Bogdan Barz

Dimer formation enhances structural differences between amyloid β-protein (1-40) and (1-42): an explicit-solvent molecular dynamics study.

Amyloid -protein (A) is central to the pathology of Alzheimers disease. A 5% difference in the primary structure of the two predominant alloforms, A and A, results in distinct assembly pathways and toxicity properties. Discrete molecular dynamics (DMD) studies of A and A assembly resulted in alloform-specific oligomer size distributions consistent with experimental findings. Here, a large ensemble of DMD–derived A and A monomers and dimers was subjected to fully atomistic molecular dynamics (MD) simulations using the OPLS-AA force field combined with two water models, SPCE and TIP3P. The resulting all-atom conformations were slightly larger, less compact, had similar turn and lower -strand propensities than those predicted by DMD. Fully atomistic A and A monomers populated qualitatively similar free energy landscapes. In contrast, the free energy landscape of A dimers indicated a larger conformational variability in comparison to that of A dimers. A dimers were characterized by an increased flexibility in the N-terminal region D1-R5 and a larger solvent exposure of charged amino acids relative to A dimers. Of the three positively charged amino acids, R5 was the most and K16 the least involved in salt bridge formation. This result was independent of the water model, alloform, and assembly state. Overall, salt bridge propensities increased upon dimer formation. An exception was the salt bridge propensity of K28, which decreased upon formation of A dimers and was significantly lower than in A dimers. The potential relevance of the three positively charged amino acids in mediating the A oligomer toxicity is discussed in the light of available experimental data.

MUFOLD: A new solution for protein 3D structure prediction

There have been steady improvements in protein structure prediction during the past 2 decades. However, current methods are still far from consistently predicting structural models accurately with computing power accessible to common users. Toward achieving more accurate and efficient structure prediction, we developed a number of novel methods and integrated them into a software package, MUFOLD. First, a systematic protocol was developed to identify useful templates and fragments from Protein Data Bank for a given target protein. Then, an efficient process was applied for iterative coarse‐grain model generation and evaluation at the Cα or backbone level. In this process, we construct models using interresidue spatial restraints derived from alignments by multidimensional scaling, evaluate and select models through clustering and static scoring functions, and iteratively improve the selected models by integrating spatial restraints and previous models. Finally, the full‐atom models were evaluated using molecular dynamics simulations based on structural changes under simulated heating. We have continuously improved the performance of MUFOLD by using a benchmark of 200 proteins from the Astral database, where no template with >25% sequence identity to any target protein is included. The average root‐mean‐square deviation of the best models from the native structures is 4.28 Å, which shows significant and systematic improvement over our previous methods. The computing time of MUFOLD is much shorter than many other tools, such as Rosetta. MUFOLD demonstrated some success in the 2008 community‐wide experiment for protein structure prediction CASP8. Proteins 2010.

Calculating potentials of mean force and diffusion coefficients from nonequilibrium processes without Jarzynski’s equality

In general, the direct application of the Jarzynski equality (JE) to reconstruct potentials of mean force (PMFs) from a small number of nonequilibrium unidirectional steered molecular-dynamics (SMD) paths is hindered by the lack of sampling of extremely rare paths with negative dissipative work. Such trajectories that transiently violate the second law of thermodynamics are crucial for the validity of JE. As a solution to this daunting problem, we propose a simple and efficient method, referred to as the FR method, for calculating simultaneously both the PMF U(z) and the corresponding diffusion coefficient D(z) along a reaction coordinate z for a classical many-particle system by employing a small number of fast SMD pullings in both forward (F) and time reverse (R) directions, without invoking JE. By employing Crooks [Phys. Rev. E 61, 2361 (2000)] transient fluctuation theorem (that is more general than JE) and the stiff-spring approximation, we show that (i) the mean dissipative work W(d) in the F and R pullings is the same, (ii) both U(z) and W(d) can be expressed in terms of the easily calculable mean work of the F and R processes, and (iii) D(z) can be expressed in terms of the slope of W(d). To test its viability, the FR method is applied to determine U(z) and D(z) of single-file water molecules in single-walled carbon nanotubes (SWNTs). The obtained U(z) is found to be in very good agreement with the results from other PMF calculation methods, e.g., umbrella sampling. Finally, U(z) and D(z) are used as input in a stochastic model, based on the Fokker-Planck equation, for describing water transport through SWNTs on a mesoscopic time scale that in general is inaccessible to MD simulations.

Kinetic Monte Carlo and cellular particle dynamics simulations of multicellular systems.

Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of cell aggregates as bioink particles. Here we formulate two computer simulation methods: (1) a kinetic Monte Carlo (KMC) and (2) a cellular particle dynamics (CPD) method, which are capable of describing and predicting the shape evolution in time of three-dimensional multicellular systems during their biomechanical relaxation. Our work is motivated by the need of developing quantitative methods for optimizing postprinting structure formation in bioprinting-assisted tissue engineering. The KMC and CPD model parameters are determined and calibrated by using an original computational-theoretical-experimental framework applied to the fusion of two spherical cell aggregates. The two methods are used to predict the (1) formation of a toroidal structure through fusion of spherical aggregates and (2) cell sorting within an aggregate formed by two types of cells with different adhesivities.

A Kinetic Approach to the Sequence–Aggregation Relationship in Disease-Related Protein Assembly

It is generally accepted that oligomers of aggregating proteins play an important role in the onset of neurodegenerative diseases. While in silico aggregation studies of full length amyloidogenic proteins are computationally expensive, the assembly of short protein fragments derived from these proteins with similar aggregating properties has been extensively studied. In the present work, molecular dynamics simulations are performed to follow peptide aggregation on the microsecond time scale. By defining aggregation states, we identify transition networks, disconnectivity graphs, and first passage time distributions to describe the kinetics of the assembly process. This approach unravels differences in the aggregation into hexamers of two peptides with different primary structures. The first is GNNQQNY, a hydrophilic fragment from the prion protein Sup35, and the second is KLVFFAE, a fragment from amyloid-β protein, with a hydrophobic core delimited by two charged amino acids. The assembly of GNNQQNY suggests a mechanism of monomer addition, with a bias toward parallel peptide pairs and a gradual increase in the amount of β-strand content. For KLVFFAE, a mechanism involving dimers rather than monomers is revealed, involving a generally higher β-strand content and a transition toward a larger number of antiparallel peptide pairs during the rearrangement of the hexamer. The differences observed for the aggregation of the two peptides suggests the existence of a sequence-aggregation relationship.

COMPUTATIONAL MODELING OF TISSUE SELF-ASSEMBLY

Starting from the beginning of the 20th century, theoretical models of living tissues have evolved along two distinct conceptual lines. The first of these views considers the tissue as a set of discrete, interacting cells, whereas the other treats it as a continuum, and monitors cell densities instead of individual cells1. Here we briefly describe a few of these models. The interested reader can find further details in the cited literature.

Computational modeling of epithelial–mesenchymal transformations

An epithelial-mesenchymal transformation (EMT) involves alterations in cell-cell and cell-matrix adhesion, the detachment of epithelial cells from their neighbors, the degradation of the basal lamina and acquisition of mesenchymal phenotype. Here we present Monte Carlo simulations for a specific EMT in early heart development: the formation of cardiac cushions. Cell rearrangements are described in accordance with Steinbergs differential adhesion hypothesis, which states that cells possess a type-dependent adhesion apparatus and are sufficiently motile to give rise to the tissue conformation with the largest number of strong bonds. We also implement epithelial and mesenchymal cell proliferation, cell type change and extracellular matrix production by mesenchymal cells. Our results show that an EMT is promoted more efficiently by an increase in cell-substrate adhesion than by a decrease in cell-cell adhesion. In addition to cushion tissue formation, the model also accounts for the phenomena of matrix invasion and mesenchymal condensation. We conclude that in order to maintain epithelial integrity during EMT the number of epithelial cells must increase at a controlled rate. Our model predictions are in qualitative agreement with available experimental data.

Minimal model of self-assembly: emergence of diversity and complexity.

Molecular self-assembly is ubiquitous in nature, yet prediction of assembly pathways from fundamental interparticle interactions has yet to be achieved. Here, we introduce a minimal self-assembly model with two attractive and two repulsive beads bound into a tetrahedron. The model is associated with a single parameter η defined as the repulsive to attractive interaction ratio. We explore self-assembly pathways and resulting assembly morphologies for different η values by discrete molecular dynamics. Our results demonstrate that η governs the assembly dynamics and resulting assembly morphologies, revealing an unexpected diversity and complexity for 0.5 ≤ η < 1. One of the key processes that governs the assembly dynamics is assembly breakage, which emerges spontaneously at η > 0 with the breakage rate increasing with η. The observed assembly pathways display a broad variety of assembly structures characteristic of aggregation of amyloidogenic proteins, including quasi-spherical oligomers that coassemble into elongated protofibrils, followed by a conversion into ordered polymorphic fibril-like aggregates. We further demonstrate that η can be meaningfully mapped onto amyloidogenic protein sequences, with the majority of amyloidogenic proteins characterized by 0.5 ≤ η < 1. Prion proteins, which are known to form highly breakage–prone fibrils, are characterized by η > 1, consistent with the model predictions. Our model thus provides a theoretical basis for understanding the universal aspects of aggregation pathways of amyloidogenic proteins relevant to human disease. As the model is not specific to proteins, these findings represent an important step toward understanding and predicting assembly dynamics of not only proteins but also viruses, colloids, and nanoparticles.

Membrane curvature and surface area per lipid affect the conformation and oligomeric state of HIV-1 fusion peptide: a combined FTIR and MD simulation study.

Fourier-transformed infrared spectroscopy (FTIR) and molecular dynamics (MD) simulation results are presented to support our hypothesis that the conformation and the oligomeric state of the HIV-1 gp41 fusion domain or fusion peptide (gp41-FP) are determined by the membrane surface area per lipid (APL), which is affected by the membrane curvature. FTIR of the gp41-FP in the Aerosol-OT (AOT) reversed micellar system showed that as APL decreases from approximately 50 to 35 A2 by varying the AOT/water ratio, the FP changes from the monomeric alpha-helical to the oligomeric beta-sheet structure. MD simulations in POPE lipid bilayer systems showed that as the APL decreases by applying a negative surface tension, helical monomers start to unfold into turn-like structures. Furthermore, an increase in the applied lateral pressure during nonequilibrium MD simulations favored the formation of beta-sheet structure. These results provide better insight into the relationship between the structures of the gp41-FP and the membrane, which is essential in understanding the membrane fusion process. The implication of the results of this work on what is the fusogenic structure of the HIV-1 FP is discussed.

Folding of pig gastric mucin non-glycosylated domains: a discrete molecular dynamics study

Mucin glycoproteins consist of tandem-repeating glycosylated regions flanked by non-repetitive protein domains with little glycosylation. These non-repetitive domains are involved in polymerization of mucin and play an important role in the pH-dependent gelation of gastric mucin, which is essential for protecting the stomach from autodigestion. We examine folding of the non-repetitive sequence of PGM-2X (242 amino acids) and the von Willebrand factor vWF-C1 domain (67 amino acids) at neutral and low pH using discrete molecular dynamics (DMD) in an implicit solvent combined with a four-bead peptide model. Using the same implicit solvent parameters, folding of both domains is simulated at neutral and low pH. In contrast to vWF-C1, PGM-2X folding is strongly affected by pH as indicated by changes in the contact order, radius of gyration, free-energy landscape, and the secondary structure. Whereas the free-energy landscape of vWF-C1 shows a single minimum at both neutral and low pH, the free-energy landscape of PGM-2X is characterized by multiple minima that are more numerous and shallower at low pH. Detailed structural analysis shows that PGM-2X partially unfolds at low pH. This partial unfolding is facilitated by the C-terminal region GLU236-PRO242, which loses contact with the rest of the domain due to effective “mean-field” repulsion among highly positively charged N- and C-terminal regions. Consequently, at low pH, hydrophobic amino acids are more exposed to the solvent. In vWF-C1, low pH induces some structural changes, including an increased exposure of CYS at position 67, but these changes are small compared to those found in PGM-2X. For PGM-2X, the DMD-derived average β-strand propensity increases from 0.26 ± 0.01 at neutral pH to 0.38 ± 0.01 at low pH. For vWF-C1, the DMD-derived average β-strand propensity is 0.32 ± 0.02 at neutral pH and 0.35 ± 0.02 at low pH. The DMD-derived structural information provides insight into pH-induced changes in the folding of two distinct mucin domains and suggests plausible mechanisms of the aggregation/gelation of mucin.