Stochastic Representations of Ion Channel Kinetics and Exact Stochastic Simulation of Neuronal Dynamics

In this paper we provide two representations for stochastic ion channel kinetics, and compare the performance of exact simulation with a commonly used numerical approximation strategy. The first representation we present is a random time change representation, popularized by Thomas Kurtz, with the second being analogous to a "Gillespie" representation. Exact stochastic algorithms are provided for the different representations, which are preferable to either (a) fixed time step or (b) piecewise constant propensity algorithms, which still appear in the literature. As examples, we provide versions of the exact algorithms for the Morris-Lecar conductance based model, and detail the error induced, both in a weak and a strong sense, by the use of approximate algorithms on this model. We include ready-to-use implementations of the random time change algorithm in both XPP and Matlab. Finally, through the consideration of parametric sensitivity analysis, we show how the representations presented here are useful in the development of further computational methods. The general representations and simulation strategies provided here are known in other parts of the sciences, but less so in the present setting.Comment: 39 pages, 6 figures, appendix with XPP and Matlab cod

Dynamic Potential-Ph Diagrams Application to Electrocatalysts for Water Oxidation

The construction and use of "dynamic potential-pH diagrams" (DPPDs), that are intended to extend the usefulness of thermodynamic Pourbaix diagrams to include kinetic considerations is described. As an example, DPPDs are presented for the comparison of electrocatalysts for water oxidation, i.e., the oxygen evolution reaction (OER), an important electrochemical reaction because of its key role in energy conversion devices and biological systems (water electrolyses, photoelectrochemical water splitting, plant photosynthesis). The criteria for obtaining kinetic data are discussed and a 3-D diagram, which shows the heterogeneous electron transfer kinetics of an electrochemical system as a function of pH and applied potential is presented. DPPDs are given for four catalysts: IrO(2), Co(3)O(4), Co(3)O(4) electrodeposited in a phosphate medium (Co-Pi) and Pt, allowing a direct comparison of the activity of different electrode materials over a broad range of experimental conditions (pH, potential, current density). In addition, the experimental setup and the factors affecting the accurate collection and presentation of data (e. g., reference electrode system, correction of ohmic drops, bubble formation) are discussed.Ministry of Education, University and Research PRIN 2008PF9TWZ, 2008N7CYL5Universita degli Studi di MilanoNational Science Foundation CHE-0808927Robert A. Welch Foundation F-0021Center for Electrochemistr

Formalizing Theories Of Development: A Fugue On The Orderliness Of Change

This chapter looks at developmental biology as performance. Each animal inherits score (the DNA), mechanisms for interpreting of the score, and mechanisms for improvisation should the score be deficient. Developmental causation is found to be both upwards from the genome, downward from the environment, and laterally between cells. Developmental plasticity, organicism, phenotypic heterogeneity, symbiotic co-development, and cytoplasmic localization are each examples of causation from the environment downward. Stereocomplementary relationships are the key components of most developmental interactions. These interactions can be placed into a formal language of graph theory. Morphogenesis can be depicted in the general structure, where nouns cover tissues, molecules and networks and verbs describe processes such as moves, differentiates, grows and apoptoses. This manner of depicting development emphasizes the distributed nature of causality in morphogenesis and can be annotated with associated information or IDs (e.g. cell types, publications, gene-expression data) that link to external online resources that may be regularly updated. This graph approach portrays dynamic processes as the drivers of developmental momentum, and, since the same processes are used many times during development, they can be viewed as modules whose underlying networks are genomic subroutines

The regions of the sequence most exposed to the solvent within the amyloidogenic state of a protein initiate the aggregation process.

Formation of misfolded aggregates is an essential part of what proteins can do. The process of protein aggregation is central to many human diseases and any aggregating event needs to be prevented within a cell and in protein design. In order to aggregate, a protein needs to unfold its native state, at least partially. The conformational state that is prone to aggregate is difficult to study, due to its aggregating potential and heterogeneous nature. Here, we use a systematic approach of limited proteolysis, in combination with electrospray ionisation mass spectrometry, to investigate the regions that are most flexible and solvent-exposed within the native, ligand-bound and amyloidogenic states of muscle acylphosphatase (AcP), a protein previously shown to form amyloid fibrils in the presence of trifluoroethanol. Seven proteases with different degrees of specificity have been used for this purpose. Following exposure to the aggregating conditions, a number of sites along the sequence of AcP become susceptible to proteolytic digestion. The pattern of proteolytic cleavages obtained under these conditions is considerably different from that of the native and ligand-bound conformations and includes a portion within the N-terminal tail of the protein (residues 6-7), the region of the sequence 18-23 and the position 94 near the C terminus. There is a significant overlap between the regions of the sequence found to be solvent-exposed from the present study and those previously identified to be critical in the rate-determining steps of aggregation from protein engineering approaches. This indicates that a considerable degree of solvent exposure is a feature of the portions of a protein that initiate the process of aggregation

Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media

To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the finite volume method, etc. All these methods have various advantages and drawbacks. The amplification of seismic waves in surface soil layers is mainly due to the velocity contrast between these layers and, possibly, to topographic effects around crests and hills. The influence of the geometry of alluvial basins on the amplification process is also know to be large. Nevertheless, strong heterogeneities and complex geometries are not easy to take into account with all numerical methods. 2D/3D models are needed in many situations and the efficiency/accuracy of the numerical methods in such cases is in question. Furthermore, the radiation conditions at infinity are not easy to handle with finite differences or finite/spectral elements whereas it is explicitely accounted in the Boundary Element Method. Various absorbing layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the spurious wave reflections especially in some difficult cases such as shallow numerical models or grazing incidences. Finally, strong earthquakes involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behaviour of soils and simultaneously investigate seismic wave propagation in complex 2D/3D geological structures! Recent advances in numerical formulations and constitutive models in such complex situations are presented and discussed in this paper. A crucial issue is the availability of the field/laboratory data to feed and validate such models.Comment: of International Journal Geomechanics (2010) 1-1

Abundances in Stars from the Red Giant Branch Tip to the Near Main Sequence in M71: II. Iron Abundance

We present [Ffe/H] abundance results that involve a sample of stars with a wide range in luminosity from luminous giants to stars near the turnoff in a globular cluster. Our sample of 25 stars in M71 includes 10 giant stars more luminous than the RHB, 3 horizontal branch stars, 9 giant stars less luminous than the RHB, and 3 stars near the turnoff. We analyzed both Fe I and Fe II lines in high dispersion spectra observed with HIRES at the W. M. Keck Observatory. We find that the [Fe/H] abundances from both Fe I and Fe II lines agree with each other and with earlier determinations. Also the [Fe/H] obtained from Fe I and Fe II lines is constant within the rather small uncertainties for this group of stars over the full range in Teff and luminosity, suggesting that NLTE effects are negligible in our iron abundance determination. In this globular cluster, there is no difference among the mean [Fe/H] of giant stars located at or above the RHB, RHB stars, giant stars located below the RHB and stars near the turnoff.Comment: Minor changes to conform to version accepted for publication, with several new figures (Paper 2 of a pair