Skip to main content
eScholarship
Open Access Publications from the University of California

Scholarly Works (85 results)

  • Article
  • Peer Reviewed
UC San Francisco Previously Published Works (2007)

We develop a computer model for how two different chemical catalysts in solution, A and B, could be driven to form AB complexes, based on the concentration gradients of a substrate or product that they share in common. If A's product is B's substrate, B will be attracted to A, mediated by a common resource that is not otherwise plentiful in the environment. By this simple physicochemical mechanism, chemical reactions could spontaneously associate to become chained together in solution. According to the model, such catalyst self-association processes may resemble other processes of "stochastic innovation," such as Darwinian evolution in biology, that involve a search among options, a selection among those options, and then a lock-in of that selection. Like Darwinian processes, this simple chemical process exhibits cooperation, competition, innovation, and a preference for consistency. This model may be useful for understanding organizational processes in prebiotic chemistry and for developing new kinds of self-organization in chemically reacting systems.

    Cover page: Stochastic innovation as a mechanism by which catalysts might self-assemble into chemical reaction networks.
    • Article
    • Peer Reviewed
    UC San Francisco Previously Published Works (2021)
    Myosin II is a biomolecular machine that is responsible for muscle contraction. Myosin II motors act cooperatively: during muscle contraction, multiple motors bind to a single actin filament and pull it against an external load, like people pulling on a rope in a tug-of-war. We model the dynamics of actomyosin filaments in order to study the evolution of motor-motor cooperativity. We find that filament backsliding-the distance an actin slides backward when a motor at the end of its cycle releases-is central to the speed and efficiency of muscle contraction. Our model predicts that this backsliding has been reduced through evolutionary adaptations to the motor's binding propensity, the strength of the motor's power stroke, and the force dependence of the motor's release from actin. These properties optimize the collective action of myosin II motors, which is not a simple sum of individual motor actions. The model also shows that these evolutionary variables can explain the speed-efficiency trade-off observed across different muscle tissues. This is an example of how evolution can tune the microscopic properties of individual proteins in order to optimize complex biological functions.
      Cover page: Evolution of mechanical cooperativity among myosin II motors
      • Article
      • Peer Reviewed
      UC San Francisco Previously Published Works (2016)
      Bacteria that are subjected to ribosome-inhibiting antibiotic drugs show an interesting behavior: Although the drug slows down cell growth, it also paradoxically increases the cell's concentration of ribosomes. We combine our earlier nonlinear model of the energy-biomass balance in undrugged Escherichia coli cells with Michaelis-Menten binding of drugs that inactivate ribosomes. Predictions are in good agreement with experiments on ribosomal concentrations and synthesis rates versus drug concentrations and growth rates. The model indicates that the added drug drives the cell to overproduce ribosomes, keeping roughly constant the level of ribosomes producing ribosomal proteins, an important quantity for cell growth. The model also predicts that ribosomal production rates should increase and then decrease with added drug. This model gives insights into the driving forces in cells and suggests new experiments.
        Cover page: Modeling the Overproduction of Ribosomes when Antibacterial Drugs Act on Cells
        • Article
        • Peer Reviewed
        UC San Francisco Previously Published Works (2007)

        It has been proposed that proteins fold by a process called "Zipping and Assembly" (Z&A). Zipping refers to the growth of local substructures within the chain, and assembly refers to the coming together of already-formed pieces. Our interest here is in whether Z&A is a general method that can fold most of sequence space, to global minima, efficiently. Using the HP model, we can address this question by enumerating full conformation and sequence spaces. We find that Z&A reaches the global energy minimum native states, even though it searches only a very small fraction of conformational space, for most sequences in the full sequence space. We find that Z&A, a mechanism-based search, is more efficient in our tests than the replica exchange search method. Folding efficiency is increased for chains having: (a) small loop-closure steps, consistent with observations by Plaxco et al. 1998;277;985-994 that folding rates correlate with contact order, (b) neither too few nor too many nucleation sites per chain, and (c) assembly steps that do not occur too early in the folding process. We find that the efficiency increases with chain length, although our range of chain lengths is limited. We believe these insights may be useful for developing faster protein conformational search algorithms.

          Cover page: Exploring zipping and assembly as a protein folding principle
          • Article
          • Peer Reviewed
          UC San Francisco Previously Published Works (2018)
          Liquid water is considered poorly understood. How are water's physical properties encoded in its molecular structure? We introduce a statistical mechanical model (CageWater) of water's hydrogen-bonding (HB) and Lennard-Jones (LJ) interactions. It predicts the energetic and volumetric and anomalous properties accurately. Yet, because the model is analytical, it is essentially instantaneous to compute. This model advances our understanding beyond current molecular simulations and experiments. Water has long been regarded as a "2-density liquid": a dense LJ liquid and a looser HB one. Instead, we find here a different antagonism underlying water structure-property relations: HBs in water-water pairs drive density, while HBs in cooperative cages drive openness. The balance shifts strongly with temperature and pressure. This model interprets the molecular structures underlying the liquid-liquid phase transition in supercooled water. It may have value in geophysics, biomolecular modeling, and engineering of materials for water purification and green chemistry.
            Cover page: Water Is a Cagey Liquid
            • Article
            • Peer Reviewed
            UC San Francisco Previously Published Works (2018)
            We investigate by Monte Carlo simulations density, diffusion, and structural anomalies of the simple two-dimensional Mercedes-Benz (MB) model of water, which is a very simple toy model for explaining the origin of water properties. MB water molecules are modeled as two-dimensional Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the MB logo. The model is in a way also a variance of silica-like models. Beside the known thermodynamic anomaly for the model we also found diffusion and structural anomalies and map out the cascade of density, structural, pair entropy, and diffusivity anomalies for MB model. The orientational order parameters with three and six-fold symmetry were determined and maximum for each one observed. The anomalies occur in hierarchy order, which is a slight variation of the hierarchy order in real water. The diffusion anomaly region is the innermost in the hierarchy while for water it is the density anomaly region.
              Cover page: Hierarchy of anomalies in the two-dimensional Mercedes-Benz model of water
              • Article
              • Peer Reviewed
              UC San Francisco Previously Published Works (2021)
              It is challenging to determine the structures of protein fibrils such as amyloids. In principle, Molecular Dynamics (MD) modeling can aid experiments, but normal MD has been impractical for these large multi-molecules. Here, we show that MELD accelerated MD (MELD x MD) can give amyloid structures from limited data. Five long-chain fibril structures are accurately predicted from NMR and Solid State NMR (SSNMR) data. Ten short-chain fibril structures are accurately predicted from more limited restraints information derived from the knowledge of strand directions. Although the present study only tests against structure predictions - which are the most detailed form of validation currently available - the main promise of this physical approach is ultimately in going beyond structures to also give mechanical properties, conformational ensembles, and relative stabilities.
                Cover page: MELD-accelerated molecular dynamics help determine amyloid fibril structures
                • Article
                • Peer Reviewed
                UC San Francisco Previously Published Works (2019)
                Many biomolecular machines need to be both fast and efficient. How has evolution optimized these machines along the tradeoff between speed and efficiency? We explore this question using optimizable dynamical models along coordinates that are plausible evolutionary degrees of freedom. Data on 11 motors and ion pumps are consistent with the hypothesis that evolution seeks an optimal balance of speed and efficiency, where any further small increase in one of these quantities would come at great expense to the other. For FoF1-ATPases in different species, we also find apparent optimization of the number of subunits in the c-ring, which determines the number of protons pumped per ATP synthesized. Interestingly, these ATPases appear to more optimized for efficiency than for speed, which can be rationalized through their key role as energy transducers in biology. The present modeling shows how the dynamical performance properties of biomolecular motors and pumps may have evolved to suit their corresponding biological actions.
                  Cover page: Opposing pressures of speed and efficiency guide the evolution of molecular machines
                  • Article
                  • Peer Reviewed
                  UC San Francisco Previously Published Works (2019)
                  How does a biomolecular machine achieve high speed at high efficiency? We explore optimization principles using a simple two-state dynamical model. With this model, we establish physical principles-such as the optimal way to distribute free-energy changes and barriers across the machine cycle-and connect them to biological mechanisms. We find that a machine can achieve high speed without sacrificing efficiency by varying its conformational free energy to directly link the downhill, chemical energy to the uphill, mechanical work and by splitting a large work step into more numerous, smaller substeps. Experimental evidence suggests that these mechanisms are commonly used by biomolecular machines. This model is useful for exploring questions of evolution and optimization in molecular machines.
                    Cover page: Mechanisms for achieving high speed and efficiency in biomolecular machines
                    • Article
                    • Peer Reviewed
                    UC San Francisco Previously Published Works (2018)
                    Proteins evolve at different rates. What drives the speed of protein sequence changes? Two main factors are a protein's folding stability and aggregation propensity. By combining the hydrophobic-polar (HP) model with the Zwanzig-Szabo-Bagchi rate theory, we find that: (i) Adaptation is strongly accelerated by selection pressure, explaining the broad variation from days to thousands of years over which organisms adapt to new environments. (ii) The proteins that adapt fastest are those that are not very stably folded, because their fitness landscapes are steepest. And because heating destabilizes folded proteins, we predict that cells should adapt faster when put into warmer rather than cooler environments. (iii) Increasing protein abundance slows down evolution (the substitution rate of the sequence) because a typical protein is not perfectly fit, so increasing its number of copies reduces the cell's fitness. (iv) However, chaperones can mitigate this abundance effect and accelerate evolution (also called evolutionary capacitance) by effectively enhancing protein stability. This model explains key observations about protein evolution rates.
                      Cover page: Protein evolution speed depends on its stability and abundance and on chaperone concentrations
                      Top