Lumpability Abstractions of Rule-based Systems

The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. In this paper we prove that this quotienting yields a sufficient condition for weak lumpability and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system. We illustrate the framework on a case study of the EGF/insulin receptor crosstalk.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Lithosphere versus asthenosphere mantle sources at the Big Pine Volcanic Field, California

[1] Here we report the first measurements of the H2O content of magmas and mantle xenoliths from the Big Pine Volcanic Field (BPVF), California, in order to constrain the melting process in the mantle, and the role of asthenospheric and lithospheric sources in this westernmost region of the Basin and Range Province, western USA. Melt inclusions trapped in primitive olivines (Fo82–90) record surprisingly high H2O contents (1.5 to 3.0 wt.%), while lithospheric mantle xenoliths record low H2O concentrations (whole rock <75 ppm). Estimates of the oxidation state of BPVF magmas, based on V partitioning in olivine, are also high (FMQ +1.0 to +1.5). Pressures and temperatures of equilibration of the BPVF melts indicate a shift over time, from higher melting temperatures (∼1320°C) and pressures (∼2 GPa) for magmas that are >500 ka, to cooler (∼1220°C) and shallower melting (∼1 GPa) conditions in younger magmas. The estimated depth of melting correlates strongly with some trace element ratios in the magmas (e.g., Ce/Pb, Ba/La), with deeper melts having values closer to upper mantle asthenosphere values, and shallower melts having values more typical of subduction zone magmas. This geochemical stratification is consistent with seismic observations of a shallow lithosphere-asthenosphere boundary (∼55 km depth). Combined trace element and cryoscopic melting models yield self-consistent estimates for the degree of melting (∼5%) and source H2O concentration (∼1000 ppm). We suggest two possible geodynamic models to explain small-scale convection necessary for magma generation. The first is related to the Isabella seismic anomaly, either a remnant of the Farallon Plate or foundered lithosphere. The second scenario is related to slow extension of the lithosphere

Force Balances in Systems of Cylindrical Polyelectrolytes

A detailed analysis is made of the model system of two parallel cylindrical polyelectrolytes which contain ionizable groups on their surfaces and are immersed in an ionic bathing medium. The interaction between the cylinders is examined by considering the interplay between repulsive electrostatic forces and attractive forces of electrodynamic origin. The repulsive force arises from the screened coulomb interaction between the surface charge distributions on the cylinders and has been treated by developing a solution to the linearized Poisson-Boltzmann equation. The boundary condition at the cylinder surfaces is determined as a self-consistent functional of the potential, with the input consisting of the density of ionizable groups and their dissociation constants. It is suggested that a reasonably accurate representation for the form of the attractive force can be obtained by performing a pairwise summation of the individual interatomic forces. A quantitative estimate is obtained using a Hamaker constant chosen on the basis of rigorous calculations on simpler systems. It is found that a balance exists between these repulsive and attractive forces at separations in good agreement with those observed in arrays of tobacco mosaic virus and in the A band myosin lattice in striated muscle. The behavior of the balance point as a function of the pH and ionic strength of the bathing medium closely parallels that seen experimentally

Physical chemistry : a molecular approach

As the first modern physical chemistry textbook to cover quantum mechanics before thermodynamics and kinetics, this book provides a contemporary approach to the study of physical chemistry. By beginning with quantum chemistry, students will learn the fundamental principles upon which all modern physical chemistry is built. The text includes a special set of "MathChapters" to review and summarize the mathematical tools required to master the material Thermodynamics is simultaneously taught from a bulk and microscopic viewpoint that enables the student to understand how bulk properties of materials are related to the properties of individual constituent molecules. This new text includes a variety of modern research topics in physical chemistry as well as hundreds of worked problems and examples.xxiii, 1360 pages : illustrations ; 26 c

Structure of Solvent-free Grafted Nanoparticles: Molecular Dynamics and Density-functional Theory

The structure of solvent-free oligomer-grafted nanoparticles has been investigated using molecular dynamics simulations and density-functional theory. At low temperatures and moderate to high oligomer lengths, the qualitative features of the core particle pair probability, structure factor, and the oligomer brush configuration obtained from the simulations can be explained by a density-functional theory that incorporates the configurational entropy of the space-filling oligomers. In particular, the structure factor at small wave numbers attains a value much smaller than the corresponding hardsphere suspension, the first peak of the pair distribution function is enhanced due to entropic attractions among the particles, and the oligomer brush expands with decreasing particle volume fraction to fill the interstitial space. At higher temperatures, the simulations reveal effects that differ from the theory and are likely caused by steric repulsions of the expanded corona chains.The authors would like to thank Professor Fernando Escobedo for suggesting the simulation model used in this work and for helpful discussions. This publication is based on work supported in part by Award No. KUS-C1-018-02, made by King Abdullah University of Science and Technology (KAUST). Additional support was provided by Grant No. DE-SC-0002128 from the (U.S.) Department of Energy (DOE), Office of Basic Energy Sciences and Grant No. CBET-1033155 from National Science Foundation (NSF)