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Open Access Publications from the University of California

Scholarly Works (7 results)

  • Thesis
  • Peer Reviewed
UC Berkeley Electronic Theses and Dissertations (2010)

We developed theories and algorithms for two coarse-grained implicit solvent models that can be deployed within a multiscale framework to enable computational studies of large-scale protein-protein associations. The first model is a residue level alpha-carbon bead model intended for simulating proteins at close range during formation of encounter complexes. This model introduces a novel forcefield term to model directional backbone hydrogen bond semi-explicitly, as well as a fourth bead flavor in its sequence-dependence to better represent the spectrum of residue-residue attractive interactions. We showed that the introduction of the orientation-dependent hydrogen bonding term resulted in more stable and realistic alpha helices and beta sheets. In addition, the addition of a fourth bead flavor reduces energetic frustrations and competition from misfolded states. The overall model showed increased folding cooperativity, and a greater structural faithfulness to experimentally solved structures. The computational efficiency of the model has also permitted us to develop molecular models of the Alzheimer's A-beta 1-40 fibril to study nucleation and elongation, providing a good proof-of-concept and laying the foundation for applications to other protein-protein assembly processes. The second model is a protein level model intended for simulating proteins during diffusional search. It treats proteins as rigid bodies interacting solely through long-range electrostatics. We first described the theory and implementation of a novel method, Poisson-Boltzmann Semi-Analytical Method (PB-SAM), to model electrostatic interactions by efficiently solving the linearized Poisson-Boltzmann equation (PBE). This novel method combines advantages of analytical and boundary element methods by representing the macromolecular surface realistically as a collection of overlapping spheres, for which polarization charges can then be iteratively solved using analytical multipole method. Unlike finite difference solvers, PB-SAM is not constrained spatially by the box size, making it suitable for simulating dynamics. We showed that this method realizes better accuracy at reduced cost relative to either finite difference or boundary element PBE solvers. We derived expressions for force and torque that account for mutual polarization in both the zero and first order derivative of the surface charges, and incorporated the complete PB-SAM method into a protein level Brownian dynamics simulation algorithm. We demonstrated for the first time dynamic propagation of multiple Brownian particles with accurate accounting of mutual polarization effects for successive timesteps, using a model system of two monomers of brome mosaic virus (PDB code: 1YC6). While PB-SAM enable us to model mutual polarization effects in systems of hitherto inaccessible spatial dimensions, we can further reduce the computation time through parallelization, faster linear algebra operations, optimizing convergence criteria and polarization cutoffs, and approximating mutual polarization effects from analytical models. Finally, we discussed multiscale strategies to connect the two models described above for large-scale protein assembly studies. The two models can be employed successively in a novel nested variant of the Northrup-Allison-McCammon formalism to compute bi-molecular kinetics rates. The kinetic parameters can in turn be inputs to chemical master equations or stochastic simulations. Such multiscale modeling can be used to determine kinetics rates and the order of association, and help investigate how changing physical interactions can alter the association rates, and consequently control overall sequences of association.

    Cover page: Computational Modeling of Protein Interactions at Multiple Lengthscales
    • Article
    • Peer Reviewed
    UC Berkeley Previously Published Works (2013)
    We have recently introduced a method termed Poisson-Boltzmann semianalytical method (PB-SAM) for solving the linearized Poisson-Boltzmann equation for large numbers of arbitrarily shaped dielectric cavities with controlled precision. In this work we extend the applicability of the PB-SAM approach by deriving force and torque expressions that fully account for mutual polarization in both the zero- and first-order derivatives of the surface charges, that can now be embedded into a Brownian dynamics scheme to look at electrostatic-driven mesoscale assembly and kinetics. We demonstrate the capabilities of the PB-SAM approach by simulating the protein concentration effects on the bimolecular rate of association of barnase and barstar, under periodic boundary conditions and evaluated through mean first passage times. We apply PB-SAM to the pseudo-first-order reaction rate conditions in which either barnase or barstar are in great excess relative to the other protein (124:1). This can be considered a specific case in which the PB-SAM approach can be applied to crowding conditions in which crowders are not inert but can form interactions with other molecules.
      Cover page: Calculating the Bimolecular Rate of Protein–Protein Association with Interacting Crowders
      • Article
      • Peer Reviewed
      UC Berkeley Previously Published Works (2010)
      We derive a new numerical approach to solving the linearized Poisson Boltzmann equation (PBE) by representing the protein surface as a collection of spheres in which the surface charges can then be iteratively solved by new analytical multipole methods previously introduced by us [Lotan & Head-Gordon, 2006]. We show that our Poisson Boltzmann semi-analytical method, PB-SAM, realizes better accuracy, more flexible memory management, and at reduced cost relative to either finite difference or boundary element method PBE solvers. We provide two new benchmarks of PBE solution accuracy to test the numerical PBE solutions based on (1) arrays of up to hundreds of spherical low dielectric geometries with asymmetric charges in which mutual polarization is treated exactly, and (2) two overlapping spheres with increasing charge asymmetry by solving the PB-SAM method to very high pole order. We illustrate the strength of the PB-SAM approach by computing the potential profile of an array of 60 T1-particle forming monomers of the bromine mosaic virus.
        Cover page: New and Efficient Poisson−Boltzmann Solver for Interaction of Multiple Proteins
        • Article
        • Peer Reviewed
        UC Berkeley Previously Published Works (2014)
        Computational modeling at the atomistic and mesoscopic levels has undergone dramatic development in the past 10 years to meet the challenge of adequately accounting for the many-body nature of intermolecular interactions. At the heart of this challenge is the ability to identify the strengths and specific limitations of pairwise-additive interactions, to improve classical models to explicitly account for many-body effects, and consequently to enhance their ability to describe a wider range of reference data and build confidence in their predictive capacity. However, the corresponding computational cost of these advanced classical models increases significantly enough that statistical convergence of condensed phase observables becomes more difficult to achieve. Here we review a hierarchy of potential energy surface models used in molecular simulations for systems with many degrees of freedom that best meet the trade-off between accuracy and computational speed in order to define a sweet spot for a given scientific problem of interest.
          Cover page: Advanced Potential Energy Surfaces for Condensed Phase Simulation
          • Article
          • Peer Reviewed
          UC Berkeley Previously Published Works (2008)
          We develop a sequence based alpha-carbon model to incorporate a mean field estimate of the orientation dependence of the polypeptide chain that gives rise to specific hydrogen bond pairing to stabilize alpha-helices and beta-sheets. We illustrate the success of the new protein model in capturing thermodynamic measures and folding mechanism of proteins L and G. Compared to our previous coarse-grained model, the new model shows greater folding cooperativity and improvements in designability of protein sequences, as well as predicting correct trends for kinetic rates and mechanism for proteins L and G. We believe the model is broadly applicable to other protein folding and protein-protein co-assembly processes, and does not require experimental input beyond the topology description of the native state. Even without tertiary topology information, it can also serve as a mid-resolution protein model for more exhaustive conformational search strategies that can bridge back down to atomic descriptions of the polypeptide chain.
            Cover page: A coarse‐grained α‐carbon protein model with anisotropic hydrogen‐bonding
            • Article
            • Peer Reviewed
            UC Berkeley Previously Published Works (2017)
            We present the open source distributed software package Poisson-Boltzmann Analytical Method (PB-AM), a fully analytical solution to the linearized PB equation, for molecules represented as non-overlapping spherical cavities. The PB-AM software package includes the generation of outputs files appropriate for visualization using visual molecular dynamics, a Brownian dynamics scheme that uses periodic boundary conditions to simulate dynamics, the ability to specify docking criteria, and offers two different kinetics schemes to evaluate biomolecular association rate constants. Given that PB-AM defines mutual polarization completely and accurately, it can be refactored as a many-body expansion to explore 2- and 3-body polarization. Additionally, the software has been integrated into the Adaptive Poisson-Boltzmann Solver (APBS) software package to make it more accessible to a larger group of scientists, educators, and students that are more familiar with the APBS framework. © 2016 Wiley Periodicals, Inc.
              Cover page: PB‐AM: An open‐source, fully analytical linear poisson‐boltzmann solver
              • Article
              • Peer Reviewed
              UC Berkeley Previously Published Works (2008)
              [Figurre: see text]. Protein aggregation can be defined as the sacrifice of stabilizing intrachain contacts of the functional state that are replaced with interchain contacts to form non-functional states. The resulting aggregate morphologies range from amorphous structures without long-range order typical of nondisease proteins involved in inclusion bodies to highly structured fibril assemblies typical of amyloid disease proteins. In this Account, we describe the development and application of computational models for the investigation of nondisease and disease protein aggregation as illustrated for the proteins L and G and the Alzheimer's Abeta systems. In each case, we validate the models against relevant experimental observables and then expand on the experimental window to better elucidate the link between molecular properties and aggregation outcomes. Our studies show that each class of protein exhibits distinct aggregation mechanisms that are dependent on protein sequence, protein concentration, and solution conditions. Nondisease proteins can have native structural elements in the denatured state ensemble or rapidly form early folding intermediates, which offers avenues of protection against aggregation even at relatively high concentrations. The possibility that early folding intermediates may be evolutionarily selected for their protective role against unwanted aggregation could be a useful strategy for reengineering sequences to slow aggregation and increase folding yield in industrial protein production. The observed oligomeric aggregates that we see for nondisease proteins L and G may represent the nuclei for larger aggregates, not just for large amorphous inclusion bodies, but potentially as the seeds of ordered fibrillar aggregates, since most nondisease proteins can form amyloid fibrils under conditions that destabilize the native state. By contrast, amyloidogenic protein sequences such as Abeta 1-40,42 and the familial Alzheimer's disease (FAD) mutants favor aggregation into ordered fibrils once the free-energy barrier for forming a critical nucleus is crossed. However, the structural characteristics and oligomer size of the soluble nucleation species have yet to be determined experimentally for any disease peptide sequence, and the molecular mechanism of polymerization that eventually delineates a mature fibril is unknown. This is in part due to the limited experimental access to very low peptide concentrations that are required to characterize these early aggregation events, providing an opportunity for theoretical studies to bridge the gap between the monomer and fibril end points and to develop testable hypotheses. Our model shows that Abeta 1-40 requires as few as 6-10 monomer chains (depending on sequence) to begin manifesting the cross-beta order that is a signature of formation of amyloid filaments or fibrils assessed in dye-binding kinetic assays. The richness of the oligomeric structures and viable filament and fibril polymorphs that we observe may offer structural clues to disease virulence variations that are seen for the WT and hereditary mutants.
                Cover page: Contrasting Disease and Nondisease Protein Aggregation by Molecular Simulation
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