Ruxandra I. Dima

Emerging ideas on the molecular basis of protein and peptide aggregation.

Several neurodegenerative diseases are associated with the unfolding and subsequent fibrillization of proteins. Although neither the assembly mechanism nor the atomic structures of the amyloid fibrils are known, recent experimental and computational studies suggest that a few general principles that govern protein aggregation may exist. Analysis of the results of several important recent studies has led to a set of tentative ideas concerning the oligomerization of proteins and peptides. General rules have been described that may be useful in predicting regions of known proteins (prions and transthyretin) that are susceptible to fluctuations, which give rise to structures that can aggregate by the nucleation-growth mechanism. Despite large variations in the sequence-dependent polymerization kinetics of several structurally unrelated proteins, there appear to be only a few plausible scenarios for protein and peptide aggregation.

Revealing the bifurcation in the unfolding pathways of GFP by using single-molecule experiments and simulations

Nanomanipulation of biomolecules by using single-molecule methods and computer simulations has made it possible to visualize the energy landscape of biomolecules and the structures that are sampled during the folding process. We use simulations and single-molecule force spectroscopy to map the complex energy landscape of GFP that is used as a marker in cell biology and biotechnology. By engineering internal disulfide bonds at selected positions in the GFP structure, mechanical unfolding routes are precisely controlled, thus allowing us to infer features of the energy landscape of the wild-type GFP. To elucidate the structures of the unfolding pathways and reveal the multiple unfolding routes, the experimental results are complemented with simulations of a self-organized polymer (SOP) model of GFP. The SOP representation of proteins, which is a coarse-grained description of biomolecules, allows us to perform forced-induced simulations at loading rates and time scales that closely match those used in atomic force microscopy experiments. By using the combined approach, we show that forced unfolding of GFP involves a bifurcation in the pathways to the stretched state. After detachment of an N-terminal α-helix, unfolding proceeds along two distinct pathways. In the dominant pathway, unfolding starts from the detachment of the primary N-terminal β-strand, while in the minor pathway rupture of the last, C-terminal β-strand initiates the unfolding process. The combined approach has allowed us to map the features of the complex energy landscape of GFP including a characterization of the structures, albeit at a coarse-grained level, of the three metastable intermediates.

Exploring protein aggregation and self-propagation using lattice models: Phase diagram and kinetics

Many seemingly unrelated neurodegenerative disorders, such as amyloid and prion diseases, are associated with propagating fibrils whose structures are dramatically different from the native states of the corresponding monomers. This observation, along with the experimental demonstration that any protein can aggregate to form either fibrils or amorphous structures (inclusion bodies) under appropriate external conditions, suggest that there must be general principles that govern aggregation mechanisms. To probe generic aspects of prion‐like behavior we use the model of Harrison, Chan, Prusiner, and Cohen. In this model, aggregation of a structure, that is conformationally distinct from the native state of the monomer, occurs by three parallel routes. Kinetic partitioning, which leads to parallel assembly pathways, occurs early in the aggregation process. In all pathways transient unfolding precedes polymerization and self‐propagation. Chain polymerization is consistent with templated assembly, with the dimer being the minimal nucleus. The kinetic effciency of Rn−1 + G → Rn (R is the aggregation prone state and G is either U, the unfolded state, or N, the native state of the monomer) is increased when polymerization occurs in the presence of a “seed” (a dimer). These results support the seeded nucleated‐polymerization model of fibril formation in amyloid peptides. To probe generic aspects of aggregation in two‐state proteins, we use lattice models with side chains. The phase diagram in the (T,C) plane (T is the temperature and C is the polypeptide concentration) reveals a bewildering array of “phases” or structures. Explicit computations for dimers show that there are at least six phases including ordered structures and amorphous aggregates. In the ordered region of the phase diagram there are three distinct structures. We find ordered dimers (OD) in which each monomer is in the folded state and the interaction between the monomers occurs via a well‐defined interface. In the domain‐swapped structures a certain fraction of intrachain contacts are replaced by interchain contacts. In the parallel dimers the interface is stabilized by favorable intermolecular hydrophobic interactions. The kinetics of folding to OD shows that aggregation proceeds directly from U in a dynamically cooperative manner without populating partially structured intermediates. These results support the experimental observation that ordered aggregation in the two‐state folders U1A and CI2 takes place from U. The contrasting aggregation processes in the two models suggest that there are several distinct mechanisms for polymerization that depend not only on the polypeptide sequence but also on external conditions (such as C, T, pH, and salt concentration).

Size, shape, and flexibility of RNA structures.

Determination of sizes and flexibilities of RNA molecules is important in understanding the nature of packing in folded structures and in elucidating interactions between RNA and DNA or proteins. Using the coordinates of the structures of RNA in the Protein Data Bank we find that the size of the folded RNA structures, measured using the radius of gyration R(G), follows the Flory scaling law, namely, R(G)=5.5N(1/3) A, where N is the number of nucleotides. The shape of RNA molecules is characterized by the asphericity Delta and the shape S parameters that are computed using the eigenvalues of the moment of inertia tensor. From the distribution of Delta, we find that a large fraction of folded RNA structures are aspherical and the distribution of S values shows that RNA molecules are prolate (S>0). The flexibility of folded structures is characterized by the persistence length l(p). By fitting the distance distribution function P(r), that is computed using the coordinates of the folded RNA, to the wormlike chain model we extracted the persistence length l(p). We find that l(p) approximately 1.5N(0.33) A which might reflect the large separation between the free energies that stabilize secondary and tertiary structures. The dependence of l(p) on N implies that the average length of helices should increase as the size of RNA grows. We also analyze packing in the structures of ribosomes (30S, 50S, and 70S) in terms of R(G), Delta, S, and l(p). The 70S and the 50S subunits are more spherical compared to most RNA molecules. The globularity in 50S is due to the presence of an unusually large number (compared to 30S subunit) of small helices that are stitched together by bulges and loops. Comparison of the shapes of the intact 70S ribosome and the constituent particles suggests that folding of the individual molecules might occur prior to assembly.

Determination of network of residues that regulate allostery in protein families using sequence analysis

Allosteric interactions between residues that are spatially apart and well separated in sequence are important in the function of multimeric proteins as well as single‐domain proteins. This observation suggests that, among the residues that are involved in long‐range communications, mutation at one site should affect interactions at a distant site. By adopting a sequence‐based approach, we present an automated approach that uses a generalization of the familiar sequence entropy in conjunction with a coupled two‐way clustering algorithm, to predict the network of interactions that trigger allosteric interactions in proteins. We use the method to identify the subset of dynamically important residues in three families, namely, the small PDZ family, G protein–coupled receptors (GPCR), and the Lectins, which are cell‐adhesion receptors that mediate the tethering and rolling of leukocytes on inflamed endothelium. For the PDZ and GPCR families, our procedure predicts, in agreement with previous studies, a network containing a small number of residues that are involved in their function. Application to the Lectin family reveals a network of residues interspersed throughout the C‐terminal end of the structure that are responsible for binding to ligands. Based on our results and previous studies, we propose that functional robustness requires that only a small subset of distantly connected residues be involved in transmitting allosteric signals in proteins.

Mechanism of Fibrin(ogen) Forced Unfolding

Fibrinogen, upon enzymatic conversion to monomeric fibrin, provides the building blocks for fibrin polymer, the scaffold of blood clots and thrombi. Little has been known about the force-induced unfolding of fibrin(ogen), even though it is the foundation for the mechanical and rheological properties of fibrin, which are essential for hemostasis. We determined mechanisms and mapped the free energy landscape of the elongation of fibrin(ogen) monomers and oligomers through combined experimental and theoretical studies of the nanomechanical properties of fibrin(ogen), using atomic force microscopy-based single-molecule unfolding and simulations in the experimentally relevant timescale. We have found that mechanical unraveling of fibrin(ogen) is determined by the combined molecular transitions that couple stepwise unfolding of the γ chain nodules and reversible extension-contraction of the α-helical coiled-coil connectors. These findings provide important characteristics of the fibrin(ogen) nanomechanics necessary to understand the molecular origins of fibrin viscoelasticity at the fiber and whole clot levels.

Mechanical Transition from α-Helical Coiled Coils to β-Sheets in Fibrin(ogen)

We characterized the α-to-β transition in α-helical coiled-coil connectors of the human fibrin(ogen) molecule using biomolecular simulations of their forced elongation and theoretical modeling. The force (F)-extension (X) profiles show three distinct regimes: (1) the elastic regime, in which the coiled coils act as entropic springs (F < 100-125 pN; X < 7-8 nm); (2) the constant-force plastic regime, characterized by a force-plateau (F ≈ 150 pN; X ≈ 10-35 nm); and (3) the nonlinear regime (F > 175-200 pN; X > 40-50 nm). In the plastic regime, the three-stranded α-helices undergo a noncooperative phase transition to form parallel three-stranded β-sheets. The critical extension of the α-helices is 0.25 nm, and the energy difference between the α-helices and β-sheets is 4.9 kcal/mol per helical pitch. The soft α-to-β phase transition in coiled coils might be a universal mechanism underlying mechanical properties of filamentous α-helical proteins.

Probing the origin of tubulin rigidity with molecular simulations

Tubulin heterodimers are the building blocks of microtubules, a major component of the cytoskeleton, whose mechanical properties are fundamental for the life of the cell. We uncover the microscopic origins of the mechanical response in microtubules by probing features of the energy landscape of the tubulin monomers and tubulin heterodimer. To elucidate the structures of the unfolding pathways and reveal the multiple unfolding routes, we performed simulations of a self-organized polymer (SOP) model of tubulin. The SOP representation, which is a coarse-grained description of chains, allows us to perform force-induced simulations at loading rates and time scales that closely match those used in single-molecule experiments. We show that the forced unfolding of each monomer involves a bifurcation in the pathways to the stretched state. After the unfolding of the C-term domain, the unraveling continues either from the N-term domain or from the middle domain, depending on the monomer and the pathway. In contrast to the unfolding complexity of the monomers, the dimer unfolds according to only one route corresponding to the unraveling of the C-term domain and part of the middle domain of β-tubulin. We find that this surprising behavior is due to the viscoelastic properties of the interface between the monomers. We map precise features of the complex energy landscape of tubulin by surveying the structures of the various metastable intermediates, which, in the dimer case, are characterized only by changes in the β-tubulin monomer.

Sop-GPU: accelerating biomolecular simulations in the centisecond timescale using graphics processors.

Theoretical exploration of fundamental biological processes involving the forced unraveling of multimeric proteins, the sliding motion in protein fibers and the mechanical deformation of biomolecular assemblies under physiological force loads is challenging even for distributed computing systems. Using a Cα‐based coarse‐grained self organized polymer (SOP) model, we implemented the Langevin simulations of proteins on graphics processing units (SOP‐GPU program). We assessed the computational performance of an end‐to‐end application of the program, where all the steps of the algorithm are running on a GPU, by profiling the simulation time and memory usage for a number of test systems. The ∼90‐fold computational speedup on a GPU, compared with an optimized central processing unit program, enabled us to follow the dynamics in the centisecond timescale, and to obtain the force‐extension profiles using experimental pulling speeds (vf = 1–10 μm/s) employed in atomic force microscopy and in optical tweezers‐based dynamic force spectroscopy. We found that the mechanical molecular response critically depends on the conditions of force application and that the kinetics and pathways for unfolding change drastically even upon a modest 10‐fold increase in vf. This implies that, to resolve accurately the free energy landscape and to relate the results of single‐molecule experiments in vitro and in silico, molecular simulations should be carried out under the experimentally relevant force loads. This can be accomplished in reasonable wall‐clock time for biomolecules of size as large as 105 residues using the SOP‐GPU package. Proteins 2010;

Tubulin bond energies and microtubule biomechanics determined from nanoindentation in silico.

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral noncovalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physicochemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations in silico of a contiguous microtubule fragment. A close match between the simulated and experimental force–deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9 ± 0.4 kcal/mol) and longitudinal (14.9 ± 1.5 kcal/mol) tubulin–tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000–26,000 pN·nm2) support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed in silico nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblies.