On a model mechanism for the spatial patterning of teeth primordia in the Alligator

We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator,Alligator mississippiensis. Detailed embryological studies by Westergaard & Ferguson (1986, 1987, 1990) show that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. Based on biological data we develop a reaction-diffusion mechanism, which crucially includes domain growth. The model can reproduce the spatial pattern development of the first seven teeth primordia in the lower half jaw ofA. mississippiensis. The results for the precise spatio-temporal sequence compare well with detailed developmental experiments

Magnetic Flux Braiding: Force-Free Equilibria and Current Sheets

We use a numerical nonlinear multigrid magnetic relaxation technique to investigate the generation of current sheets in three-dimensional magnetic flux braiding experiments. We are able to catalogue the relaxed nonlinear force-free equilibria resulting from the application of deformations to an initially undisturbed region of plasma containing a uniform, vertical magnetic field. The deformations are manifested by imposing motions on the bounding planes to which the magnetic field is anchored. Once imposed the new distribution of magnetic footpoints are then taken to be fixed, so that the rest of the plasma must then relax to a new equilibrium configuration. For the class of footpoint motions we have examined, we find that singular and nonsingular equilibria can be generated. By singular we mean that within the limits imposed by numerical resolution we find that there is no convergence to a well-defined equilibrium as the number of grid points in the numerical domain is increased. These singular equilibria contain current "sheets" of ever-increasing current intensity and decreasing width; they occur when the footpoint motions exceed a certain threshold, and must include both twist and shear to be effective. On the basis of these results we contend that flux braiding will indeed result in significant current generation. We discuss the implications of our results for coronal heating.Comment: 13 pages, 12 figure

Modelling the spatial patterning of the primordia in the lower jaw of alligator mississippiensis

We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator, Alligator mississippiensis. Detailed embryological studies12–14 have shown that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. The development of the spatial pattern occurs on a timescale comparable to jaw growth. Based on biological data we develop a dynamic patterning mechanism, which crucially includes domain growth. The mechanism can reproduce the spatial pattern development of the first seven teeth primordia in the lower jaw of A. mississippiensis. The results for the precise spatio-temporal sequence compare well with experiment

A multiscale hybrid model for pro-angiogenic calcium signals in a vascular endothelial cell

Cytosolic calcium machinery is one of the principal signaling mechanisms by which endothelial cells (ECs) respond to external stimuli during several biological processes, including vascular progression in both physiological and pathological conditions. Low concentrations of angiogenic factors (such as VEGF) activate in fact complex pathways involving, among others, second messengers arachidonic acid (AA) and nitric oxide (NO), which in turn control the activity of plasma membrane calcium channels. The subsequent increase in the intracellular level of the ion regulates fundamental biophysical properties of ECs (such as elasticity, intrinsic motility, and chemical strength), enhancing their migratory capacity. Previously, a number of continuous models have represented cytosolic calcium dynamics, while EC migration in angiogenesis has been separately approached with discrete, lattice-based techniques. These two components are here integrated and interfaced to provide a multiscale and hybrid Cellular Potts Model (CPM), where the phenomenology of a motile EC is realistically mediated by its calcium-dependent subcellular events. The model, based on a realistic 3-D cell morphology with a nuclear and a cytosolic region, is set with known biochemical and electrophysiological data. In particular, the resulting simulations are able to reproduce and describe the polarization process, typical of stimulated vascular cells, in various experimental conditions.Moreover, by analyzing the mutual interactions between multilevel biochemical and biomechanical aspects, our study investigates ways to inhibit cell migration: such strategies have in fact the potential to result in pharmacological interventions useful to disrupt malignant vascular progressio

Edge pinch instability of liquid metal sheet in a transverse high-frequency AC magnetic field

We analyze the linear stability of the edge of a thin liquid metal layer subject to a transverse high-frequency AC magnetic field. The layer is treated as a perfectly conducting liquid sheet that allows us to solve the problem analytically for both a semi-infinite geometry with a straight edge and a thin disk of finite radius. It is shown that the long-wave perturbations of a straight edge are monotonically unstable when the wave number exceeds some critical value $k_c,$ which is determined by the surface tension and the linear density of the electromagnetic force acting on the edge. The higher the density of electromagnetic force, the shorter the critical wavelength. The perturbations with wavelength shorter than the critical are stabilized by the surface tension, whereas the growth rate of long wave perturbations reduces as $\sim k$ for wave numbers $k\to 0$. Thus, there is the fastest growing perturbation with the wave number k_\max=2/3 k_c. By applying the general approach developed for the semi-infinite sheet, we find that a circular disk becomes linearly unstable with respect to exponentially growing perturbation with the azimuthal wave number $m=2$ when the magnetic Bond number exceeds $Bm_c=3\pi$. The instability characteristics agree well with the experimental data.Comment: 11 pages, 11 figures, minor grammatical changes; to appear in Phys. Rev.

A Mathematical model for Astrocytes mediated LTP at Single Hippocampal Synapses

Many contemporary studies have shown that astrocytes play a significant role in modulating both short and long form of synaptic plasticity. There are very few experimental models which elucidate the role of astrocyte over Long-term Potentiation (LTP). Recently, Perea & Araque (2007) demonstrated a role of astrocytes in induction of LTP at single hippocampal synapses. They suggested a purely pre-synaptic basis for induction of this N-methyl-D- Aspartate (NMDA) Receptor-independent LTP. Also, the mechanisms underlying this pre-synaptic induction were not investigated. Here, in this article, we propose a mathematical model for astrocyte modulated LTP which successfully emulates the experimental findings of Perea & Araque (2007). Our study suggests the role of retrograde messengers, possibly Nitric Oxide (NO), for this pre-synaptically modulated LTP.Comment: 51 pages, 15 figures, Journal of Computational Neuroscience (to appear

A practical Java tool for small-molecule compound appraisal

The increased use of small-molecule compound screening by new users from a variety of different academic backgrounds calls for adequate software to administer, appraise, analyse and exchange information obtained from screening experiments. While software and spreadsheet solutions exist, there is a need for software that can be easily deployed and is convenient to use.The Java application cApp addresses this need and aids in the handling and storage of information on small-molecule compounds. The software is intended for the appraisal of compounds with respect to their physico-chemical properties, analysis in relation to adherence to likeness rules as well as recognition of pan-assay interference components and cross-linking with identical entries in the PubChem Compound Database. Results are displayed in a tabular form in a graphical interface, but can also be written in an HTML or PDF format. The output of data in ASCII format allows for further processing of data using other suitable programs. Other features include similarity searches against user-provided compound libraries and the PubChem Compound Database, as well as compound clustering based on a MaxMin algorithm.cApp is a personal database solution for small-molecule compounds which can handle all major chemical formats. Being a standalone software, it has no other dependency than the Java virtual machine and is thus conveniently deployed. It streamlines the analysis of molecules with respect to physico-chemical properties and drug discovery criteria; cApp is distributed under the GNU Affero General Public License version 3 and available from http://www.structuralchemistry.org/pcsb/. To download cApp, users will be asked for their name, institution and email address. A detailed manual can also be downloaded from this site, and online tutorials are available at http://www.structuralchemistry.org/pcsb/capp.php

Data-Driven Modelling of the Inositol Trisphosphate Receptor (IPR) and its Role in Calcium-Induced Calcium Release (CICR)

We review the current state of the art of data-driven modelling of the inositol trisphosphate receptor (IPR). After explaining that the IPR plays a crucial role as a central regulator in calcium dynamics, several sources of relevant experimental data are introduced. Single ion channels are best studied by recording single-channel currents under different ligand concentrations via the patch-clamp technique. The particular relevance of modal gating, the spontaneous switching between different levels of channel activity that occur even at constant ligand concentrations, is highlighted. In order to investigate the interactions of IPRs, calcium release from small clusters of channels, so-called calcium puffs, can be used. We then present the mathematical framework common to all models based on single-channel data, aggregated continuous-time Markov models, and give a short review of statistical approaches for parameterising these models with experimental data. The process of building a Markov model that integrates various sources of experimental data is illustrated using two recent examples, the model by Ullah et al. and the “Park–Drive” model by Siekmann et al. (Biophys. J. 2012), the only models that account for all sources of data currently available. Finally, it is demonstrated that the essential features of the Park–Drive model in different models of calcium dynamics are preserved after reducing it to a two-state model that only accounts for the switching between the inactive “park” and the active “drive” modes. This highlights the fact that modal gating is the most important mechanism of ligand regulation in the IPR. It also emphasises that data-driven models of ion channels do not necessarily have to lead to detailed models but can be constructed so that relevant data is selected to represent ion channels at the appropriate level of complexity for a given application

Clinical features and outcomes of hospitalised patients with COVID-19 and Parkinsonian disorders: A multicentre UK-based study

Background Parkinson’s disease has been identified as a risk factor for severe Coronavirus disease 2019 (COVID-19) outcomes. However, whether the significant high risk of death from COVID-19 in people with Parkinson’s disease is specific to the disease itself or driven by other concomitant and known risk factors such as comorbidities, age, and frailty remains unclear. Objective To investigate clinical profiles and outcomes of people with Parkinson’s disease and atypical parkinsonian syndromes who tested positive for COVID-19 in the hospital setting in a multicentre UK-based study. Methods A retrospective cohort study of Parkinson’s disease patients with a positive SARS-CoV-2 test admitted to hospital between February 2020 and July 2021. An online survey was used to collect data from clinical care records, recording patient, Parkinson’s disease and COVID-19 characteristics. Associations with time-to-mortality and severe outcomes were analysed using either the Cox proportional hazards model or logistic regression models, as appropriate. Results Data from 552 admissions were collected: 365 (66%) male; median (inter-quartile range) age 80 (74–85) years. The 34-day all-cause mortality rate was 38.4%; male sex, increased age and frailty, Parkinson’s dementia syndrome, requirement for respiratory support and no vaccination were associated with increased mortality risk. Community-acquired COVID-19 and co-morbid chronic neurological disorder were associated with increased odds of requiring respiratory support. Hospital-acquired COVID-19 and delirium were associated with requiring an increase in care level post-discharge. Conclusions This first, multicentre, UK-based study on people with Parkinson’s disease or atypical parkinsonian syndromes, hospitalised with COVID-19, adds and expands previous findings on clinical profiles and outcomes in this population

Phase-Locked Signals Elucidate Circuit Architecture of an Oscillatory Pathway

This paper introduces the concept of phase-locking analysis of oscillatory cellular signaling systems to elucidate biochemical circuit architecture. Phase-locking is a physical phenomenon that refers to a response mode in which system output is synchronized to a periodic stimulus; in some instances, the number of responses can be fewer than the number of inputs, indicative of skipped beats. While the observation of phase-locking alone is largely independent of detailed mechanism, we find that the properties of phase-locking are useful for discriminating circuit architectures because they reflect not only the activation but also the recovery characteristics of biochemical circuits. Here, this principle is demonstrated for analysis of a G-protein coupled receptor system, the M3 muscarinic receptor-calcium signaling pathway, using microfluidic-mediated periodic chemical stimulation of the M3 receptor with carbachol and real-time imaging of resulting calcium transients. Using this approach we uncovered the potential importance of basal IP3 production, a finding that has important implications on calcium response fidelity to periodic stimulation. Based upon our analysis, we also negated the notion that the Gq-PLC interaction is switch-like, which has a strong influence upon how extracellular signals are filtered and interpreted downstream. Phase-locking analysis is a new and useful tool for model revision and mechanism elucidation; the method complements conventional genetic and chemical tools for analysis of cellular signaling circuitry and should be broadly applicable to other oscillatory pathways