Theory of kinetic partitioning in protein folding with possible applications to prions

α-Helix-Mediated Protein Adhesion

Proteins have been adopted by natural living organisms to create robust bioadhesive materials, such as biofilms and amyloid plaques formed in microbes and barnacles. In these cases, β-sheet stacking is recognized as a key feature that is closely related to the interfacial adhesion of proteins. Herein, we challenge this well-known recognition by proposing an α-helix-mediated interfacial adhesion model for proteins. By using bovine serum albumin (BSA) as a model protein, it was discovered that the reduction of disulfide bonds in BSA results in random coils from unfolded BSA dragging α-helices to gather at the solid/liquid interface (SLI). The hydrophobic residues in the α-helix then expose and break through the hydration layer of the SLI, followed by the random deposition of hydrophilic and hydrophobic residues to achieve interfacial adhesion. As a result, the first assembled layer is enriched in the α-helix secondary structure, which is then strengthened by intermolecular disulfide bonds and further initiates stepwise layering protein assembly. In this process, β-sheet stacking is transformed from the α-helix in a gradually evolving manner. This finding thus indicates a valuable clue that β-sheet-featuring amyloid may form after the interfacial adhesion of proteins. Furthermore, the finding of the α-helix-mediated interfacial adhesion model of proteins affords a unique strategy to prepare protein nanofilms with a well-defined layer number, presenting robust and modulable adhesion on various substrates and exhibiting good resistance to acid, alkali, organic solvent, ultrasonic, and adhesive tape peeling.

Lymphotactin: how a protein can adopt two folds

Metamorphic proteins such as lymphotactin are a notable exception of the empirical principle that structured natural proteins possess a unique three-dimensional structure. In particular, the human chemokine lymphotactin protein exists in two distinct conformations (one monomeric and one dimeric) under physiological conditions. In this work, we use a C(alpha) Go model to show how this very peculiar behavior can be reproduced. From the study of the thermodynamics and of the kinetics, we characterize the interconversion mechanism. In particular, this takes place through the docking of the two chains living in a third monomeric, partially unfolded, state which shows a residual structure involving a set of local contacts common to the two native conformations. The main feature of two fold proteins appears to be the sharing of a common set of local contacts between the two distinct folds as confirmed by the study of two designed two fold proteins. Metamorphic proteins may be more common than expected.

Uncovering the properties of energy-weighted conformation space networks with a hydrophobic-hydrophilic model

The conformation spaces generated by short hydrophobic-hydrophilic (HP) lattice chains are mapped to conformation space networks (CSNs). The vertices (nodes) of the network are the conformations and the links are the transitions between them. It has been found that these networks have "small-world" properties without considering the interaction energy of the monomers in the chain, i. e. the hydrophobic or hydrophilic amino acids inside the chain. When the weight based on the interaction energy of the monomers in the chain is added to the CSNs, it is found that the weighted networks show the "scale-free" characteristic. In addition, it reveals that there is a connection between the scale-free property of the weighted CSN and the folding dynamics of the chain by investigating the relationship between the scale-free structure of the weighted CSN and the noted parameter Z score. Moreover, the modular (community) structure of weighted CSNs is also studied. These results are helpful to understand the topological properties of the CSN and the underlying free-energy landscapes.

A lattice protein with an amyloidogenic latent state: stability and folding kinetics

We have designed a model lattice protein that has two stable folded states, the lower free energy native state and a latent state of somewhat higher energy. The two states have a sizable part of their structures in common (two "alpha-helices") and differ in the content of "alpha-helices" and "beta-strands" in the rest of their structures; i.e. for the native state, this part is alpha-helical, and for the latent state it is composed of beta-strands. Thus, the lattice protein free energy surface mimics that of amyloidogenic proteins that form well organized fibrils under appropriate conditions. A Go-like potential was used and the folding process was simulated with a Monte Carlo method. To gain insight into the equilibrium free energy surface and the folding kinetics, we have combined standard approaches (reduced free energy surfaces, contact maps, time-dependent populations of the characteristic states, and folding time distributions) with a new approach. The latter is based on a principal coordinate analysis of the entire set of contacts, which makes possible the introduction of unbiased reaction coordinates and the construction of a kinetic network for the folding process. The system is found to have four characteristic basins, namely a semicompact globule, an on-pathway intermediate (the bifurcation basin), and the native and latent states. The bifurcation basin is shallow and consists of the structure common to the native and latent states, with the rest disorganized. On the basis of the simulation results, a simple kinetic model describing the transitions between the characteristic states was developed, and the rate constants for the essential transitions were estimated. During the folding process the system dwells in the bifurcation basin for a relatively short time before it proceeds to the native or latent state. We suggest that such a bifurcation may occur generally for proteins in which native and latent states have a sizable part of their structures in common. Moreover, there is the possibility of introducing changes in the system (e.g., mutations), which guide the system toward the native or misfolded state.

Osmolyte trimethylamine N-oxide converts recombinant alpha-helical prion protein to its soluble beta-structured form at high temperature

The thermal unfolding of full-length human recombinant alpha-helical prion protein (alpha-PrP) in neutral pH is reversible, whereas, in the presence of the osmolyte N-trimethylamine oxide (TMAO), the protein acquires a beta-sheet structure at higher temperatures and the thermal unfolding of the protein is irreversible. Lysozyme, an amyloidogenic protein similar to prion protein, regains alpha-helical structure on cooling from its thermally unfolded form in buffer and in TMAO solutions. The thermal stability of alpha-PrP decreases, whereas that of lysozyme increases in TMAO solution. Light-scattering and turbidity values indicate that beta-sheet prion protein exists as soluble oligomers that increase thioflavin T fluorescence and bind to 1-anilino 8-naphthalene sulfonic acid (ANS). The oligomers are resistant to proteinase K digestion and during incubation for long periods they form linear amyloids>5 microm long. The comparable fluorescence polarization of the tryptophan groups and their accessibility to acrylamide in alpha-PrP and oligomers indicate that the unstructured N-terminal segments of the protein, which contain the tryptophan groups, do not associate among themselves during oligomerization. Partial unfolding of alpha-helical prion protein in TMAO solution leads to its structural conversion to misfolded beta-sheet form. The formation of the misfolded prion protein oligomers and their polymerization to amyloids in TMAO are unusual, since the osmolyte generally induces denatured protein to fold to a native-like state and protects proteins from thermal denaturation and aggregation.

Predicting alternate structure attainment and amyloidogenesis: a nonlinear signal analysis approach

Chain hydrophobicity values have been used in prediction of alternate structure attainment by a polypeptide. Nonlinear signal analysis on the hydrophobicity values gives important clues about the propensities of particular stretches of a protein to form local or nonlocal contacts. These contacts determine the folding behavior of a polypeptide and helps in predicting the final structure that can be attained. A nonlinear signal analysis called the recurrent quantification analysis has been carried out using the hydrophobicity values on a wide range of proteins obtained from human, plant, and fungal sources. Here, we show that such an analysis gives us an easy handle in determining sequences within the proteins that may be important in beta-sheet formation leading to amyloidosis.

Structural Bases of the Redox-dependent Conformational Switch in the Serpin PAI-2

Depending on the redox-status, the serpin plasminogen activator inhibitor type 2 (PAI-2) can exist in either a stable monomeric or polymerogenic form. The latter form, which spontaneously forms loop-sheet polymers, has an open beta-sheet A and is stabilized by a disulfide bond between C79 (in the CD-loop) and C161 (at the bottom of PAI-2). Reduction of this bond results in a closing of the beta-sheet A and converts PAI-2 to a stable monomeric form. Here we show that the stable monomeric and polymerogenic forms of PAI-2 are fully interconvertible, depending on redox-status of the environment. Our intramolecular distance measurements indicate that the CD-loop folds mainly on one side of the stable monomeric form of the inhibitor. However, the loop can translocate about 54A to the bottom of PAI-2 so that the C79-C161 disulfide bond can form under oxidizing conditions. We show also that the redox-active C79 can form a disulfide-link to the matrix protein vitronectin, suggesting that vitronectin can stabilize active PAI-2 in extracellular compartments. PAI-2 is therefore a rare example of a redox-sensitive protein for which the activity and polymerization ability are regulated by reversible disulfide bond formation leading to major translocation of a loop and significant conformational changes in the molecule.

Discrimination of single amino acid mutations of the p53 protein by means of deterministic singularities of recurrence quantification analysis

p53 is mutated in roughly 50% of all human tumors, predominantly in the DNA-binding domain codons. Structural, biochemical, and functional studies have reported that the different p53 mutants possess a broad range of behaviors that include the elimination of the tumor-suppression function of wild-type protein, the acquisition of dominant-negative function over the wild-type form, and the establishment of gain-of-function activities. The contribution of each of these types of mutations to tumor progression, grade of malignancy, and response to anticancer treatments has been so far analyzed only for a few "hot-spots." In an attempt to identify new approaches to systematically characterize the complete spectrum of p53 mutations, we applied recurrence quantification analysis (RQA), a non-linear signal analysis technique, to p53 primary structure. Moving from the study of the p53 hydrophobicity pattern, which revealed important similarities with the singular deterministic structuring of prions, we could statistically discriminate, on a pure amino acid sequence basis, between experimentally characterized DNA-contact defective and conformational p53 mutants with a very high percentage of success. This result indicates that RQA is a mathematical tool particularly advantageous for the development of a database of p53 mutations that integrates epidemiological data with structural and functional categorizations.

Minimal model for studying prion-like folding pathways

The Monte Carlo technique is used to simulate the energy landscape and the folding kinetics of a minimal prion-like protein model. We show that the competition between hydrogen-bonding and hydrophobic interactions yields two energetically favored secondary structures, an alpha-helix and a beta-hairpin. Folding simulations indicate that the probability of reaching the alpha-helix form from a denatured random conformation is much higher than the probability of reaching the beta-sheet form, even though the beta-sheet has a lower energy. The existence of a lower energy beta-sheet state gives the possibility for the normal alpha-helix structure to take a structural transformation into the beta-sheet structure under external influences.

beta-Hairpins, alpha-helices, and the intermediates among the secondary structures in the energy landscape of a peptide from a distal beta-hairpin of SH3 domain

Energy landscape of a peptide, extracted from a distal beta-hairpin of src SH3 domain, in explicit water was obtained with the multicanonical molecular dynamics. A variety of beta-hairpins with various strand-strand hydrogen bonds were found in the energy landscape at 300 K. There was no energy barrier between random-coil and hairpins. Thus, the peptide conformation can easily change from the random-coil to the hairpins in the thermal fluctuations at 300 K. The landscape also included two clusters of alpha-helices, among which an energy barrier existed, and besides, these helix clusters were separated from the other conformations. Thus, the free-energy barrier exists among the helices and the other conformations. Intermediate clusters were found between the helix and the hairpin clusters. The current study showed that the isolated state of this peptide in water fluctuates among random-coil, beta-hairpin, and alpha-helix. In SH3 domain, which has a topology of mainly beta-protein, the whole-protein folding may proceed when the segment is folded in the beta-hairpin and the other parts of the protein are coupled with the beta-hairpin in an energetically or kinetically favorite way.

Protein design depends on the size of the amino acid alphabet

We consider the design of proteins to be simultaneously thermodynamically stable in multiple independent and correlated conformations. We first show that a protein can be trained to fold to multiple independent conformations and calculate its capacity. The number of configurations that it can remember is proportional to the logarithm of the number of amino acid species A, independent of chain length. Next we investigate the recognition of correlated conformations, which we apply to funnel design around a single configuration. The maximum basin of attraction, as parametrized in our model, also depends on the number of amino acid species as ln A. We argue that the extent to which the protein energy landscape can be manipulated is fixed, effecting a trade off between well breadth, well depth, and well number. This emerging picture motivates a clearer understanding of the scope and limits of protein and heteropolymer function.

Structural and folding properties of a lattice prion model

Searching through and conducting Monte Carlo folding simulations on 10(6) different 27 mer sequences, we have selected a prionlike lattice model whose energy spectrum and folding properties demonstrate characteristic prion behavior. The energetic competition and structural partition between two closely spaced energy minima yield unique kinetic and thermodynamic properties that can be qualitatively compared with experimental results. Folding simulations indicate that the probability of reaching the first excited state from a denatured random conformation is much higher than the probability of reaching the global energy-minimum state.

How many conformations can a protein remember?

We show that a protein can be trained to recognize multiple conformations, analogous to an associative memory, and provide capacity calculations based on energy fluctuations and information theory. Unlike the linear capacity of a Hopfield network, the number of conformations which can be remembered by a protein sequence depends on the size of the amino acid alphabet as lnA, independent of protein length. This admits the possibility of certain proteins, such as prions, evolving to fold to independent stable conformations, as well as novel possibilities for protein and heteropolymer design.

Understanding hierarchical protein evolution from first principles

We propose a model that explains the hierarchical organization of proteins in fold families. The model, which is based on the evolutionary selection of proteins by their native state stability, reproduces patterns of amino acids conserved across protein families. Due to its dynamic nature, the model sheds light on the evolutionary time-scales. By studying the relaxation of the correlation function between consecutive mutations at a given position in proteins, we observe separation of the evolutionary time-scales: at short time intervals families of proteins with similar sequences and structures are formed, while at long time intervals the families of structurally similar proteins that have low sequence similarity are formed. We discuss the evolutionary implications of our model. We provide a "profile" solution to our model and find agreement between predicted patterns of conserved amino acids and those actually observed in nature.

A minimalist model protein with multiple folding funnels

Kinetic and structural studies of wild-type proteins such as prions and amyloidogenic proteins provide suggestive evidence that proteins may adopt multiple long-lived states in addition to the native state. All of these states differ structurally because they lie far apart in configuration space, but their stability is not necessarily caused by cooperative (nucleation) effects. In this study, a minimalist model protein is designed to exhibit multiple long-lived states to explore the dynamics of the corresponding wild-type proteins. The minimalist protein is modeled as a 27-monomer sequence confined to a cubic lattice with three different monomer types. An order parameter-the winding index-is introduced to characterize the extent of folding. The winding index has several advantages over other commonly used order parameters like the number of native contacts. It can distinguish between enantiomers, its calculation requires less computational time than the number of native contacts, and reduced-dimensional landscapes can be developed when the native state structure is not known a priori. The results for the designed model protein prove by existence that the rugged energy landscape picture of protein folding can be generalized to include protein "misfolding" into long-lived states.

Population analyses of kinetic partitioning in protein folding

A simple lattice model of protein folding is studied in order to analyze the kinetic partitioning phenomena in the energy landscape perspective. By restricting the area of conformational space, it becomes possible to follow many Monte Carlo trajectories until they reach equilibrium. Alteration of population of trajectories is monitored and the relations between the energy landscape and kinetics are examined. Kinetic partitioning phenomena are categorized into different types in terms of characteristic time constants and partitioning ratio. In a specific partitioning process, refolding proceeds along the parallel pathways; the time constants have a temperature dependence similar to that observed in hen lysozyme. High-energy conformations are classified into groups according to the probability that the trajectories starting from those conformations will reach each energy valley. The partitioning ratio is determined by the way in which the conformational space is organized into these groups.

What is the role of non-native intermediates of beta-lactoglobulin in protein folding?

The mechanism of alpha-->beta transition in folding of beta-lactoglobulin is discussed based on free energy landscape analysis of a long lattice model. It is found that helical propensity of beta-lactoglobulin is driven by conformational entropy and is intrinsically coded in its native structure. We propose a view on a role of folding intermediate, which is "on-pathway" but rich in non-native structures. The present results suggest that the native structure topology plays an important role in alpha-->beta transition.

The role of hydrophobicity patterns in prion folding as revealed by recurrence quantification analysis of primary structure

It has been suggested that the number and strength of local contacts are the major factors governing conformation accessibility of model two ground-state polypeptide chains. This phenomenology has been posed as a possible factor influencing prion folding. To test this conjecture, recurrence quantification analysis was applied to two model 36mers, and the Syrian hamster prion protein. A unique divergence of the radius function for the recurrence quantification variable %DET of hydrophobicity patterns was observed for both 36mers, and in a critical region of the hamster prion protein. This divergence suggests a partition between strong short- and long-range hydrophobicity patterns, and may be an important factor in prion phenomenology, along with other global thermodynamic factors.

Thermodynamics of model prions and its implications for the problem of prion protein folding

Prion disease is caused by the propagation of a particle containing PrPSc, a misfolded form of the normal cellular prion protein (PrPC). PrPC can re-fold to form PrPSc with loss of alpha-helical structure and formation of extensive beta-sheet structure. Here, we model this prion folding problem with a simple, low-resolution lattice model of protein folding. If model proteins are allowed to re-fold upon dimerization, a minor proportion of them (up to approximately 17%) encrypts an alternative native state as a homodimer. The structures in this homodimeric native state re-arrange so that they are very different in conformation from the monomeric native state. We find that model proteins that are relatively less stable as monomers are more susceptible to the formation of alternative native states as homodimers. These results suggest that less-stable proteins have a greater need for a well-designed energy landscape for protein folding to overcome an increased chance of encrypting substantially different native conformations stabilized by multimeric interactions. This conceptual framework for aberrant folding should be relevant in Alzheimer's disease and other disorders associated with protein aggregation.