even under conditions where the folding energy landscape is relatively optimized (designed sequences folding at their temperature of maximum folding rate), the folding of protein-like heteropolymers is accelerated when their thermodynamic cooperativity is enhanced by enhancing the nonadditivity of their energy potentials. At lower temperatures, where kinetic traps presumably play a more significant role in defining folding rates, we observe still greater cooperativity-induced acceleration. Consistent with these observations, we find that the folding kinetics of our computational models more closely approximates single-exponential behavior as their cooperativity approaches optimal levels. These observations suggest that the rapid folding of naturally occurring proteins is, in part, a consequence of their remarkably cooperative folding.     

Native Topology of the Designed Protein Top7 is Not Conducive to Cooperative Folding

Many single-domain proteins with <100 residues fold cooperatively; but the recently designed 92-residue Top7 protein exhibits clearly non-two-state behaviors. In apparent agreement with experiment, we found that coarse-grained, native-centric chain models, including potentials with and without elementary desolvation barriers, predicted that Top7 has a stable intermediate state in which the C-terminal fragment is folded while the rest of the chain remains disordered. We observed noncooperative folding in Top7 models that incorporated nonnative hydrophobic interactions as well. In contrast, free energy profiles deduced from models with desolvation barriers for a set of thirteen natural proteins with similar chain lengths and secondary structure elements suggested that they fold much more cooperatively than Top7. Buttressed by related studies on smaller natural proteins with chain lengths of ∼40 residues, our findings argue that the de novo native topology of Top7 likely imposed a significant restriction on the cooperativity achievable by any design for this target structure.     

Thermodynamic analysis of the folding of the streptococcal protein G IgG-binding domains B1 and B2: why small proteins tend to have high denaturation temperatures.

We have cloned, expressed, and characterized two naturally occurring variations of the IgG-binding domain of streptococcal protein G. The domain is a stable cooperative folding unit of 56 amino acids, which maintains a unique folded structure without disulfide cross-links or tight ligand binding. We have studied the thermodynamics of the unfolding reaction for the two versions of this domain, designated B1 and B2, which differ by six amino acids. They have denaturation temperatures of 87.5 degrees C and 79.4 degrees C, respectively at pH 5.4, as determined by differential scanning calorimetry. Thermodynamic state functions for the unfolding reaction (delta G, delta H, delta S, and delta Cp) have been determined and reveal several interesting insights into the behavior of very small proteins. First, though the B1 domain has a heat denaturation point close to 90 degrees C, it is not unusually stable at physiologically relevant temperatures (delta G = 25 kJ/mol at 37 degrees C). This behavior occurs because the stability profile (delta G vs temperature) is flat and shallow due to the small delta S and delta Cp for unfolding. Related to this point is the second observation that small changes in the free energy of unfolding of the B-domain due to mutation or change in solvent conditions lead to large shifts in the heat denaturation temperature. Third, the magnitude and relative contributions of hydrophobic vs nonhydrophobic forces (per amino acid residue) to the total free energy of folding of the B-domain are remarkably typical of other globular proteins of much larger size.     

Folding landscapes of ankyrin repeat proteins: experiments meet theory

Nearly 6% of eukaryotic protein sequences contain ankyrin repeat (AR) domains, which consist of several repeats and often function in binding. AR proteins show highly cooperative folding despite a lack of long-range contacts. Both theory and experiment converge to explain that formation of the interface between elements is more favorable than formation of any individual repeat unit. IkappaBalpha and Notch both undergo partial folding upon binding perhaps influencing the binding free energy. The simple architecture, combined with identification of consensus residues that are important for stability, has enabled systematic perturbation of the energy landscape by single point mutations that affect stability or by addition of consensus repeats. The folding energy landscapes appear highly plastic, with small perturbations re-routing folding pathways.     

Computational protein design with explicit consideration of surface hydrophobic patches

De novo protein design requires the identification of amino-acid sequences that favor the target-folded conformation and are soluble in water. One strategy for promoting solubility is to disallow hydrophobic residues on the protein surface during design. However, naturally occurring proteins often have hydrophobic amino acids on their surface that contribute to protein stability via the partial burial of hydrophobic surface area or play a key role in the formation of protein-protein interactions. A less restrictive approach for surface design that is used by the modeling program Rosetta is to parameterize the energy function so that the number of hydrophobic amino acids designed on the protein surface is similar to what is observed in naturally occurring monomeric proteins. Previous studies with Rosetta have shown that this limits surface hydrophobics to the naturally occurring frequency (～28%), but that it does not prevent the formation of hydrophobic patches that are considerably larger than those observed in naturally occurring proteins. Here, we describe a new score term that explicitly detects and penalizes the formation of hydrophobic patches during computational protein design. With the new term, we are able to design protein surfaces that include hydrophobic amino acids at naturally occurring frequencies, but do not have large hydrophobic patches. By adjusting the strength of the new score term, the emphasis of surface redesigns can be switched between maintaining solubility and maximizing folding free energy.     

The folding landscape of Streptomyces griseus protease B reveals the energetic costs and benefits associated with evolving kinetic stability

Like most extracellular bacterial proteases, Streptomyces griseus protease B (SGPB) and alpha-lytic protease (alphaLP) are synthesized with covalently attached pro regions necessary for their folding. In this article, we characterize the folding free energy landscape of SGPB and compare it to the folding landscapes of alphaLP and trypsin, a mammalian homolog that folds independently of its zymogen peptide. In contrast to the thermodynamically stable native state of trypsin, SGPB and alphaLP fold to native states that are thermodynamically marginally stable or unstable, respectively. Instead, their apparent stability arises kinetically, from unfolding free energy barriers that are both large and highly cooperative. The unique unfolding transitions of SGPB and alphaLP extend their functional lifetimes under highly degradatory conditions beyond that seen for trypsin; however, the penalty for evolving kinetic stability is remarkably large in that each factor of 2.4-8 in protease resistance is accompanied by a cost of ~10(5) in the spontaneous folding rate and ~5-9 kcal/mole in thermodynamic stability. These penalties have been overcome by the coevolution of increasingly effective pro regions to facilitate folding. Despite these costs, kinetic stability appears to be a potent mechanism for developing native-state properties that maximize protease longevity.     

Transferable Coarse-Grained Potential for De Novo Protein Folding and Design

Protein folding and design are major biophysical problems, the solution of which would lead to important applications especially in medicine. Here we provide evidence of how a novel parametrization of the Caterpillar model may be used for both quantitative protein design and folding. With computer simulations it is shown that, for a large set of real protein structures, the model produces designed sequences with similar physical properties to the corresponding natural occurring sequences. The designed sequences require further experimental testing. For an independent set of proteins, previously used as benchmark, the correct folded structure of both the designed and the natural sequences is also demonstrated. The equilibrium folding properties are characterized by free energy calculations. The resulting free energy profiles not only are consistent among natural and designed proteins, but also show a remarkable precision when the folded structures are compared to the experimentally determined ones. Ultimately, the updated Caterpillar model is unique in the combination of its fundamental three features: its simplicity, its ability to produce natural foldable designed sequences, and its structure prediction precision. It is also remarkable that low frustration sequences can be obtained with such a simple and universal design procedure, and that the folding of natural proteins shows funnelled free energy landscapes without the need of any potentials based on the native structure.     

Simulating protein evolution in sequence and structure space

Naturally occurring proteins comprise a special subset of all plausible sequences and structures selected through evolution. Simulating protein evolution with simplified and all-atom models has shed light on the evolutionary dynamics of protein populations, the nature of evolved sequences and structures, and the extent to which today's proteins are shaped by selection pressures on folding, structure and function. Extensive mapping of the native structure, stability and folding rate in sequence space using lattice proteins has revealed organizational principles of the sequence/structure map important for evolutionary dynamics. Evolutionary simulations with lattice proteins have highlighted the importance of fitness landscapes, evolutionary mechanisms, population dynamics and sequence space entropy in shaping the generic properties of proteins. Finally, evolutionary-like simulations with all-atom models, in particular computational protein design, have helped identify the dominant selection pressures on naturally occurring protein sequences and structures.     

Ruggedness in the Free Energy Landscape Dictates Misfolding of the Prion Protein

Experimental determination of the key features of the free energy landscapes of proteins, which dictate their adeptness to fold correctly, or propensity to misfold and aggregate and which are modulated upon a change from physiological to aggregation-prone conditions, is a difficult challenge. In this study, sub-millisecond kinetic measurements of the folding and unfolding of the mouse prion protein reveal how the free energy landscape becomes more complex upon a shift from physiological (pH 7) to aggregation-prone (pH 4) conditions. Folding and unfolding utilize the same single pathway at pH 7, but at pH 4, folding occurs on a pathway distinct from the unfolding pathway. Moreover, the kinetics of both folding and unfolding at pH 4 depend not only on the final conditions but also on the conditions under which the processes are initiated. Unfolding can be made to switch to occur on the folding pathway by varying the initial conditions. Folding and unfolding pathways appear to occupy different regions of the free energy landscape, which are separated by large free energy barriers that change with a change in the initial conditions. These barriers direct unfolding of the native protein to proceed via an aggregation-prone intermediate previously identified to initiate the misfolding of the mouse prion protein at low pH, thus identifying a plausible mechanism by which the ruggedness of the free energy landscape of a protein may modulate its aggregation propensity.     

Folding of Top7 in unbiased all‐atom Monte Carlo simulations

For computational studies of protein folding, proteins with both helical and β‐sheet secondary structure elements are very challenging, as they expose subtle biases of the physical models. Here, we present reproducible folding of a 92 residue α/β protein (residues 3–94 of Top7, PDB ID: 1QYS) in computer simulations starting from random initial conformations using a transferable physical model which has been previously shown to describe the folding and thermodynamic properties of about 20 other smaller proteins of different folds. Top7 is a de novo designed protein with two α‐helices and a five stranded β‐sheet. Experimentally, it is known to be unusually stable for its size, and its folding transition distinctly deviates from the two‐state behavior commonly seen in natural single domain proteins. In our all‐atom implicit solvent parallel tempering Monte Carlo simulations, Top7 shows a rapid transition to a group of states with high native‐like secondary structure, and a much slower subsequent transition to the native state with a root mean square deviation of about 3.5 Å from the experimentally determined structure. Consistent with experiments, we find Top7 to be thermally extremely stable, although the simulations also find a large number of very stable non‐native states with high native‐like secondary structure. Proteins 2013; 81:1446–1456. © 2013 Wiley Periodicals, Inc.     

Using motion planning to map protein folding landscapes and analyze folding kinetics of known native structures.

We investigate a novel approach for studying the kinetics of protein folding. Our framework has evolved from robotics motion planning techniques called probabilistic roadmap methods (PRMs) that have been applied in many diverse fields with great success. In our previous work, we presented our PRM-based technique and obtained encouraging results studying protein folding pathways for several small proteins. In this paper, we describe how our motion planning framework can be used to study protein folding kinetics. In particular, we present a refined version of our PRM-based framework and describe how it can be used to produce potential energy landscapes, free energy landscapes, and many folding pathways all from a single roadmap which is computed in a few hours on a desktop PC. Results are presented for 14 proteins. Our ability to produce large sets of unrelated folding pathways may potentially provide crucial insight into some aspects of folding kinetics, such as proteins that exhibit both two-state and three-state kinetics that are not captured by other theoretical techniques.     

The evolutionary landscape of functional model proteins.

To study the distinct influences of structure and function on evolution, we propose a minimalist model for proteins with binding pockets, called functional model proteins, based on a shifted-HP model on a two-dimensional square lattice. These model proteins are not maximally compact and contain an empty lattice site surrounded by at least three nearest neighbors, thus providing a binding pocket. Functional model proteins possess a unique native state, cooperative folding and tolerance to mutation. Due to the explicit functionality in these models (by design), we have been able to explore their fitness or evolutionary landscapes, as characterized by the size and distribution of homologous families and by the complexity of the inter-relatedness of the functional model proteins. Mindful that these minimalist models are highly idealized and two-dimensional, functional model proteins should nevertheless provide a useful means for exploring the constraints of maintaining structure and function on the evolution of proteins.     

Reliable protein folding on complex energy landscapes: the free energy reaction path

A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical denaturant, or pH, are adjusted to induce folding. A theory based on this insight predicts that 1), proteins with complex energy landscapes can fold reliably to their native state; 2), reliable folding can occur as an equilibrium or out-of-equilibrium process; and 3), reliable folding only occurs when the rate r is below a limiting value, which can be calculated from measurements of the free energy. We test these predictions against numerical simulations of model proteins with a single energy scale.     

The influence of intrinsic folding mechanism of an unfolded protein on the coupled folding-binding process during target recognition

Intrinsically disordered proteins (IDPs) are extensively involved in dynamic signaling processes which require a high association rate and a high dissociation rate for rapid binding/unbinding events and at the same time a sufficient high affinity for specific recognition. Although the coupled folding-binding processes of IDPs have been extensively studied, it is still impossible to predict whether an unfolded protein is suitable for molecular signaling via coupled folding-binding. In this work, we studied the interplay between intrinsic folding mechanisms and coupled folding-binding process for unfolded proteins through molecular dynamics simulations. We first studied the folding process of three representative IDPs with different folded structures, that is, c-Myb, AF9, and E3 rRNase. We found the folding free energy landscapes of IDPs are downhill or show low barriers. To further study the influence of intrinsic folding mechanism on the binding process, we modulated the folding mechanism of barnase via circular permutation and simulated the coupled folding-binding process between unfolded barnase permutant and folded barstar. Although folding of barnase was coupled to target binding, the binding kinetics was significantly affected by the intrinsic folding free energy barrier, where reducing the folding free energy barrier enhances binding rate up to two orders of magnitude. This accelerating effect is different from previous results which reflect the effect of structure flexibility on binding kinetics. Our results suggest that coupling the folding of an unfolded protein with no/low folding free energy barrier with its target binding may provide a way to achieve high specificity and rapid binding/unbinding kinetics simultaneously.     

Protein Thermostability Calculations Using Alchemical Free Energy Simulations

Thermal stability of proteins is crucial for both biotechnological and therapeutic applications. Rational protein engineering therefore frequently aims at increasing thermal stability by introducing stabilizing mutations. The accurate prediction of the thermodynamic consequences caused by mutations, however, is highly challenging as thermal stability changes are caused by alterations in the free energy of folding. Growing computational power, however, increasingly allows us to use alchemical free energy simulations, such as free energy perturbation or thermodynamic integration, to calculate free energy differences with relatively high accuracy. In this article, we present an automated protocol for setting up alchemical free energy calculations for mutations of naturally occurring amino acids (except for proline) that allows an unprecedented, automated screening of large mutant libraries. To validate the developed protocol, we calculated thermodynamic stability differences for 109 mutations in the microbial Ribonuclease Barnase. The obtained quantitative agreement with experimental data illustrates the potential of the approach in protein engineering and design.     

How cooperative are protein folding and unfolding transitions?

A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two‐state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non‐cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier‐less “downhill” folding, as well as for continuous “uphill” unfolding transitions, indicate that gradual non‐cooperative processes may be ubiquitous features on the free energy landscape of protein folding.