47,696 research outputs found
Morphogenesis and proportionate growth: A finite element investigation of surface growth with coupled diffusion
Modeling the spontaneous evolution of morphology in natural systems and its
preservation by proportionate growth remains a major scientific challenge. Yet,
it is conceivable that if the basic mechanisms of growth and the coupled
kinetic laws that orchestrate their function are accounted for, a minimal
theoretical model may exhibit similar growth behaviors. The ubiquity of surface
growth, a mechanism by which material is added or removed on the boundaries of
the body, has motivated the development of theoretical models, which can
capture the diffusion-coupled kinetics that govern it. However, due to their
complexity, application of these models has been limited to simplified
geometries. In this paper, we tackle these complexities by developing a finite
element framework to study the diffusion-coupled growth and morphogenesis of
finite bodies formed on uniform and flat substrates. We find that in this
simplified growth setting, the evolving body exhibits a sequence of distinct
growth stages that are reminiscent of natural systems, and appear spontaneously
without any externally imposed regulation or coordination. The computational
framework developed in this work can serve as the basis for future models that
are able to account for growth in arbitrary geometrical settings, and can shed
light on the basic physical laws that orchestrate growth and morphogenesis in
the natural world
Effects of receptor clustering on ligand dissociation: Theory and simulations
Receptor-ligand binding is a critical first step in signal transduction and
the duration of the interaction can impact signal generation. In mammalian
cells, clustering of receptors may be facilitated by heterogeneous zones of
lipids, known as lipid rafts. In vitro experiments show that disruption of
rafts significantly alters the dissociation of fibroblast growth factor-2
(FGF-2) from heparan sulfate proteoglycans, co-receptors for FGF-2. In this
paper, we develop a continuum stochastic formalism in order to (i) study how
rebinding affects the dissociation of ligands from a planar substrate, and (ii)
address the question of how receptor clustering influences ligand rebinding. We
find that clusters reduce the effective dissociation rate dramatically when the
clusters are dense and the overall surface density of receptors is low. The
effect is much less pronounced in the case of high receptor density and shows
non-monotonic behavior with time. These predictions are verified via lattice
Monte Carlo simulations. Comparison with experimental results suggests that the
theory does not capture the complete biological system. We speculate that
additional co-operative mechanisms might be present in order to increase ligand
retention, and present one possible ``internal diffusion'' model.Comment: Expanded text and added figures, revised version to appear in
Biophys.
Pairing mean-field theory for the dynamics of dissociation of molecular Bose-Einstein condensates
We develop a pairing mean-field theory to describe the quantum dynamics of
the dissociation of molecular Bose-Einstein condensates into their constituent
bosonic or fermionic atoms. We apply the theory to one, two, and
three-dimensional geometries and analyze the role of dimensionality on the atom
production rate as a function of the dissociation energy. As well as
determining the populations and coherences of the atoms, we calculate the
correlations that exist between atoms of opposite momenta, including the column
density correlations in 3D systems. We compare the results with those of the
undepleted molecular field approximation and argue that the latter is most
reliable in fermionic systems and in lower dimensions. In the bosonic case we
compare the pairing mean-field results with exact calculations using the
positive- stochastic method and estimate the range of validity of the
pairing mean-field theory. Comparisons with similar first-principle simulations
in the fermionic case are currently not available, however, we argue that the
range of validity of the present approach should be broader for fermions than
for bosons in the regime where Pauli blocking prevents complete depletion of
the molecular condensate.Comment: 16 pages, 10 figure
Identification of complex biological network classes using extended correlation analysis
Modeling and analysis of complex biological networks necessitates suitable handling of data on a parallel scale. Using the IkB-NF-kB pathway model and a basis of sensitivity analysis, analytic methods are presented, extending correlation from the network kinetic reaction rates to that of the rate reactions. Alignment of correlated processed components, vastly outperforming correlation of the data source, advanced sets of biological classes possessing similar network activities. Additional construction generated a naturally structured, cardinally based system for component-specific investigation. The computationally driven procedures are described, with results demonstrating viability as mechanisms useful for fundamental oscillatory network activity investigation
Nonlinear Protein Degradation and the Function of Genetic Circuits
The functions of most genetic circuits require sufficient degrees of
cooperativity in the circuit components. While mechanisms of cooperativity have
been studied most extensively in the context of transcriptional initiation
control, cooperativity from other processes involved in the operation of the
circuits can also play important roles. In this study, we examine a simple
kinetic source of cooperativity stemming from the nonlinear degradation of
multimeric proteins. Ample experimental evidence suggests that protein subunits
can degrade less rapidly when associated in multimeric complexes, an effect we
refer to as cooperative stability. For dimeric transcription factors, this
effect leads to a concentration-dependence in the degradation rate because
monomers, which are predominant at low concentrations, will be more rapidly
degraded. Thus cooperative stability can effectively widen the accessible range
of protein levels in vivo. Through theoretical analysis of two exemplary
genetic circuits in bacteria, we show that such an increased range is important
for the robust operation of genetic circuits as well as their evolvability. Our
calculations demonstrate that a few-fold difference between the degradation
rate of monomers and dimers can already enhance the function of these circuits
substantially. These results suggest that cooperative stability needs to be
considered explicitly and characterized quantitatively in any systematic
experimental or theoretical study of gene circuits.Comment: 42 pages, 10 figure
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
Spectroscopy of Ultracold, Trapped Cesium Feshbach Molecules
We explore the rich internal structure of Cs_2 Feshbach molecules. Pure
ultracold molecular samples are prepared in a CO_2-laser trap, and a multitude
of weakly bound states is populated by elaborate magnetic-field ramping
techniques. Our methods use different Feshbach resonances as input ports and
various internal level crossings for controlled state transfer. We populate
higher partial-wave states of up to eight units of rotational angular momentum
(l-wave states). We investigate the molecular structure by measurements of the
magnetic moments for various states. Avoided level crossings between different
molecular states are characterized through the changes in magnetic moment and
by a Landau-Zener tunneling method. Based on microwave spectroscopy, we present
a precise measurement of the magnetic-field dependent binding energy of the
weakly bound s-wave state that is responsible for the large background
scattering length of Cs. This state is of particular interest because of its
quantum-halo character.Comment: 15 pages, 12 figures, 4 table
A Self-Consistent Model of the Circumstellar Debris Created by a Giant Hypervelocity Impact in the HD172555 System
Spectral modeling of the large infrared excess in the Spitzer IRS spectra of
HD 172555 suggests that there is more than 10^19 kg of sub-micron dust in the
system. Using physical arguments and constraints from observations, we rule out
the possibility of the infrared excess being created by a magma ocean planet or
a circumplanetary disk or torus. We show that the infrared excess is consistent
with a circumstellar debris disk or torus, located at approximately 6 AU, that
was created by a planetary scale hypervelocity impact. We find that radiation
pressure should remove submicron dust from the debris disk in less than one
year. However, the system's mid-infrared photometric flux, dominated by
submicron grains, has been stable within 4 percent over the last 27 years, from
IRAS (1983) to WISE (2010). Our new spectral modeling work and calculations of
the radiation pressure on fine dust in HD 172555 provide a self-consistent
explanation for this apparent contradiction. We also explore the unconfirmed
claim that 10^47 molecules of SiO vapor are needed to explain an emission
feature at 8 um in the Spitzer IRS spectrum of HD 172555. We find that unless
there are 10^48 atoms or 0.05 Earth masses of atomic Si and O vapor in the
system, SiO vapor should be destroyed by photo-dissociation in less than 0.2
years. We argue that a second plausible explanation for the 8 um feature can be
emission from solid SiO, which naturally occurs in submicron silicate "smokes"
created by quickly condensing vaporized silicate.Comment: Accepted to the Astrophysical Journa
Dissociative Autoionization in (1+2)-photon Above Threshold Excitation of H2 Molecules
We have theoretically studied the effect of dissociative autoionization on
the photoelectron energy spectrum in (1+2)-photon above threshold
ionization(ATI) of H2 molecules. We have considered excitation from the ground
state X-singlet-Sigma-g+(v=0,j) to the doubly excited autoionizing states of
singlet-Sigma-u+ and singlet-Pi-u+ symmetry, via the intermediate resonant
B-singlet-Sigma-u+(v=5,j) states. We have shown that the photoelectron energy
spectrum is oscillatory in nature and shows three distinct peaks above the
photoelectron energy 0.7 eV. This feature has been observed in a recent
experiment by Rottke et al, J. Phys. B, Vol. 30, p-4049 (1997).Comment: 11 pages and 4 figure
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