Computational inference in systems biology

Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem. The computational costs associated with repeatedly solving the ODEs are often high. Aimed at reducing this cost, new concepts using gradient matching have been proposed. This paper combines current adaptive gradient matching approaches, using Gaussian processes, with a parallel tempering scheme, and conducts a comparative evaluation with current methods used for parameter inference in ODEs

Greenhouse gas balance over thaw-freeze cycles in discontinuous zone permafrost

Peat in the discontinuous permafrost zone contains a globally significant reservoir of carbon that has undergone multiple permafrost-thaw cycles since the end of the mid-Holocene (~3700 years before present). Periods of thaw increase C decomposition rates which leads to the release of CO2 and CH4 to the atmosphere creating potential climate feedback. To determine the magnitude and direction of such feedback, we measured CO2 and CH4 emissions and modeled C accumulation rates and radiative fluxes from measurements of two radioactive tracers with differing lifetimes to describe the C balance of the peatland over multiple permafrost-thaw cycles since the initiation of permafrost at the site. At thaw features, the balance between increased primary production and higher CH4 emission stimulated by warmer temperatures and wetter conditions favors C sequestration and enhanced peat accumulation. Flux measurements suggest that frozen plateaus may intermittently (order of years to decades) act as CO2 sources depending on temperature and net ecosystem respiration rates, but modeling results suggest that—despite brief periods of net C loss to the atmosphere at the initiation of thaw—integrated over millennia, these sites have acted as net C sinks via peat accumulation. In greenhouse gas terms, the transition from frozen permafrost to thawed wetland is accompanied by increasing CO2 uptake that is partially offset by increasing CH4 emissions. In the short-term (decadal time scale) the net effect of this transition is likely enhanced warming via increased radiative C emissions, while in the long-term (centuries) net C deposition provides a negative feedback to climate warming

Limits and dynamics of stochastic neuronal networks with random heterogeneous delays

Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the delays distributions, a quenched or averaged propagation of chaos takes place in these networks, and that the network equations converge towards a delayed McKean-Vlasov equation with distributed delays. Our approach is mostly fitted to neuroscience applications. We instantiate in particular a classical neuronal model, the Wilson and Cowan system, and show that the obtained limit equations have Gaussian solutions whose mean and standard deviation satisfy a closed set of coupled delay differential equations in which the distribution of delays and the noise levels appear as parameters. This allows to uncover precisely the effects of noise, delays and coupling on the dynamics of such heterogeneous networks, in particular their role in the emergence of synchronized oscillations. We show in several examples that not only the averaged delay, but also the dispersion, govern the dynamics of such networks.Comment: Corrected misprint (useless stopping time) in proof of Lemma 1 and clarified a regularity hypothesis (remark 1

Thermal Impact on Spiking Properties in Hodgkin-Huxley Neuron with Synaptic Stimulus

The effect of environmental temperature on neuronal spiking behaviors is investigated by numerically simulating the temperature dependence of spiking threshold of the Hodgkin-Huxley neuron subject to synaptic stimulus. We find that the spiking threshold exhibits a global minimum in a "comfortable temperature" range where spike initiation needs weakest synaptic strength, indicating the occurrence of optimal use of synaptic transmission in neural system. We further explore the biophysical origin of this phenomenon in ion channel gating kinetics and also discuss its possible biological relevance in information processing in neural systems.Comment: 10 pages, 4 figure

New conditional symmetries and exact solutions of nonlinear reaction-diffusion-convection equations. II

In the first part of this paper math-ph/0612078, a complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It was shown that all the known results for reaction-diffusion equations with power diffusivities follow as particular cases from those obtained in math-ph/0612078 but not vise versa. In the second part the symmetries obtained in are successfully applied for constructing exact solutions of the relevant equations. In the particular case, new exact solutions of nonlinear reaction-diffusion-convection (RDC) equations arising in application and their natural generalizations are found

A propensity criterion for networking in an array of coupled chaotic systems

We examine the mutual synchronization of a one dimensional chain of chaotic identical objects in the presence of a stimulus applied to the first site. We first describe the characteristics of the local elements, and then the process whereby a global nontrivial behaviour emerges. A propensity criterion for networking is introduced, consisting in the coexistence within the attractor of a localized chaotic region, which displays high sensitivity to external stimuli,and an island of stability, which provides a reliable coupling signal to the neighbors in the chain. Based on this criterion we compare homoclinic chaos, recently explored in lasers and conjectured to be typical of a single neuron, with Lorenz chaos.Comment: 4 pages, 3 figure

The Shapes of Flux Domains in the Intermediate State of Type-I Superconductors

In the intermediate state of a thin type-I superconductor magnetic flux penetrates in a disordered set of highly branched and fingered macroscopic domains. To understand these shapes, we study in detail a recently proposed "current-loop" (CL) model that models the intermediate state as a collection of tense current ribbons flowing along the superconducting-normal interfaces and subject to the constraint of global flux conservation. The validity of this model is tested through a detailed reanalysis of Landau's original conformal mapping treatment of the laminar state, in which the superconductor-normal interfaces are flared within the slab, and of a closely-related straight-lamina model. A simplified dynamical model is described that elucidates the nature of possible shape instabilities of flux stripes and stripe arrays, and numerical studies of the highly nonlinear regime of those instabilities demonstrate patterns like those seen experimentally. Of particular interest is the buckling instability commonly seen in the intermediate state. The free-boundary approach further allows for a calculation of the elastic properties of the laminar state, which closely resembles that of smectic liquid crystals. We suggest several new experiments to explore of flux domain shape instabilities, including an Eckhaus instability induced by changing the out-of-plane magnetic field, and an analog of the Helfrich-Hurault instability of smectics induced by an in-plane field.Comment: 23 pages, 22 bitmapped postscript figures, RevTex 3.0, submitted to Phys. Rev. B. Higher resolution figures may be obtained by contacting the author

Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

Excerpt: Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation

Magnetic Field-Induced Condensation of Triplons in Han Purple Pigment BaCuSi2_2O6_6

Besides being an ancient pigment, BaCuSi$_2$O$_6$ is a quasi-2D magnetic insulator with a gapped spin dimer ground state. The application of strong magnetic fields closes this gap creating a gas of bosonic spin triplet excitations called triplons. The topology of the spin lattice makes BaCuSi$_2$O$_6$ an ideal candidate for studying the Bose-Einstein condensation of triplons as a function of the external magnetic field, which acts as a chemical potential. In agreement with quantum Monte Carlo numerical simulations, we observe a distinct lambda-anomaly in the specific heat together with a maximum in the magnetic susceptibility upon cooling down to liquid Helium temperatures.Comment: published on August 20, 200

Numerical Solution of Differential Equations by the Parker-Sochacki Method

A tutorial is presented which demonstrates the theory and usage of the Parker-Sochacki method of numerically solving systems of differential equations. Solutions are demonstrated for the case of projectile motion in air, and for the classical Newtonian N-body problem with mutual gravitational attraction.Comment: Added in July 2010: This tutorial has been posted since 1998 on a university web site, but has now been cited and praised in one or more refereed journals. I am therefore submitting it to the Cornell arXiv so that it may be read in response to its citations. See "Spiking neural network simulation: numerical integration with the Parker-Sochacki method:" J. Comput Neurosci, Robert D. Stewart & Wyeth Bair and http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2717378