Cruise Report 64-S-5 Shrimp

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A Comparison of Bimolecular Reaction Models for Stochastic Reaction Diffusion Systems

Stochastic reaction-diffusion models have become an important tool in studying how both noise in the chemical reaction process and the spatial movement of molecules influences the behavior of biological systems. There are two primary spatially-continuous models that have been used in recent studies: the diffusion limited reaction model of Smoluchowski, and a second approach popularized by Doi. Both models treat molecules as points undergoing Brownian motion. The former represents chemical reactions between two reactants through the use of reactive boundary conditions, with two molecules reacting instantly upon reaching a fixed separation (called the reaction-radius). The Doi model uses reaction potentials, whereby two molecules react with a fixed probability per unit time, $\lambda$, when separated by less than the reaction radius. In this work we study the rigorous relationship between the two models. For the special case of a protein diffusing to a fixed DNA binding site, we prove that the solution to the Doi model converges to the solution of the Smoluchowski model as $\lambda \to \infty$, with a rigorous $O(\lambda^{-1/2 + \epsilon})$ error bound (for any fixed $\epsilon > 0$). We investigate by numerical simulation, for biologically relevant parameter values, the difference between the solutions and associated reaction time statistics of the two models. As the reaction-radius is decreased, for sufficiently large but fixed values of $\lambda$, these differences are found to increase like the inverse of the binding radius.Comment: 21 pages, 3 Figures, Fixed typo in titl

Uniform asymptotic approximation of diffusion to a small target: Generalized reaction models

The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the reactant diffuses. We develop uniform in time asymptotic expansions in the reaction radius of the full solution to the corresponding diffusion equations for two separate reactant-target interaction mechanisms: the Doi or volume reactivity model and the Smoluchowski-Collins-Kimball partial-absorption surface reactivity model. In the former, the reactant and target react with a fixed probability per unit time when within a specified separation. In the latter, upon reaching a fixed separation, they probabilistically react or the reactant reflects away from the target. Expansions of the solution to each model are constructed by projecting out the contribution of the first eigenvalue and eigenfunction to the solution of the diffusion equation and then developing matched asymptotic expansions in Laplace-transform space. Our approach offers an equivalent, but alternative, method to the pseudopotential approach we previously employed [Isaacson and Newby, Phys. Rev. E 88, 012820 (2013)PLEEE81539-375510.1103/PhysRevE.88.012820] for the simpler Smoluchowski pure-absorption reaction mechanism. We find that the resulting asymptotic expansions of the diffusion equation solutions are identical with the exception of one parameter: the diffusion-limited reaction rates of the Doi and partial-absorption models. This demonstrates that for biological systems in which the reaction radius is a small parameter, properly calibrated Doi and partial-absorption models may be functionally equivalent

An Unstructured Mesh Convergent Reaction-Diffusion Master Equation for Reversible Reactions

The convergent reaction-diffusion master equation (CRDME) was recently developed to provide a lattice particle-based stochastic reaction-diffusion model that is a convergent approximation in the lattice spacing to an underlying spatially-continuous particle dynamics model. The CRDME was designed to be identical to the popular lattice reaction-diffusion master equation (RDME) model for systems with only linear reactions, while overcoming the RDME's loss of bimolecular reaction effects as the lattice spacing is taken to zero. In our original work we developed the CRDME to handle bimolecular association reactions on Cartesian grids. In this work we develop several extensions to the CRDME to facilitate the modeling of cellular processes within realistic biological domains. Foremost, we extend the CRDME to handle reversible bimolecular reactions on unstructured grids. Here we develop a generalized CRDME through discretization of the spatially continuous volume reactivity model, extending the CRDME to encompass a larger variety of particle-particle interactions. Finally, we conclude by examining several numerical examples to demonstrate the convergence and accuracy of the CRDME in approximating the volume reactivity model.Comment: 35 pages, 9 figures. Accepted, J. Comp. Phys. (2018

Modeling genetic circuit behavior in transiently transfected mammalian cells

Binning cells by plasmid copy number is a common practice for analyzing transient transfection data. In many kinetic models of transfected cells, protein production rates are assumed to be proportional to plasmid copy number. The validity of this assumption in transiently transfected mammalian cells is not clear; models based on this assumption appear unable to reproduce experimental flow cytometry data robustly. We hypothesize that protein saturation at high plasmid copy number is a reason previous models break down and validate our hypothesis by comparing experimental data and a stochastic chemical kinetics model. The model demonstrates that there are multiple distinct physical mechanisms that can cause saturation. On the basis of these observations, we develop a novel minimal bin-dependent ODE model that assumes different parameters for protein production in cells with low versus high numbers of plasmids. Compared to a traditional Hill-function-based model, the bin-dependent model requires only one additional parameter, but fits flow cytometry input-output data for individual modules up to twice as accurately. By composing together models of individually fit modules, we use the bin-dependent model to predict the behavior of six cascades and three feed-forward circuits. The bin-dependent models are shown to provide more accurate predictions on average than corresponding (composed) Hill-function-based models and predictions of comparable accuracy to EQuIP, while still providing a minimal ODE-based model that should be easy to integrate as a subcomponent within larger differential equation circuit models. Our analysis also demonstrates that accounting for batch effects is important in developing accurate composed models.Accepted manuscrip

Radial velocities from the N2K Project: 6 new cold gas giant planets orbiting HD 55696, HD 98736, HD 148164, HD 203473, and HD 211810

The N2K planet search program was designed to exploit the planet-metallicity correlation by searching for gas giant planets orbiting metal-rich stars. Here, we present the radial velocity measurements for 378 N2K target stars that were observed with the HIRES spectrograph at Keck Observatory between 2004 and 2017. With this data set, we announce the discovery of six new gas giant exoplanets: a double-planet system orbiting HD 148164 ($M \sin i$ of 1.23 and 5.16 M$_{\rm JUP}$) and single planet detections around HD 55696 ($M \sin i$ = 3.87 M$_{\rm JUP}$), HD 98736 ($M \sin i$ = 2.33 M$_{\rm JUP}$), HD 203473 ($M \sin i$ = 7.8 M$_{\rm JUP}$), and HD 211810 ($M \sin i$ = 0.67 M$_{\rm JUP}$). These gas giant companions have orbital semi-major axes between 1.0 and 6.2 AU and eccentricities ranging from 0.13 to 0.71. We also report evidence for three gravitationally bound companions with $M \sin i$ between 20 to 30 M$_{\rm JUP}$, placing them in the mass range of brown dwarfs, around HD 148284, HD 214823, and HD 217850, and four low mass stellar companions orbiting HD 3404, HD 24505, HD 98630, and HD 103459. In addition, we present updated orbital parameters for 42 previously announced planets. We also report a nondetection of the putative companion HD 73256 b. Finally, we highlight the most promising candidates for direct imaging and astrometric detection, and find that many hot Jupiters from our sample could be detectable by state-of-the-art telescopes such as Gaia.Comment: Accepted by the Astronomical Journal. 75 pages, 49 figure