Hydrodynamic effects in proteins

Hydrodynamic Radii of Intrinsically Disordered Proteins: Fast Prediction by Minimum Dissipation Approximation and Experimental Validation

The diffusion coefficients of globular and fully unfolded proteins can be predicted with high accuracy solely from their mass or chain length. However, this approach fails for intrinsically disordered proteins (IDPs) containing structural domains. We propose a rapid predictive methodology for estimating the diffusion coefficients of IDPs. The methodology uses accelerated conformational sampling based on self-avoiding random walks and includes hydrodynamic interactions between coarse-grained protein subunits, modeled using the generalized Rotne-Prager-Yamakawa approximation. To estimate the hydrodynamic radius, we rely on the minimum dissipation approximation recently introduced by Cichocki et al. Using a large set of experimentally measured hydrodynamic radii of IDPs over a wide range of chain lengths and domain contributions, we demonstrate that our predictions are more accurate than the Kirkwood approximation and phenomenological approaches. Our technique may prove to be valuable in predicting the hydrodynamic properties of both fully unstructured and multidomain disordered proteins.

Impact of Hydrodynamic Interactions on the Kinetic Pathway of Protein Folding

Protein folding is a fundamental process critical to cellular function and human health, but it remains a grand challenge in biophysics. Hydrodynamic interaction (HI) plays a vital role in the self-organization of soft and biological materials, yet its role in protein folding is not fully understood despite folding occurring in a fluid environment. Here, we use the fluid particle dynamics method to investigate many-body hydrodynamic couplings between amino acid residues and fluid motion in the folding kinetics of a coarse-grained four-α-helices bundle protein. Our results reveal that HI helps select fast folding pathways to the native state without being kinetically trapped, significantly speeding up the folding kinetics compared to its absence. First, the directional flow along the protein backbone expedites protein collapse. Then, the incompressibility-induced squeezing flow effects retard the accumulation of non-native hydrophobic contacts, thus preventing the protein from being trapped in local energy minima during the conformational search of the native structure. We also find that the significance of HI in folding kinetics depends on temperature, with a pronounced effect under biologically relevant conditions. Our findings suggest that HI, particularly the short-range squeezing effect, may be crucial in avoiding protein misfolding.

The role of flow in the self-assembly of dragline spider silk proteins

Hydrodynamic flow in the spider duct induces conformational changes in dragline spider silk proteins (spidroins) and drives their assembly, but the underlying physical mechanisms are still elusive. Here we address this challenging multiscale problem with a complementary strategy of atomistic and coarse-grained molecular dynamics simulations with uniform flow. The conformational changes at the molecular level were analyzed for single-tethered spider silk peptides. Uniform flow leads to coiled-to-stretch transitions and pushes alanine residues into β sheet and poly-proline II conformations. Coarse-grained simulations of the assembly process of multiple semi-flexible block copolymers using multi-particle collision dynamics reveal that the spidroins aggregate faster but into low-order assemblies when they are less extended. At medium-to-large peptide extensions (50%-80%), assembly slows down and becomes reversible with frequent association and dissociation events, whereas spidroin alignment increases and alanine repeats form ordered regions. Our work highlights the role of flow in guiding silk self-assembly into tough fibers by enhancing alignment and kinetic reversibility, a mechanism likely relevant also for other proteins whose function depends on hydrodynamic flow.

Rotational Dynamics of a Protein under Shear Flow Studied by the Eckart Frame Formalism

Proteins are natural polymers that play an essential role in both living organisms and biotechnological applications. During certain bioprocessing steps, they can be exposed to significant mechanical stress induced by, for example, shear flow or sonication, resulting in reduced therapeutic efficacy, aggregation, or even a loss of activity. For this reason, there is a need to understand and determine the susceptibility of the protein activity to the experienced mechanical stress. To acquire this knowledge, it is necessary to study the rotational dynamics of the protein. Commonly, the rotational dynamics of soft molecules is interpreted based on a theoretical analysis performed in an inertial laboratory frame. However, the obtained angular velocity mixes pure rotations and vibrations with angular momentum, consequently lacking a clear dynamical interpretation. On the other hand, the use of the noninertial internal Eckart frame allows the determination of pure angular velocity as it minimizes the coupling between the rotational and vibrational degrees of freedom. In the present work, by conducting open-boundary molecular dynamics simulations and exploiting the Eckart frame formalism, we study the rotational dynamics of a small protein under the shear flow of various strengths. Our results show that the angular velocity increases nonlinearly with increasing shear rate. Furthermore, the protein gains vibrational angular momentum at higher shear rates, which is reflected in the higher angular velocity computed by employing the Eckart frame formalism and confirmed by analysis of the contributions to the total kinetic energy of the biomolecule.

Orientationally Averaged Version of the Rotne-Prager-Yamakawa Tensor Provides a Fast but Still Accurate Treatment of Hydrodynamic Interactions in Brownian Dynamics Simulations of Biological Macromolecules

The Brownian dynamics (BD) simulation technique is widely used to model the diffusive and conformational dynamics of complex systems comprising biological macromolecules. For the diffusive properties of macromolecules to be described correctly by BD simulations, it is necessary to include hydrodynamic interactions (HIs). When modeled at the Rotne-Prager-Yamakawa (RPY) level of theory, for example, the translational and rotational diffusion coefficients of isolated macromolecules can be accurately reproduced; when HIs are neglected, however, diffusion coefficients can be underestimated by an order of magnitude or more. The principal drawback to the inclusion of HIs in BD simulations is their computational expense, and several previous studies have sought to accelerate their modeling by developing fast approximations for the calculation of the correlated random displacements. Here, we explore the use of an alternative way to accelerate the calculation of HIs, i.e., by replacing the full RPY tensor with an orientationally averaged (OA) version which retains the distance dependence of the HIs but averages out their orientational dependence. We seek here to determine whether such an approximation can be justified in application to the modeling of typical proteins and RNAs. We show that the use of an OA-RPY tensor allows translational diffusion of macromolecules to be modeled with very high accuracy at the cost of rotational diffusion being underestimated by ∼25%. We show that this finding is independent of the type of macromolecule simulated and the level of structural resolution employed in the models. We also show, however, that these results are critically dependent on the inclusion of a non-zero term that describes the divergence of the diffusion tensor: when this term is omitted from simulations that use the OA-RPY model, unfolded macromolecules undergo rapid collapse. Our results indicate that the orientationally averaged RPY tensor is likely to be a useful, fast, approximate way of including HIs in BD simulations of intermediate-scale systems.

An Orientationally Averaged Version of the Rotne-Prager-Yamakawa Tensor Provides A Fast But Still Accurate Treatment Of Hydrodynamic Interactions In Brownian Dynamics Simulations Of Biological Macromolecules

The Brownian dynamics (BD) simulation technique is widely used to model the diffusive and conformational dynamics of complex systems comprising biological macromolecules. For the diffusive properties of macromolecules to be described correctly by BD simulations, it is necessary to include hydrodynamic interactions (HI). When modeled at the Rotne-Prager-Yamakawa (RPY) level of theory, for example, the translational and rotational diffusion coefficients of isolated macromolecules can be accurately reproduced; when HIs are neglected, however, diffusion coefficients can be underestimated by an order of magnitude or more. The principal drawback to the inclusion of HIs in BD simulations is their computational expense, and several previous studies have sought to accelerate their modeling by developing fast approximations for the calculation of the correlated random displacements. Here we explore the use of an alternative way to accelerate calculation of HIs, i.e., by replacing the full RPY tensor with an orientationally averaged (OA) version which retains the distance dependence of the HIs but averages out their orientational dependence. We seek here to determine whether such an approximation can be justified in application to the modeling of typical proteins and RNAs. We show that the use of an OA RPY tensor allows translational diffusion of macromolecules to be modeled with very high accuracy at the cost of rotational diffusion being underestimated by ∼25%. We show that this finding is independent of the type of macromolecule simulated and the level of structural resolution employed in the models. We also show, however, that these results are critically dependent on the inclusion of a non-zero term that describes the divergence of the diffusion tensor: when this term is omitted from simulations that use the OA RPY model, unfolded macromolecules undergo rapid collapse. Our results indicate that the orientationally averaged RPY tensor is likely to be a useful, fast approximate way of including HIs in BD simulations of intermediate-scale systems.

Effects of Sequence Composition, Patterning and Hydrodynamics on the Conformation and Dynamics of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs) perform diverse functions in cellular organization, transport and signaling. Unlike the well-defined structures of the classical natively folded proteins, IDPs and IDRs dynamically span large conformational and structural ensembles. This dynamic disorder impedes the study of the relationship between the amino acid sequences of the IDPs and their spatial structures and dynamics, with different experimental techniques often offering seemingly contradictory results. Although experimental and theoretical evidence indicates that some IDP properties can be understood based on their average biophysical properties and amino acid composition, other aspects of IDP function are dictated by the specifics of the amino acid sequence. We investigate the effects of several key variables on the dimensions and the dynamics of IDPs using coarse-grained polymer models. We focus on the sequence "patchiness" informed by the sequence and biophysical properties of different classes of IDPs-and in particular FG nucleoporins of the nuclear pore complex (NPC). We show that the sequence composition and patterning are well reflected in the global conformational variables such as the radius of gyration and hydrodynamic radius, while the end-to-end distance and dynamics are highly sequence-specific. We find that in good solvent conditions highly heterogeneous sequences of IDPs can be well mapped onto averaged minimal polymer models for the purpose of prediction of the IDPs dimensions and dynamic relaxation times. The coarse-grained simulations are in a good agreement with the results of atomistic MD. We discuss the implications of these results for the interpretation of the recent experimental measurements, and for the further applications of mesoscopic models of FG nucleoporins and IDPs more broadly.

Amyloidogenesis via interfacial shear in a containerless biochemical reactor aboard the International Space Station

Fluid interfaces significantly influence the dynamics of protein solutions, effects that can be isolated by performing experiments in microgravity, greatly reducing the amount of solid boundaries present, allowing air-liquid interfaces to become dominant. This investigation examined the effects of protein concentration on interfacial shear-induced fibrillization of insulin in microgravity within a containerless biochemical reactor, the ring-sheared drop (RSD), aboard the international space station (ISS). Human insulin was used as a model amyloidogenic protein for studying protein kinetics with applications to in situ pharmaceutical production, tissue engineering, and diseases such as Alzheimer’s, Parkinson’s, infectious prions, and type 2 diabetes. Experiments investigated three main stages of amyloidogenesis: nucleation studied by seeding native solutions with fibril aggregates, fibrillization quantified using intrinsic fibrillization rate after fitting measured solution intensity to a sigmoidal function, and gelation observed by detection of solidification fronts. Results demonstrated that in surface-dominated amyloidogenic protein solutions: seeding with fibrils induces fibrillization of native protein, intrinsic fibrillization rate is independent of concentration, and that there is a minimum fibril concentration for gelation with gelation rate and rapidity of onset increasing monotonically with increasing protein concentration. These findings matched well with results of previous studies within ground-based analogs.

NMR and dynamic light scattering give different diffusion information for short-living protein oligomers. Human serum albumin in water solutions of metal ions

Diffusive behavior of human serum albumin (HSA) in the presence of Mg²⁺ and Cu²⁺ ions was studied by pulsed field gradient nuclear magnetic resonance (PFG NMR) and dynamic light scattering (DLS). According to NMR data yielding measurements of HSA self-diffusion coefficient, a weighted average of the protein monomers and oligomers diffusion mobility in the presence of metal ions was observed. While the short-time collective diffusion measured by DLS showed one type of diffusing species in ion-free HSA solution and two molecular forms of HSA in the presence of metal ions. The light intensity correlation function analysis showed that HSA oligomers have a limited lifetime (lower limit is about 0.4 ms) intermediate between characteristic time scales of PFG NMR and DLS experiments. For a theoretical description of concentration dependence of HSA self- and collective diffusion coefficients, the phenomenological approach based on the frictional formalism of non-equilibrium thermodynamics was used (Vink theory), allowing analysis of the solvent-solute and solute-solute interactions in protein solutions. In the presence of metal ions, a significant increase of HSA protein-protein friction coefficient was shown. Based on theoretical analysis of collective diffusion data, the positive values of second virial coefficients A₂ for HSA monomers were obtained. The A₂ values were found to be higher for the HSA with metal ions compared with the ion-free HSA solution. This is due to the more pronounced contribution of repulsion in protein-protein interactions of HSA monomers in the presence of Mg²⁺ and Cu²⁺ ions.

Effects of Shear Rate and Protein Concentration on Amyloidogenesis via Interfacial Shear

The influence of hydrodynamics on protein fibrillization kinetics is relevant to biophysics, biochemical reactors, medicine, and disease. This investigation focused on the effects of interfacial shear on the fibrillization kinetics of insulin. Human insulin served as a model protein for studying shear-induced fibrillization with relevance to amyloid diseases such as Alzheimer's, Parkinson's, prions, and type 2 diabetes. Insulin solutions at different protein concentrations were subjected to shear flows with prescribed interfacial angular velocities using a knife-edge (surface) viscometer (KEV) operating in a laminar axisymmetric flow regime where inertia is significant. Fibrillization kinetics were quantified using intrinsic fibrillization rate and times (onset, half, and end) determined through spectroscopic measurement of monomer extinction curves and fitting to a sigmoidal function. Additionally, the occurrence of gelation was determined through macroscopic imaging and transient fibril microstructure was captured using fluorescence microscopy. The results showed that increasing interfacial shear rate produced a monotonic increase in intrinsic fibrillization rate and a monotonic decrease in fibrillization time. Protein concentration did not significantly impact the intrinsic fibrillization rate or times; however, a minimum fibril concentration for gelation was found. Protein microstructure showed increasing aggregation and plaque/cluster formation with time.

Coarse-Grain Modeling of Shear-Induced Binding between von Willebrand Factor and Collagen

Von Willebrand factor (VWF) is a large multimeric protein that aids in blood clotting. Near injury sites, hydrodynamic force from increased blood flow elongates VWF, exposing binding sites for platelets and collagen. To investigate VWF binding to collagen that is exposed on injured arterial surfaces, Brownian dynamics simulations are performed with a coarse-grain molecular model. Accounting for hydrodynamic interactions in the presence of a stationary surface, shear flow conditions are modeled. Binding between beads in coarse-grain VWF and collagen sites on the surface is described via reversible ligand-receptor-type bond formation, which is governed via Bell model kinetics. For conditions in which binding is energetically favored, the model predicts a high probability for binding at low shear conditions; this is counter to experimental observations but in agreement with what prior modeling studies have revealed. To address this discrepancy, an additional binding criterion that depends on the conformation of a submonomer feature in the model local to a given VWF binding site is implemented. The modified model predicts shear-induced binding, in very good agreement with experimental observations; this is true even for conditions in which binding is significantly favored energetically. Biological implications of the model modification are discussed in terms of mechanisms of VWF activity.

Fluctuating Finite Element Analysis (FFEA): A continuum mechanics software tool for mesoscale simulation of biomolecules

Fluctuating Finite Element Analysis (FFEA) is a software package designed to perform continuum mechanics simulations of proteins and other globular macromolecules. It combines conventional finite element methods with stochastic thermal noise, and is appropriate for simulations of large proteins and protein complexes at the mesoscale (length-scales in the range of 5 nm to 1 μm), where there is currently a paucity of modelling tools. It requires 3D volumetric information as input, which can be low resolution structural information such as cryo-electron tomography (cryo-ET) maps or much higher resolution atomistic co-ordinates from which volumetric information can be extracted. In this article we introduce our open source software package for performing FFEA simulations which we have released under a GPLv3 license. The software package includes a C ++ implementation of FFEA, together with tools to assist the user to set up the system from Electron Microscopy Data Bank (EMDB) or Protein Data Bank (PDB) data files. We also provide a PyMOL plugin to perform basic visualisation and additional Python tools for the analysis of FFEA simulation trajectories. This manuscript provides a basic background to the FFEA method, describing the implementation of the core mechanical model and how intermolecular interactions and the solvent environment are included within this framework. We provide prospective FFEA users with a practical overview of how to set up an FFEA simulation with reference to our publicly available online tutorials and manuals that accompany this first release of the package.

Hydrodynamic Steering in Protein Association Revisited: Surprisingly Minuscule Effects of Considerable Torques

We investigate the previously postulated hydrodynamic steering phenomenon, resulting from complication of molecular shapes, its magnitude and possible relevance for protein-ligand and protein-protein diffusional encounters, and the kinetics of diffusion-controlled association. We consider effects of hydrodynamic interactions in a prototypical model system consisting of a cleft enzyme and an elongated substrate, and real protein-protein complexes, that of barnase and barstar, and human growth hormone and its binding protein. The kinetics of diffusional encounters is evaluated on the basis of rigid-body Brownian dynamics simulations in which hydrodynamic interactions between molecules are modeled using the bead-shell method for detailed description of molecular surfaces, and the first-passage-time approach. We show that magnitudes of steering torques resulting from the hydrodynamic coupling of associating molecules, evaluated for the studied systems on the basis of the Stokes-Einstein type relations for arbitrarily shaped rigid bodies, are comparable with magnitudes of torques resulting from electrostatic interactions of binding partners. Surprisingly, however, unlike in the case of electrostatic torques that strongly affect the diffusional encounter, overall effects of hydrodynamic steering torques on the association kinetics, while clearly discernible in Brownian dynamics simulations, are rather minute. We explain this result as a consequence of the thermal agitation of the binding partners. Our finding is relevant for the general understanding of a wide spectrum of molecular processes in solution but there is also a more practical aspect to it if one considers the low level of shape detail of models that are usually employed to evaluate hydrodynamic interactions in particle-based Stokesian and Brownian dynamics simulations of multicomponent biomolecular systems. Results described in the current work justify, in part at least, such a low-resolution description.

Inducing protein aggregation by extensional flow

Relative to other extrinsic factors, the effects of hydrodynamic flow fields on protein stability and conformation remain poorly understood. Flow-induced protein remodeling and/or aggregation is observed both in Nature and during the large-scale industrial manufacture of proteins. Despite its ubiquity, the relationships between the type and magnitude of hydrodynamic flow, a protein's structure and stability, and the resultant aggregation propensity are unclear. Here, we assess the effects of a defined and quantified flow field dominated by extensional flow on the aggregation of BSA, β₂-microglobulin (β₂m), granulocyte colony stimulating factor (G-CSF), and three monoclonal antibodies (mAbs). We show that the device induces protein aggregation after exposure to an extensional flow field for 0.36-1.8 ms, at concentrations as low as 0.5 mg mL^-1 In addition, we reveal that the extent of aggregation depends on the applied strain rate and the concentration, structural scaffold, and sequence of the protein. Finally we demonstrate the in situ labeling of a buried cysteine residue in BSA during extensional stress. Together, these data indicate that an extensional flow readily unfolds thermodynamically and kinetically stable proteins, exposing previously sequestered sequences whose aggregation propensity determines the probability and extent of aggregation.

Perspective: On the importance of hydrodynamic interactions in the subcellular dynamics of macromolecules

An outstanding challenge in computational biophysics is the simulation of a living cell at molecular detail. Over the past several years, using Stokesian dynamics, progress has been made in simulating coarse grained molecular models of the cytoplasm. Since macromolecules comprise 20%-40% of the volume of a cell, one would expect that steric interactions dominate macromolecular diffusion. However, the reduction in cellular diffusion rates relative to infinite dilution is due, roughly equally, to steric and hydrodynamic interactions, HI, with nonspecific attractive interactions likely playing rather a minor role. HI not only serve to slow down long time diffusion rates but also cause a considerable reduction in the magnitude of the short time diffusion coefficient relative to that at infinite dilution. More importantly, the long range contribution of the Rotne-Prager-Yamakawa diffusion tensor results in temporal and spatial correlations that persist up to microseconds and for intermolecular distances on the order of protein radii. While HI slow down the bimolecular association rate in the early stages of lipid bilayer formation, they accelerate the rate of large scale assembly of lipid aggregates. This is suggestive of an important role for HI in the self-assembly kinetics of large macromolecular complexes such as tubulin. Since HI are important, questions as to whether continuum models of HI are adequate as well as improved simulation methodologies that will make simulations of more complex cellular processes practical need to be addressed. Nevertheless, the stage is set for the molecular simulations of ever more complex subcellular processes.

Effects of Spatially Dependent Mobilities on the Kinetics of the Diffusion-Controlled Association Derived from the First-Passage-Time Approach

Brownian dynamics (BD) simulations and the first-passage-time approach are applied to investigate diffusion-controlled association in a biologically relevant model system consisting of a fixed receptor with an elongated cavity and a capsule-like ligand that fits this cavity precisely. Before the binding at the receptor cavity, the ligand undergoes translational and rotational diffusion, either free or under the influence of electrostatic interactions with the receptor. The spatial dependence of the translational and rotational mobilities of the ligand resulting from its hydrodynamic interactions (HIs) with the receptor is accounted for in BD simulations, and an accurate numerical approach is applied for the evaluation of the spatially dependent mobility tensor of the ligand. Different magnitudes of electrostatic interactions (either attraction or repulsion) between the ligand and receptor are considered. The effective range of receptor-ligand electrostatic interactions is varied to account for their screening under different conditions of ionic strength. The effects of HIs on the kinetics of the diffusion-controlled association, evaluated for different electrostatic properties of binding partners, are thoroughly analyzed and discussed.

Protein Simulations in Fluids: Coupling the OPEP Coarse-Grained Force Field with Hydrodynamics

A novel simulation framework that integrates the OPEP coarse-grained (CG) model for proteins with the Lattice Boltzmann (LB) methodology to account for the fluid solvent at mesoscale level is presented. OPEP is a very efficient, water-free and electrostatic-free force field that reproduces at quasi-atomistic detail processes like peptide folding, structural rearrangements, and aggregation dynamics. The LB method is based on the kinetic description of the solvent in order to solve the fluid mechanics under a wide range of conditions, with the further advantage of being highly scalable on parallel architectures. The capabilities of the approach are presented, and it is shown that the strategy is effective in exploring the role of hydrodynamics on protein relaxation and peptide aggregation. The end result is a strategy for modeling systems of thousands of proteins, such as in the case of dense protein suspensions. The future perspectives of the multiscale approach are also discussed.

STABILITY OF A CYLINDRICAL SOLUTE-SOLVENT INTERFACE: EFFECT OF GEOMETRY, ELECTROSTATICS, AND HYDRODYNAMICS

The solute-solvent interface that separates biological molecules from their surrounding aqueous solvent characterizes the conformation and dynamics of such molecules. In this work, we construct a solvent fluid dielectric boundary model for the solvation of charged molecules and apply it to study the stability of a model cylindrical solute-solvent interface. The motion of the solute-solvent interface is defined to be the same as that of solvent fluid at the interface. The solvent fluid is assumed to be incompressible and is described by the Stokes equation. The solute is modeled simply by the ideal-gas law. All the viscous force, hydrostatic pressure, solute-solvent van der Waals interaction, surface tension, and electrostatic force are balanced at the solute-solvent interface. We model the electrostatics by Poisson's equation in which the solute-solvent interface is treated as a dielectric boundary that separates the low-dielectric solute from the high-dielectric solvent. For a cylindrical geometry, we find multiple cylindrically shaped equilibrium interfaces that describe polymodal (e.g., dry and wet) states of hydration of an underlying molecular system. These steady-state solutions exhibit bifurcation behavior with respect to the charge density. For their linearized systems, we use the projection method to solve the fluid equation and find the dispersion relation. Our asymptotic analysis shows that, for large wavenumbers, the decay rate is proportional to wavenumber with the proportionality half of the ratio of surface tension to solvent viscosity, indicating that the solvent viscosity does affect the stability of a solute-solvent interface. Consequences of our analysis in the context of biomolecular interactions are discussed.

Sliding of proteins non-specifically bound to DNA: Brownian dynamics studies with coarse-grained protein and DNA models

DNA binding proteins efficiently search for their cognitive sites on long genomic DNA by combining 3D diffusion and 1D diffusion (sliding) along the DNA. Recent experimental results and theoretical analyses revealed that the proteins show a rotation-coupled sliding along DNA helical pitch. Here, we performed Brownian dynamics simulations using newly developed coarse-grained protein and DNA models for evaluating how hydrodynamic interactions between the protein and DNA molecules, binding affinity of the protein to DNA, and DNA fluctuations affect the one dimensional diffusion of the protein on the DNA. Our results indicate that intermolecular hydrodynamic interactions reduce 1D diffusivity by 30%. On the other hand, structural fluctuations of DNA give rise to steric collisions between the CG-proteins and DNA, resulting in faster 1D sliding of the protein. Proteins with low binding affinities consistent with experimental estimates of non-specific DNA binding show hopping along the CG-DNA. This hopping significantly increases sliding speed. These simulation studies provide additional insights into the mechanism of how DNA binding proteins find their target sites on the genome.

The OPEP protein model: from single molecules, amyloid formation, crowding and hydrodynamics to DNA/RNA systems

The OPEP coarse-grained protein model has been applied to a wide range of applications since its first release 15 years ago. The model, which combines energetic and structural accuracy and chemical specificity, allows the study of single protein properties, DNA-RNA complexes, amyloid fibril formation and protein suspensions in a crowded environment. Here we first review the current state of the model and the most exciting applications using advanced conformational sampling methods. We then present the current limitations and a perspective on the ongoing developments.

Dynamic simulation of concentrated macromolecular solutions with screened long-range hydrodynamic interactions: algorithm and limitations

Hydrodynamic interactions exert a critical effect on the dynamics of macromolecules. As the concentration of macromolecules increases, by analogy to the behavior of semidilute polymer solutions or the flow in porous media, one might expect hydrodynamic screening to occur. Hydrodynamic screening would have implications both for the understanding of macromolecular dynamics as well as practical implications for the simulation of concentrated macromolecular solutions, e.g., in cells. Stokesian dynamics (SD) is one of the most accurate methods for simulating the motions of N particles suspended in a viscous fluid at low Reynolds number, in that it considers both far-field and near-field hydrodynamic interactions. This algorithm traditionally involves an O(N(3)) operation to compute Brownian forces at each time step, although asymptotically faster but more complex SD methods are now available. Motivated by the idea of hydrodynamic screening, the far-field part of the hydrodynamic matrix in SD may be approximated by a diagonal matrix, which is equivalent to assuming that long range hydrodynamic interactions are completely screened. This approximation allows sparse matrix methods to be used, which can reduce the apparent computational scaling to O(N). Previously there were several simulation studies using this approximation for monodisperse suspensions. Here, we employ newly designed preconditioned iterative methods for both the computation of Brownian forces and the solution of linear systems, and consider the validity of this approximation in polydisperse suspensions. We evaluate the accuracy of the diagonal approximation method using an intracellular-like suspension. The diffusivities of particles obtained with this approximation are close to those with the original method. However, this approximation underestimates intermolecular correlated motions, which is a trade-off between accuracy and computing efficiency. The new method makes it possible to perform large-scale and long-time simulation with an approximate accounting of hydrodynamic interactions.

Nanoprobing of misfolding and interactions of amyloid β 42 protein

The assembly of amyloid β (Aβ) proteins into nanostructures is currently considered a major pathway of Alzheimer's disease development, but the molecular mechanisms of this self-assembly process remains unclear. Recently, we showed that single-molecule AFM force spectroscopy (SMFS) is capable of probing the dynamics and interaction between Aβ40 peptides, and these studies allowed us to shed new light on transiently existing Aβ40 misfolding states. In this study, we applied the same SMFS approach to characterize the misfolding of Aβ42 peptide, the most toxic Aβ alloform. The quantitative analysis of SMFS data demonstrated that Aβ interaction leads to the formation of dimers with a lifetime in the range of a second. Interaction via C-terminal segments prevailed at pH 7, but interaction within the peptide center prevailed at acidic pH levels. The difference in the misfolding properties for Aβ40 and Aβ42 peptides and the mechanisms of amyloid nanoassembly are discussed.

FROM THE CLINICAL EDITOR

Despite decades of intense research, Alzheimer's disease still remains incurable. This novel study focuses on the assembly of amyloid β proteins into nanostructures, which is a key mechanism in Alzheimer's disease development. Single molecule atomic force spectroscopy is utilized to shed light on the molecular mechanisms of this self-assembly process.

Structure, folding dynamics, and amyloidogenesis of D76N β2-microglobulin: roles of shear flow, hydrophobic surfaces, and α-crystallin

Systemic amyloidosis is a fatal disease caused by misfolding of native globular proteins, which then aggregate extracellularly as insoluble fibrils, damaging the structure and function of affected organs. The formation of amyloid fibrils in vivo is poorly understood. We recently identified the first naturally occurring structural variant, D76N, of human β₂-microglobulin (β₂m), the ubiquitous light chain of class I major histocompatibility antigens, as the amyloid fibril protein in a family with a new phenotype of late onset fatal hereditary systemic amyloidosis. Here we show that, uniquely, D76N β₂m readily forms amyloid fibrils in vitro under physiological extracellular conditions. The globular native fold transition to the fibrillar state is primed by exposure to a hydrophobic-hydrophilic interface under physiological intensity shear flow. Wild type β₂m is recruited by the variant into amyloid fibrils in vitro but is absent from amyloid deposited in vivo. This may be because, as we show here, such recruitment is inhibited by chaperone activity. Our results suggest general mechanistic principles of in vivo amyloid fibrillogenesis by globular proteins, a previously obscure process. Elucidation of this crucial causative event in clinical amyloidosis should also help to explain the hitherto mysterious timing and location of amyloid deposition.

A molecule-centered method for accelerating the calculation of hydrodynamic interactions in Brownian dynamics simulations containing many flexible biomolecules

Inclusion of hydrodynamic interactions (HIs) is essential in simulations of biological macromolecules that treat the solvent implicitly if the macromolecules are to exhibit correct translational and rotational diffusion. The present work describes the development and testing of a simple approach aimed at allowing more rapid computation of HIs in coarse-grained Brownian dynamics simulations of systems that contain large numbers of flexible macromolecules. The method combines a complete treatment of intramolecular HIs with an approximate treatment of the intermolecular HIs which assumes that the molecules are effectively spherical; all of the HIs are calculated at the Rotne-Prager-Yamakawa level of theory. When combined with Fixman's Chebyshev polynomial method for calculating correlated random displacements, the proposed method provides an approach that is simple to program but sufficiently fast that it makes it computationally viable to include HIs in large-scale simulations. Test calculations performed on very coarse-grained models of the pyruvate dehydrogenase (PDH) E2 complex and on oligomers of ParM (ranging in size from 1 to 20 monomers) indicate that the method reproduces the translational diffusion behavior seen in more complete HI simulations surprisingly well; the method performs less well at capturing rotational diffusion but its discrepancies diminish with increasing size of the simulated assembly. Simulations of residue-level models of two tetrameric protein models demonstrate that the method also works well when more structurally detailed models are used in the simulations. Finally, test simulations of systems containing up to 1024 coarse-grained PDH molecules indicate that the proposed method rapidly becomes more efficient than the conventional BD approach in which correlated random displacements are obtained via a Cholesky decomposition of the complete diffusion tensor.

Process characterization of hCTLA4Ig production in transgenic rice cell cultures using a 3-L bioreactor

Most of the technical know-how and experience of bioreactor engineering is applicable to plant cell cultures. In this study, transgenic rice cell cultures using RAmy3D promoter were used for the production of human cytotoxic T-lymphocyte antigen 4-immunoglobulin (hCTLA4Ig). In process aspect, the rice cells during production phase are strongly influenced by hydrodynamic stresses, such as shear stress and bubble burst. Therefore, the effects of agitation and aeration rates on cell growth and hCTLA4Ig production were investigated in a 3-L multi-bioreactor. By increasing over 240 rpm, the detrimental effects on cell growth and hCTLA4Ig production were observed. At an aeration rate of 0.3 vvm, relative cell viability sharply decreased 2 days earlier than those of lower aeration rates. In addition, it was confirmed that the specific yields and the specific productivity at 0.3 vvm were superior to those values at 0.05 vvm. Overall, higher aeration rate showed the improved hCTLA4Ig production in combination experiment. High aeration rates in general, however, have an undesired effect as excessive aeration was found to negatively affect the quality of hCTLA4Ig. Consequently, the hydrodynamic conditions must be tightly regulated during bioreactor operation in order to enhance hCTLA4Ig productivity and quality in transgenic rice cell cultures.