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-$P$ 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