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Heme is an active center in many proteins. Here we explore computationally the role of heme in protein folding and protein structure. We model heme proteins using a hybrid model employing the AWSEM Hamiltonian, a coarse-grained forcefield for the protein chain along with AMBER, an all-atom forcefield for the heme. We carefully designed transferable force fields that model the interactions between the protein and the heme. The types of protein–ligand interactions in the hybrid model include thioester covalent bonds, coordinated covalent bonds, hydrogen bonds, and electrostatics. We explore the influence of different types of hemes (heme b and heme c) on folding and structure prediction. Including both types of heme improves the quality of protein structure predictions. The free energy landscape shows that both types of heme can act as nucleation sites for protein folding and stabilize the protein folded state. In binding the heme, coordinated covalent bonds and thioester covalent bonds for heme c drive the heme toward the native pocket. The electrostatics also facilitates the search for the binding site.

The accurate reading of genetic information during transcription is essential for the expression of genes. Sequence binding specificity very often is attributed to short-range, usually specific interactions between amino acid residues and individual nucleotide bases through hydrogen bonding or hydrophobic contacts: "base readout" (direct readout). In contrast, many proteins recognize DNA sequences in an alternative fashion via "shape readout" (indirect readout), where many elements of the DNA sequence cooperate to localize the transcription factor. In this study, we use a coarse-grained protein-DNA model to investigate the origin of the sequence specificity of the protein PU.1 binding to its binding sites for a series of DNA sequences. We find that the binding specificity of PU.1 is achieved primarily via a nonspecific electrostatically driven DNA mechanism involving the change in the elastic properties of the DNA. To understand the underlying mechanism, we analyze how the mechanical properties of DNA change in relation to the location of the PU.1 bound along DNA. The simulations first show that electrostatic interactions between PU.1 and DNA can cause complex DNA conformational/dynamics changes. Using a semiflexible polymer theory, we find that PU.1 influences the DNA dynamics through a second-order mechanical effect. When PU.1 binds nonspecifically to the DNA via electrostatics, the DNA becomes stiffer and the protein slides along DNA in a search mode. In contrast, once the protein finds its specific binding site, the DNA becomes softer there. PU.1 thus locks into place through configurational entropy effects, which we suggest is a generic mechanism for indirect readout.

Amyloid-forming proteins aggregate within and between neuronal cells, and the resulting deposits are associated with neurodegenerative diseases. The amyloidogenic property of these proteins, in fact, arises from a relatively short part of the whole amino acid sequence. Recent studies have also shown that some short subsequences drive amorphous aggregation; the resulting aggregates are structurally distinct from amyloid aggregates and may thus play different functional and pathogenic roles than amyloid aggregates. Although the process of conformational conversion between amyloid and amorphous aggregates has attracted much attention, the detailed molecular mechanism underlying such a conformational conversion is not yet clear. In this mini-review, I review some aggregation studies that employ the concept of nucleated polymerization to describe early stage on-pathway protein aggregation. I specifically look into one of the most important aggregation properties, critical nucleus size, for a variety of amyloid proteins/fragments and demonstrate that this quantity can be used to help understand the molecular mechanism of early stage protein aggregation. I argue that a similar nucleated polymerization scheme can be applied to study functional/amorphous aggregates without a fundamental difference from a theoretical perspective. I hypothesize that the physical principle underlying the conformational conversion between pathogenic and functional aggregates is associated with several morphological properties (e.g., lateral alignment and intrinsic polymorphism) that can be modulated through proline-mediated conformational rigidity of the sequence. This phenomenon may thus be responsible for the length-dependent amyloidogenesis of amyloid-forming proteins. This notion may shed light on predicting amyloidogenic propensity by correlating the change of a protein’s mechanical properties with the resulting protein morphologies at the sequence level.

The nucleation of protein aggregates and their growth are important in determining the structure of the cell's membraneless organelles as well as the pathogenesis of many diseases. The large number of molecular types of such aggregates along with the intrinsically stochastic nature of aggregation challenges our theoretical and computational abilities. Kinetic Monte Carlo simulation using the Gillespie algorithm is a powerful tool for modeling stochastic kinetics, but it is computationally demanding when a large number of diverse species is involved. To explore the mechanisms and statistics of aggregation more efficiently, we introduce a new approach to model stochastic aggregation kinetics which introduces noise into already statistically averaged equations obtained using mathematical moment closure schemes. Stochastic moment equations summarize succinctly the dynamics of the large diversity of species with different molecularity involved in aggregation but still take into account the stochastic fluctuations that accompany not only primary and secondary nucleation but also aggregate elongation, dissociation, and fragmentation. This method of "second stochasticization" works well where the fluctuations are modest in magnitude as is often encountered

The accurate and reliable prediction of the 3D structures of proteins and their assemblies remains difficult even though the number of solved structures soars and prediction techniques improve. In this study, a free and open access web server, AWSEM-Suite, whose goal is to predict monomeric protein tertiary structures from sequence is described. The model underlying the server’s predictions is a coarse-grained protein force field which has its roots in neural network ideas that has been optimized using energy landscape theory. Employing physically motivated potentials and knowledge-based local structure biasing terms, the addition of homologous template and co-evolutionary restraints to AWSEM-Suite greatly improves the predictive power of pure AWSEM structure prediction. From the independent evaluation metrics released in the CASP13 experiment, AWSEM-Suite proves to be a reasonably accurate algorithm for free modeling, standing at the eighth position in the free modeling category of CASP13. The AWSEM-Suite server also features a front end with a user-friendly interface. The AWSEM-Suite server is a powerful tool for predicting monomeric protein tertiary structures that is most useful when a suitable structure template is not available. The AWSEM-Suite server is freely available at: https://awsem.rice.edu.

As a master transcription regulator, Fis protein influences over two hundred genes of E-coli. Fis protein’s non-specific binding to DNA is widely acknowledged, and its kinetics of dissociation from DNA is strongly influenced by its surroundings: the dissociation rate increases as the concentration of Fis protein in the solution-phase increases. In this study, we use computational methods to explore the global binding energy landscape of the Fis1:Fis2:DNA ternary complex. The complex contains a binary-Fis molecular dyad whose formation relies on complex structural rearrangements. The simulations allow us to distinguish several different pathways for the dissociation of the protein from DNA with different functional outcomes, and involving different protein stoichiometries: 1. Simple exchange of proteins and 2. Cooperative unbinding of two Fis proteins to yield bare DNA. In the case of exchange, the protein on the DNA is replaced by solution-phase protein through competition for DNA binding sites. This process seen in fluorescence imaging experiments has been called facilitated dissociation. In the latter case of cooperative unbinding of pairs, two neighboring Fis proteins on DNA form a unique binary-Fis configuration via protein-protein interactions, which in turn leads to the co-dissociation of both molecules simultaneously, a process akin to the “molecular stripping” seen in the NFκB/IκB genetic broadcasting system. This simulation shows that the existence of multiple binding configurations of transcription factors can have a significant impact on the kinetics and outcome of transcription factor dissociation from DNA, with important implications for the systems biology of gene regulation by Fis.

Folded proteins show a high degree of structural order and undergo (fairly constrained) collective motions related to their functions. On the other hand, intrinsically disordered proteins (IDPs), while lacking a well-defined three-dimensional structure, do exhibit some structural and dynamical ordering, but are less constrained in their motions than folded proteins. The larger structural plasticity of IDPs emphasizes the importance of entropically driven motions. Many IDPs undergo function-related disorder-to-order transitions driven by their interaction with specific binding partners. As experimental techniques become more sensitive and become better integrated with computational simulations, we are beginning to see how the modest structural ordering and large amplitude collective motions of IDPs endow them with an ability to mediate multiple interactions with different partners in the cell. To illustrate these points, here, we use Prostate-associated gene 4 (PAGE4), an IDP implicated in prostate cancer (PCa) as an example. We first review our previous efforts using molecular dynamics simulations based on atomistic AWSEM to study the conformational dynamics of PAGE4 and how its motions change in its different physiologically relevant phosphorylated forms. Our simulations quantitatively reproduced experimental observations and revealed how structural and dynamical ordering are encoded in the sequence of PAGE4 and can be modulated by different extents of phosphorylation by the kinases HIPK1 and CLK2. This ordering is reflected in changing populations of certain secondary structural elements as well as in the regularity of its collective motions. These ordered features are directly correlated with the functional interactions of WT-PAGE4, HIPK1-PAGE4 and CLK2-PAGE4 with the AP-1 signaling axis. These interactions give rise to repeated transitions between (high HIPK1-PAGE4, low CLK2-PAGE4) and (low HIPK1-PAGE4, high CLK2-PAGE4) cell phenotypes, which possess differing sensitivities to the standard PCa therapies, such as androgen deprivation therapy (ADT). We argue that, although the structural plasticity of an IDP is important in promoting promiscuous interactions, the modulation of the structural ordering is important for sculpting its interactions so as to rewire with agility biomolecular interaction networks with significant functional consequences.

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.

Significance Protein aggregation and amyloid formation seem to be at the heart of the pathology of multiple neurodegenerative diseases, including Alzheimer’s disease. A β protein has long been considered one of the protein components that contributes to the pathogenesis and the progression of the disease. The concepts of energy landscape analysis established in the theory of protein folding are applied here to create a quantitative image of the aggregation energy landscape of A β . The resulting “amyloid funnel” not only helps visualize the complexity of the early stages of aggregation of WT A β but also, predicts the effects of mutations at specific sites on aggregation behavior.

The protein frustratometer is an energy landscape theory-inspired algorithm that aims at localizing and quantifying the energetic frustration present in protein molecules. Frustration is a useful concept for analyzing proteins' biological behavior. It compares the energy distributions of the native state with respect to structural decoys. The network of minimally frustrated interactions encompasses the folding core of the molecule. Sites of high local frustration often correlate with functional regions such as binding sites and regions involved in allosteric transitions. We present here an upgraded version of a webserver that measures local frustration. The new implementation that allows the inclusion of electrostatic energy terms, important to the interactions with nucleic acids, is significantly faster than the previous version enabling the analysis of large macromolecular complexes within a user-friendly interface. The webserver is freely available at URL: http://frustratometer.qb.fcen.uba.ar. Fil: Parra, Rodrigo Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Química Biológica; Argentina Fil: Schafer, Nicholas P.. University Aarhus; Dinamarca Fil: Radusky, Leandro Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Química Biológica; Argentina Fil: Tsai, Min-Yeh. Rice University; Estados Unidos Fil: Guzovsky, Ana Brenda. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Química Biológica; Argentina Fil: Wolynes, Peter G.. Rice University; Estados Unidos Fil: Ferreiro, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Química Biológica; Argentina

While being long in range and therefore weakly specific, electrostatic interactions are able to modulate the stability and folding landscapes of some proteins. The relevance of electrostatic forces for steering the docking of proteins to each other is widely acknowledged, however, the role of electrostatics in establishing specifically funneled landscapes and their relevance for protein structure prediction are still not clear. By introducing Debye-Huckel potentials that mimic long-range electrostatic forces into the Associative memory, Water mediated, Structure, and Energy Model (AWSEM), a transferable protein model capable of predicting tertiary structures, we assess the effects of electrostatics on the landscapes of thirteen monomeric proteins and four dimers. For the monomers, we find that adding electrostatic interactions does not improve structure prediction. Simulations of ribosomal protein S6 show, however, that folding stability depends monotonically on electrostatic strength. The trend in predicted melting temperatures of the S6 variants agrees with experimental observations. Electrostatic effects can play a range of roles in binding. The binding of the protein complex KIX-pKID is largely assisted by electrostatic interactions, which provide direct charge-charge stabilization of the native state and contribute to the funneling of the binding landscape. In contrast, for several other proteins, including the DNA-binding protein FIS, electrostatics causes frustration in the DNA-binding region, which favors its binding with DNA but not with its protein partner. This study highlights the importance of long-range electrostatics in functional responses to problems where proteins interact with their charged partners, such as DNA, RNA, as well as membranes.

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.

In this work, we present a kinetic analysis for protein aggregation using the kinetic Ising model, which serves as a new application of a previously proposed model [Liang et al., J. Chin. Chem. Soc.­ 2003, 50, 335]. Considering protein as a single spin unit, we map two states of a unit to the aggregation-prone (AP) and the fibril (F) states. This work shows that the model can successfully capture the nucleation-growth features of protein aggregation from experiments, which offers thermodynamic interpretations of aggregation properties, such as lag-time and fibril stability.

The b-hairpin is a building block in the β-sheet structure. Understanding the formation of the β-hairpin may provide insight into the formation of β-sheet structures in, for example, protein amyloids. In this study, we performed molecular dynamics (MD) simulations to investigate the temperature-dependent transition behaviors of the GB1 β-hairpin peptide. The simulated results are analysed in terms of distances between pairs of peptide bonds and site-dependent dihedral angles. Our results show that the properties of the hairpin can be site-dependent and that the dependency is primarily associated with the hairpin's geometrical shape and specific interactions, such as hydrophobic clustering. Thus our study provides a foundation for the interpretation of probe-dependent experimental results.

In this theoretical study, we aimed to simulate the sum-frequency generation (SFG) spectroscopy of a thin polystyrene layer physically adsorbed on the graphene sheet and to figure out the orientation distribution of the phenyl units. To simplify the problem, we started the investigation by constructing molecular models with styrene and ethylbenzene monomers and styrene oligomers up to four units adsorbed on a finite-sized graphene hexagon. Geometric optimization results showed that the phenyl rings of the adsorbate always orientate close to the surface normal with a small tilt angle. The adsorption is weak but not negligible. SFG spectra have been simulated based on these calculated structures, vibrational frequencies, and dipole and polarizability derivatives to compare with experimental reports of polystyrene adsorbed on other surfaces.

Aggregates of proteins containing polyglutamine (polyQ) repeats are strongly associated with several neurodegenerative diseases. The length of the repeats correlates with the severity of the disease. Previous studies have shown that pure polyQ peptides aggregate by nucleated growth polymerization and that the size of the critical nucleus (n*) decreases from tetrameric to dimeric and monomeric as length increases from Q18 to Q26. Why the critical nucleus size changes with repeat-length has been unclear. Using the associative memory, water-mediated, structure and energy model, we construct the aggregation free energy landscapes for polyQ peptides of different repeat-lengths. These studies show that the monomer of the shorter repeat-length (Q20) prefers an extended conformation and that its aggregation indeed has a trimeric nucleus (n* ∼ 3), while a longer repeat-length monomer (Q30) prefers a β-hairpin conformation which then aggregates in a downhill fashion at 0.1 mM. For an intermediate length peptide (Q26), there is an equal preference for hairpin and extended forms in the monomer which leads to a mixed inhomogeneous nucleation mechanism for fibrils. The predicted changes of monomeric structure and nucleation mechanism are confirmed by studying the aggregation free energy profile for a polyglutamine repeat with site-specific PG mutations that favor the hairpin form, giving results in harmony with experiments on this system.

With a deformed object of a rigid rod inside, the local dislocations may be tracked relatively easily with respect to the internal rigid rod. We apply this concept on protein folding–unfolding to track the internal structural changes of an unfolded protein in solution. Proposed here is a protein internal coordination based on the major axis X of an ellipsoidal protein and the stable intrinsic transition dipole moment μ of the protein during unfolding. In this methodology, small-angle X-ray scattering (SAXS) is used to provide the protein global morphologies in the native and unfolded states. Furthermore, time-resolved fluorescence anisotropy (TRFA) provides the relative orientation between X and μ of Trp59 of the model protein cytochrome c. Hence observed in the protein unfolding with denaturants, acid, urea, or GuHCl, is the elongation of the native protein conformation along a reoriented protein major axis; accompanied are the different extents of relocations of the terminal α helices and loop structures of the protein in the corresponding unfolding.

Hydrogen exchange experiments reveal the existence of a foldon structure in Cytochrome c. We performed constant temperature Molecular Dynamics simulations of Cytochrome c to investigate the macroscopic behavior of the foldons. The results showed that the tertiary interactions in Cytochrome c play an important role in the stabilization of the N- and C-terminal helices. We also observed the macroscopic behavior of a black foldon in the process of thermal unfolding. Our results support that Cytochrome c folding occurs in accordance with the classical pathway concept of Levinthal.

Kinetic studies of protein aggregation processes based on the nucleation-polymerization (NP) mechanism and/or its variants are often formulated in terms of the law of mass action. Although these works have greatly enhanced our knowledge in the microscopic descriptions of fibril/aggregate formation (e.g., fragmentation and other secondary pathways), they have to inevitably deal with a huge number of filament species Fn (n=1 to 10∧3 ∼ 10∧4 or even more) as well as a number of kinetic parameters. Very often some kinetic assumptions for the species with a wide distribution of sizes and shapes would be needed in order to simplify the calculation. In contrast, starting from a phase-transition perspective, one is able to provide thermodynamic insight into the nucleation-controlled kinetic behavior. In this work, we propose to apply the kinetic Ising model to investigate the thermodynamics and kinetics of protein aggregation. At mean-field (MF) level, our model can offer thermodynamic interpretation to the lag time; in particular, it can explain the effect of temperature, concentration, and seeding on the change of kinetic profiles. Using four real proteins as examples, we show that the calculated fibril stability is consistent with experimental measurements. In addition, their kinetics can be classified according to a generalized scheme of the model. Our results suggest that protein aggregation could be studied within the framework of the Ginzberg-Landau phase transition theory.

Hydrogen exchange experiments (Krishna et al. in J. Mol. Biol. 359:1410, 2006) reveal that folding–unfolding of cytochrome c occurs along a defined pathway in a sequential, stepwise manner. The simplified zipper-like model involving nonadditive coupling is proposed to describe the classical “on pathway” folding–unfolding behavior of cytochrome c. Using free energy factors extracted from HX experiments, the model can predict and explain cytochrome c behavior in spectroscopy studies looking at folding equilibria and kinetics. The implications of the proposed model are discussed for such problems as classical pathway vs. energy landscape conceptions, structure and function of a native fold, and interplay of secondary and tertiary interactions.

Herein, we propose a modified version of the Wako-Saitô-Muñoz-Eaton (WSME) model. The proposed model introduces an empirical temperature parameter for the hypothetical structural units (i.e., foldons) in proteins to include site-dependent thermodynamic behavior. The thermodynamics for both our proposed model and the original WSME model were investigated. For a system with beta-hairpin topology, a mathematical treatment (contact-pair treatment) to facilitate the calculation of its partition function was developed. The results show that the proposed model provides better insight into the site-dependent thermodynamic behavior of the system, compared with the original WSME model. From this site-dependent point of view, the relationship between probe-dependent experimental results and model's thermodynamic predictions can be explained. The model allows for suggesting a general principle to identify foldon behavior. We also find that the backbone hydrogen bonds may play a role of structural constraints in modulating the cooperative system. Thus, our study may contribute to the understanding of the fundamental principles for the thermodynamics of protein folding.

Analyzing experimental data of thermodynamic properties of proteins reveals large discrepancies existing between data obtained using different experimental methods, for example, those obtained by spectroscopy methods and those by calorimetry. The interpretation is that some experimental methods probe local or site-specific properties of protein, others probe global properties. To develop a statistical mechanical model for site-specific properties of proteins we extend the Wako-Saito-Munoz-Eaton (WSME) model by introducing a set of site-dependent parameters, Ti, which has a mid-point temperature interpretation. This model has been applied to the GB1 C-terminal β-hairpin, which has also been investigated using Molecular Dynamics (MD) simulations. Our MD results support the novel modification to the WSME model by providing reasonable insight into the local thermodynamic behavior of the system. Furthermore, our model is equivalent to a statistical mechanical formulation of the foldon behavior, identified by Englander, et al in hydrogen-exchange (HX) experiments and other experimental techniques, e.g., absorption spectroscopy (Abs), circular dichroism (CD), small angle x-ray scattering (SAXA), etc. Using the simple β-hairpin model as an example, we hope to illustrate that our model is generally useful for the interpretation of site-dependent thermodynamic properties of proteins as well as for the study of protein folding.