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Open Access Publications from the University of California

Scholarly Works (5 results)

  • Article
  • Peer Reviewed
UC Santa Barbara Previously Published Works (2015)
Quantitative biology relies on the construction of accurate mathematical models, yet the effectiveness of these models is often predicated on making simplifying approximations that allow for direct comparisons with available experimental data. The Michaelis-Menten (MM) approximation is widely used in both deterministic and discrete stochastic models of intracellular reaction networks, owing to the ubiquity of enzymatic activity in cellular processes and the clear biochemical interpretation of its parameters. However, it is not well understood how the approximation applies to the discrete stochastic case or how it extends to spatially inhomogeneous systems. We study the behaviour of the discrete stochastic MM approximation as a function of system size and show that significant errors can occur for small volumes, in comparison with a corresponding mass-action system. We then explore some consequences of these results for quantitative modelling. One consequence is that fluctuation-induced sensitivity, or stochastic focusing, can become highly exaggerated in models that make use of MM kinetics even if the approximations are excellent in a deterministic model. Another consequence is that spatial stochastic simulations based on the reaction-diffusion master equation can become highly inaccurate if the model contains MM terms.
    • Article
    • Peer Reviewed
    UC Santa Barbara Previously Published Works (2014)
    The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity.
      Cover page: Local error estimates for adaptive simulation of the reaction–diffusion master equation via operator splitting
      • Article
      • Peer Reviewed
      UC Santa Barbara Previously Published Works (2022)
      Focal polarization is necessary for finely arranged cell-cell interactions. The yeast mating projection, with its punctate polarisome, is a good model system for this process. We explored the critical role of the polarisome scaffold protein Spa2 during yeast mating with a hypothesis motivated by mathematical modeling and tested by in vivo experiments. Our simulations predicted that two positive feedback loops generate focal polarization, including a novel feedback pathway involving the N-terminal domain of Spa2. We characterized the latter using loss-of-function and gain-of-function mutants. The N-terminal region contains a Spa2 Homology Domain (SHD) which is conserved from yeast to humans, and when mutated largely reproduced the spa2Δ phenotype. Our work together with published data show that the SHD domain recruits Msb3/4 that stimulates Sec4-mediated transport of Bud6 to the polarisome. There, Bud6 activates Bni1-catalyzed actin cable formation, recruiting more Spa2 and completing the positive feedback loop. We demonstrate that disrupting this loop at any point results in morphological defects. Gain-of-function perturbations partially restored focal polarization in a spa2 loss-of-function mutant without restoring localization of upstream components, thus supporting the pathway order. Thus, we have collected data consistent with a novel positive feedback loop that contributes to focal polarization during pheromone-induced polarization in yeast.
        Cover page: A positive feedback loop involving the Spa2 SHD domain contributes to focal polarization
        • Article
        • Peer Reviewed
        UC Irvine Previously Published Works (2020)
        Obesity is associated with risk of colorectal adenoma (CRA) and colorectal cancer. The signaling pathway activated by metformin (LKB1/AMPK/mTOR) is implicated in tumor suppression in ApcMin/+ mice via metformin-induced reduction in polyp burden, increased ratio of pAMPK/AMPK, decreased pmTOR/mTOR ratio, and decreased pS6Ser235/S6Ser235 ratio in polyps. We hypothesized that metformin would affect colorectal tissue S6Ser235 among obese patients with recent history of CRA. A phase IIa clinical biomarker trial was conducted via the U.S. National Cancer Institute-Chemoprevention Consortium. Nondiabetic, obese subjects (BMI ≥30) ages 35 to 80 with recent history of CRA were included. Subjects received 12 weeks of oral metformin 1,000 mg twice every day. Rectal mucosa biopsies were obtained at baseline and end-of-treatment (EOT) endoscopy. Tissue S6Ser235 and Ki-67 immunostaining were analyzed in a blinded fashion using Histo score (Hscore) analysis. Among 32 eligible subjects, the mean baseline BMI was 34.9. Comparing EOT to baseline tissue S6Ser235 by IHC, no significant differences were observed. Mean (SD) Hscore at baseline was 1.1 (0.57) and 1.1 (0.51) at EOT; median Hscore change was 0.034 (P = 0.77). Similarly, Ki-67 levels were unaffected by the intervention. The adverse events were consistent with metformin's known side-effect profile. Among obese patients with CRA, 12 weeks of oral metformin does not reduce rectal mucosa pS6 or Ki-67 levels. Further research is needed to determine what effects metformin has on the target tissue of origin as metformin continues to be pursued as a colorectal cancer chemopreventive agent.
          Cover page: A Phase IIa Trial of Metformin for Colorectal Cancer Risk Reduction among Individuals with History of Colorectal Adenomas and Elevated Body Mass Index
          • Article
          • Peer Reviewed
          UC Irvine Previously Published Works (2008)

          Preclinical studies of chemoprevention drugs given in combination at low doses show remarkable efficacy in preventing adenomas with little additional toxicities, suggesting a strategy to improve risk to benefit ratios for preventing recurrent adenomas. Three hundred seventy-five patients with history of resected (> or =3 mm) adenomas were randomly assigned to receive oral difluoromethylornithine (DFMO) 500 mg and sulindac 150 mg once daily or matched placebos for 36 months, stratified by use of low-dose aspirin (81 mg) at baseline and clinical site. Follow-up colonoscopy was done 3 years after randomization or off-study. Colorectal adenoma recurrence was compared among the groups with log-binomial regression. Comparing the outcome in patients receiving placebos to those receiving active intervention, (a) the recurrence of one or more adenomas was 41.1% and 12.3% (risk ratio, 0.30; 95% confidence interval, 0.18-0.49; P < 0.001); (b) 8.5% had one or more advanced adenomas, compared with 0.7% of patients (risk ratio, 0.085; 95% confidence interval, 0.011-0.65; P < 0.001); and (c) 17 (13.2%) patients had multiple adenomas (>1) at the final colonoscopy, compared with 1 (0.7%; risk ratio, 0.055; 0.0074-0.41; P < 0.001). Serious adverse events (grade > or =3) occurred in 8.2% of patients in the placebo group, compared with 11% in the active intervention group (P = 0.35). There was no significant difference in the proportion of patients reporting hearing changes from baseline. Recurrent adenomatous polyps can be markedly reduced by a combination of low oral doses of DFMO and sulindac and with few side effects.

            Cover page: Difluoromethylornithine plus sulindac for the prevention of sporadic colorectal adenomas: a randomized placebo-controlled, double-blind trial.
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