Competition between protein folding and aggregation: A three-dimensional lattice-model simulation

The Early Phase of β2-Microglobulin Aggregation: Perspectives From Molecular Simulations

Protein β2-microglobulin is the causing agent of two amyloidosis, dialysis related amyloidosis (DRA), affecting the bones and cartilages of individuals with chronic renal failure undergoing long-term hemodialysis, and a systemic amyloidosis, found in one French family, which impairs visceral organs. The protein’s small size and its biomedical significance attracted the attention of theoretical scientists, and there are now several studies addressing its aggregation mechanism in the context of molecular simulations. Here, we review the early phase of β2-microglobulin aggregation, by focusing on the identification and structural characterization of monomers with the ability to trigger aggregation, and initial small oligomers (dimers, tetramers, hexamers etc.) formed in the so-called nucleation phase. We focus our analysis on results from molecular simulations and integrate our views with those coming from in vitro experiments to provide a broader perspective of this interesting field of research. We also outline directions for future computer simulation studies.

Theoretical Study of the Initial Stages of Self-Assembly of a Carboxysome's Facet

Bacterial microcompartments, BMCs, are organelles that exist within wide variety of bacteria and act as nanofactories. Among the different types of known BMCs, the carboxysome has been studied the most. The carboxysome plays an important role in the light-independent part of the photosynthesis process, where its icosahedral-like proteinaceous shell acts as a membrane that controls the transport of metabolites. Although a structural model exists for the carboxysome shell, it remains largely unknown how the shell proteins self-assemble. Understanding the self-assembly process can provide insights into how the shell affects the carboxysome's function and how it can be modified to create new functionalities, such as artificial nanoreactors and artificial protein membranes. Here, we describe a theoretical framework that employs Monte Carlo simulations with a coarse-grain potential that reproduces well the atomistic potential of mean force; employing this framework, we are able to capture the initial stages of the 2D self-assembly of CcmK2 hexamers, a major protein-shell component of the carboxysome's facet. The simulations reveal that CcmK2 hexamers self-assemble into clusters that resemble what was seen experimentally in 2D layers. Further analysis of the simulation results suggests that the 2D self-assembly of carboxysome's facets is driven by a nucleation-growth process, which in turn could play an important role in the hierarchical self-assembly of BMC shells in general.

On the spherical prototype of a complex dissipative late-stage formation seen in terms of least action Vojta-Natanson principle

The spherical prototype of a crystalline and/or disorderly formation may help in understanding the final stages of many complex biomolecular arrangements. These stages are important for both naturally organized simple biosystems, such as protein (or, other amphiphilic) aggregates in vivo, as well as certain their artificial counterparts, mimicking either in vitro or in silico their structure-property principal relationship. For our particular one-seed based realization of a protein crystal/aggregate late-stage nucleus grown from nearby fluctuating environment, it turns out that the (osmotic-type) pressure could be, due to local inhomogeneities, and their dynamics shown up in the double layer tightly surrounding the growing object, still an appreciably detectable quantity. This is due to the fact that a special-type generalized thermodynamic (Vojta-Natanson) momentum, subjected to the nucleus' surface, is manifested interchangeably, whereas the total energy of the solution in the double layer could not be such within the stationary regime explored. It is plausible since the double layer width, related to the object's surface, contributes ultimately, while based on the so-defined momentum's changes, to the pressure within this narrow flickering zone, while leaving the total energy fairly unchanged. From the hydrodynamic point of view, the system behaves quite trivially, since the circumventing flow should rather be of laminar, thus not-with-matter supplying, character.

Oscillatory molecular driving force for protein folding at high concentration: a molecular simulation

This paper presents a Langevin dynamics simulation that suggests a novel way to fold protein at high concentration, a fundamental issue in neurodegenerative diseases in vivo and the production of recombinant proteins in vitro. The simulation indicates that the folding of a coarse-grained beta-barrel protein at high concentration follows the "collapse-rearrangement" mechanism but it yields products of various forms, including single proteins in the native, misfolded, and uncollapsed forms and protein aggregates. Misfolded and uncollapased proteins are the "nucleus" of the aggregates that also encapsulate some correctly folded proteins (native proteins). An optimum hydrophobic interaction strength (epsilon*(p)) between the hydrophobic beads of the model protein, which results from a compromise between the kinetics of collapse and rearrangement, is identified for use in increasing the rate of folding over aggregating. Increased protein concentration hinders the structural transitions in both collapse and rearrangement and thus favors aggregation. A new method for protein folding at high concentration is proposed, which uses an oscillatory molecular driving force (epsilon*(p)) to promote the dissociation of aggregates in the low epsilon*(p) regime while promoting folding at a high epsilon*(p). The advantage of this method in enhancing protein folding while depressing aggregation is illustrated by a comparison with the methods based on direct dilution or applying a denaturant gradient.

In silico protein fragmentation reveals the importance of critical nuclei on domain reassembly

Protein complementation assays (PCAs) based on split protein fragments have become powerful tools that facilitate the study and engineering of intracellular protein-protein interactions. These assays are based on the observation that a given protein can be split into two inactive fragments and these fragments can reassemble into the original properly folded and functional structure. However, one experimentally observed limitation of PCA systems is that the folding of a protein from its fragments is dramatically slower relative to that of the unsplit parent protein. This is due in part to a poor understanding of how PCA design parameters such as split site position in the primary sequence and size of the resulting fragments contribute to the efficiency of protein reassembly. We used a minimalist on-lattice model to analyze how the dynamics of the reassembly process for two model proteins was affected by the location of the split site. Our results demonstrate that the balanced distribution of the "folding nucleus," a subset of residues that are critical to the formation of the transition state leading to productive folding, between protein fragments is key to their reassembly.

Protein aggregation in silico

Protein aggregation is a challenge to the successful manufacture of protein therapeutics; it can impose severe limitations on purification yields and compromise formulation stability. Advances in computer power, and the wealth of computational studies pertaining to protein folding, have facilitated the development of molecular simulation as a tool to investigate protein misfolding and aggregation. Here, we highlight the successes of protein aggregation studies carried out in silico, with a particular emphasis on studies related to biotechnology. To conclude, we discuss future prospects for the field, and identify several biotechnology-related problems that would benefit from molecular simulation.

Thermodynamics of folding and association of lattice-model proteins

Closely related to the "protein folding problem" is the issue of protein misfolding and aggregation. Protein aggregation has been associated with the pathologies of nearly 20 human diseases and presents serious difficulties during the manufacture of pharmaceutical proteins. Computational studies of multiprotein systems have recently emerged as a powerful complement to experimental efforts aimed at understanding the mechanisms of protein aggregation. We describe the thermodynamics of systems containing two lattice-model 64-mers. A parallel tempering algorithm abates problems associated with glassy systems and the weighted histogram analysis method improves statistical quality. The presence of a second chain has a substantial effect on single-chain conformational preferences. The melting temperature is substantially reduced, and the increase in the population of unfolded states is correlated with an increase in interactions between chains. The transition from two native chains to a non-native aggregate is entropically favorable. Non-native aggregates receive approximately 25% of their stabilizing energy from intraprotein contacts not found in the lowest-energy structure. Contact maps show that for non-native dimers, nearly 50% of the most probable interprotein contacts involve pairs of residues that form native contacts, suggesting that a domain-swapping mechanism is involved in self-association.

A Monte Carlo Simulation of the Aggregation, Phase-Separation, and Gelation of Model Globular Molecules

Monte Carlo computer simulation on a square 3-D lattice is used to model state behavior of globular copolymers. Two types of globular molecules were defined. One consisted of a single type of subunit (a homopolymer) while the second contained a core of strongly attractive subunits and an outer layer of less strongly attractive subunits (a heteropolymer). Systems of globules were simulated at varied volume fraction (V(F)) and reduced temperature (T(R)), and state diagrams were constructed. These state diagrams contained state boundaries defined by the V(F)/T(R) combinations at which the system formed a percolating network and at which the various component subunits in the globule unfolded. Simulated systems could exist in a number of states (between 4 and 7), depending on the V(F), T(R), whether the molecule was a homo- or heteroglobule and whether the globules were allowed to interact with each other or not. All systems exhibited a gelation/crossover line that resembled a lower critical solution temperature. All systems also exhibited a critical gelation concentration, above which a continuous network was formed. The critical gelation concentration varied between about 2-4% V(F) depending on the type of system. This is comparable to experimental critical gelation concentrations of in the region of 4% (w/w) for a range of associating polymers and biopolymers such as globular proteins and polysaccharides. Other states were formed which included one where elongated, fibril-like aggregated strands were formed, and a micelle-like aggregated state. The results are discussed in terms of the known state behavior of associating polymers and biopolymers (proteins and polysaccharides).

Effect of single-point sequence alterations on the aggregation propensity of a model protein

Sequences of contemporary proteins are believed to have evolved through a process that optimized their overall fitness, including their resistance to deleterious aggregation. Biotechnological processing may expose therapeutic proteins to conditions that are much more conducive to aggregation than those encountered in a cellular environment. An important task of protein engineering is to identify alternative sequences that would protect proteins when processed at high concentrations without altering their native structure associated with specific biological function. Our computational studies exploit parallel tempering simulations of coarse-grained model proteins to demonstrate that isolated amino acid residue substitutions can result in significant changes in the aggregation resistance of the protein in a crowded environment while retaining protein structure in isolation. A thermodynamic analysis of protein clusters subject to competing processes of folding and association shows that moderate mutations can produce effects similar to those caused by changes in system conditions, including temperature, concentration, and solvent composition, that affect the aggregation propensity. The range of conditions where a protein can resist aggregation can therefore be tuned by sequence alterations, although the protein generally may retain its generic ability for aggregation.

Spontaneous fibril formation by polyalanines; discontinuous molecular dynamics simulations

Fibrillary protein aggregates rich in beta-sheet structure have been implicated in the pathology of several neurodegenerative diseases. In this work, we investigate the formation of fibrils by performing discontinuous molecular dynamics simulations on systems containing 12 to 96 model Ac-KA(14)K-NH(2) peptides using our newly developed off-lattice, implicit-solvent, intermediate-resolution model, PRIME. We find that, at a low concentration, random-coil peptides assemble into alpha-helices at low temperatures. At intermediate concentrations, random-coil peptides assemble into alpha-helices at low temperatures and large beta-sheet structures at high temperatures. At high concentrations, the system forms beta-sheets over a wide range of temperatures. These assemble into fibrils above a critical temperature which decreases with concentration and exceeds the isolated peptide's folding temperature. At very high temperatures and all concentrations, the system is in a random-coil state. All of these results are in good qualitative agreement with those by Blondelle and co-workers on Ac-KA(14)K-NH(2) peptides. The fibrils observed in our simulations mimic the structural characteristics observed in experiments in terms of the number of sheets formed, the values of the intra- and intersheet separations, and the parallel peptide arrangement within each beta-sheet. Finally, we find that when the strength of the hydrophobic interaction between nonpolar side chains is high compared to the strength of hydrogen bonding, amorphous aggregates, rather than fibrillar aggregates, are formed.

Molecular simulation of protein aggregation

Computer simulation offers unique possibilities for investigating molecular-level phenomena difficult to probe experimentally. Drawing from a wealth of studies concerning protein folding, computational studies of protein aggregation are emerging. These studies have been successful in capturing aspects of aggregation known from experiment and are being used to refine experimental methods aimed at abating aggregation. Here we review molecular-simulation studies of protein aggregation conducted in our laboratory. Specific attention is devoted to issues with implications for biotechnology.

Model study of prionlike folding behavior in aggregated proteins

We investigate the folding behavior of protein sequences by numerically studying all sequences with a maximally compact lattice model through exhaustive enumeration. We get the prionlike behavior of protein folding. Individual proteins remaining stable in the isolated native state may change their conformations when they aggregate. We observe the folding properties as the interfacial interaction strength changes and find that the strength must be strong enough before the propagation of the most stable structures happens.

Protein-folding landscapes in multichain systems

Computational studies of proteins have significantly improved our understanding of protein folding. These studies are normally carried out by using chains in isolation. However, in many systems of practical interest, proteins fold in the presence of other molecules. To obtain insight into folding in such situations, we compare the thermodynamics of folding for a Miyazawa-Jernigan model 64-mer in isolation to results obtained in the presence of additional chains. The melting temperature falls as the chain concentration increases. In multichain systems, free-energy landscapes for folding show an increased preference for misfolded states. Misfolding is accompanied by an increase in interprotein interactions; however, near the folding temperature, the transition from folded chains to misfolded and associated chains is entropically driven. A majority of the most probable interprotein contacts are also native contacts, suggesting that native topology plays a role in early stages of aggregation.

The competition between protein folding and aggregation: off-lattice minimalist model studies

Protein aggregation has been associated with a number of human diseases, and is a serious problem in the manufacture of recombinant proteins. Of particular interest to the biotechnology industry is deleterious aggregation that occurs during the refolding of proteins from inclusion bodies. As a complement to experimental efforts, computer simulations of multi-chain systems have emerged as a powerful tool to investigate the competition between folding and aggregation. Here we report results from Langevin dynamics simulations of minimalist model proteins. Order parameters are developed to follow both folding and aggregation. By mapping natural units to real units, the simulations are shown to be carried out under experimentally relevant conditions. Data pertaining to the contacts formed during the association process show that multiple mechanisms for aggregation exist, but certain pathways are statistically preferred. Kinetic data show that there are multiple time scales for aggregation, although most association events take place at times much shorter than those required for folding. Last, we discuss results presented here as a basis for future work aimed at rational design of mutations to reduce aggregation propensity, as well as for development of small-molecular weight refolding enhancers.

Lattice models of peptide aggregation: Evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.

Oligomerization of amyloid Abeta16-22 peptides using hydrogen bonds and hydrophobicity forces

The 16-22 amino-acid fragment of the beta-amyloid peptide associated with the Alzheimer's disease, Abeta, is capable of forming amyloid fibrils. Here we study the aggregation mechanism of Abeta16-22 peptides by unbiased thermodynamic simulations at the atomic level for systems of one, three, and six Abeta16-22 peptides. We find that the isolated Abeta16-22 peptide is mainly a random coil in the sense that both the alpha-helix and beta-strand contents are low, whereas the three- and six-chain systems form aggregated structures with a high beta-sheet content. Furthermore, in agreement with experiments on Abeta16-22 fibrils, we find that large parallel beta-sheets are unlikely to form. For the six-chain system, the aggregated structures can have many different shapes, but certain particularly stable shapes can be identified.

Sampling the self-assembly pathways of KFFE hexamers

The formation of amyloid fibrils is often encountered in Alzheimer's disease, type II diabetes, and transmissible spongiform encephalopathies. In the last few years, however, mounting evidence has suggested that the soluble oligomers of amyloid-forming peptides are also cytotoxic agents. Understanding the early pathway steps of amyloid self-assembly at atomic detail might therefore be crucial for the development of specific inhibitors to prevent amyloidosis in humans. Using the activation-relaxation technique and a generic energy model, we study in detail the aggregation of a hexamer of KFFE peptide. Our simulations show that a monomer remains disordered, but that six monomers placed randomly in an open box self-associate to adopt, with various orientations, three possible distant low-energy structures. Two of these structures show a double-layer beta-sheet organization, in agreement with the structure of amyloid fibrils as observed by x-ray diffraction, whereas the third one consists of a barrel-like curved single-layer hexamer. Based on these results, we propose a bidirectional growth mode of amyloid fibril, involving alternate lateral and longitudinal growths.

Assembly and kinetic folding pathways of a tetrameric beta-sheet complex: molecular dynamics simulations on simplified off-lattice protein models

We have performed discontinuous molecular dynamic simulations of the assembly and folding kinetics of a tetrameric beta-sheet complex that contains four identical four-stranded antiparallel beta-sheet peptides. The potential used in the simulation is a hybrid Go-type potential characterized by the bias gap parameter g, an artificial measure of a model protein's preference for its native state, and the intermolecular contact parameter eta, which measures the ratio of intermolecular to intramolecular native attractions. The formation of the beta-sheet complex and its equilibrium properties strongly depend on the size of the intermolecular contact parameter eta. The ordered beta-sheet complex in the folded state and nonaligned beta-sheets or tangled chains in the misfolded state are distinguished by measuring the squared radius of gyration Rg2 and the fraction of native contacts Q. The folding yield for the folded state is high at intermediate values of eta, but is low at both small and large values of eta. The folded state at small eta is liquid-like, but is solid-like at both intermediate and large eta. The misfolded state at small eta contains nonaligned beta-sheets and tangled chains with poor secondary structure at large eta. Various folding pathways via dimeric and trimeric intermediates are observed, depending on eta. Comparison with experimental results on protein aggregation indicates that intermediate eta values are most appropriate for modeling fibril formation and small eta values are most appropriate for modeling the formation of amorphous aggregates.

Effect of rate of chemical or thermal renaturation on refolding and aggregation of a simple lattice protein

We used dynamic Monte Carlo simulation to investigate how changing the rate of chemical or thermal renaturation affects the folding and aggregation behavior of a system of simple, two-dimensional lattice protein molecules. Four renaturation methods were simulated: infinitely slow cooling; slow but finite cooling; quenching; and pulse renaturation. The infinitely slow cooling method, which is equivalent to dialysis or diafiltration, provides refolding yields that are relatively high and aggregates that are relatively small (mostly dimers or trimers). The slow but finite cooling method, which is equivalent to multiple-step dilution, provides refolding yields that are almost as high as those observed in the infinitely slow cooling case, but in a relatively short period of time. Quenching, which is equivalent to one-step dilution or quick quenching, is extremely slow and has low re- folding yields. A maximum appears in the refolding yield as a function of denaturant concentration in the simulation but disappears after a very long duration. Finally, the pulse renaturation method provides refolding yields that are substantially higher than those observed in the other three methods, even at high packing fractions. As in the early stages of quenching, there is a maximum in the refolding yield as a function of denaturant concentration when relatively large numbers of denatured chains are added to the refolding solution at each step.

A kinetic model for enzyme interfacial activity and stability: pa-hydroxynitrile lyase at the diisopropyl ether/water interface

A kinetic framework is developed to describe enzyme activity and stability in two-phase liquid-liquid systems. In particular, the model is applied to the enzymatic production of benzaldehyde from mandelonitrile by Prunus amygdalus hydroxynitrile lyase (pa-Hnl) adsorbed at the diisopropyl ether (DIPE)/aqueous buffer interface (pH = 5.5). We quantitatively describe our previously obtained experimental kinetic results (Hickel et al., 1999; 2001), and we successfully account for the aqueous-phase enzyme concentration dependence of product formation rates and the observed reaction rates at early times. Multilayer growth explains the early time reversibility of enzyme adsorption at the DIPE/buffer interface observed by both enzyme-activity and dynamic-interfacial-tension washout experiments that replace the aqueous enzyme solution with a buffer solution. The postulated explanation for the unusual stability of pa-Hnl adsorbed at the DIPE/buffer interface is attributed to a two-layer adsorption mechanism. In the first layer, slow conformational change from the native state leads to irreversible attachment and partial loss of catalytic activity. In the second layer, pa-Hnl is reversibly adsorbed without loss in catalytic activity. The measured catalytic activity is the combined effect of the deactivation kinetics of the first layer and of the adsorption kinetics of each layer. For the specific case of pa-Hnl adsorbed at the DIPE/buffer interface, this combined effect is nearly constant for several hours resulting in no apparent loss of catalytic activity. Our proposed kinetic model can be extended to other interfacially active enzymes and other organic solvents. Finally, we indicate how interfacial-tension lag times provide a powerful tool for rational solvent selection and enzyme engineering.

Clustering of solitons in weakly correlated wavefronts

We demonstrate theoretically and experimentally the spontaneous clustering of solitons in partially coherent wavefronts during the final stages of pattern formation initiated by modulation instability and noise.

Folding thermodynamics of model four-strand antiparallel beta-sheet proteins

The thermodynamic properties for three different types of off-lattice four-strand antiparallel beta-strand protein models interacting via a hybrid Go-type potential have been investigated. Discontinuous molecular dynamic simulations have been performed for different sizes of the bias gap g, an artificial measure of a model protein's preference for its native state. The thermodynamic transition temperatures are obtained by calculating the squared radius of gyration R(g)(2), the root-mean-squared pair separation fluctuation Delta(B), the specific heat C(v), the internal energy of the system E, and the Lindemann disorder parameter Delta(L). Despite these models' simplicity, they exhibit a complex set of protein transitions, consistent with those observed in experimental studies on real proteins. Starting from high temperature, these transitions include a collapse transition, a disordered-to-ordered globule transition, a folding transition, and a liquid-to-solid transition. The high temperature transitions, i.e., the collapse transition and the disordered-to-ordered globule transition, exist for all three beta-strand proteins, although the native-state geometry of the three model proteins is different. However the low temperature transitions, i.e., the folding transition and the liquid-to-solid transition, strongly depend on the native-state geometry of the model proteins and the size of the bias gap.