Building nonparametric nn-body force fields using Gaussian process regression

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force fields of a given order using Gaussian process (GP) priors. The formalism of GP regression is first reviewed, particularly in relation to its application in learning local atomic energies and forces. For accurate regression it is fundamental to incorporate prior knowledge into the GP kernel function. To this end, this chapter details how properties of smoothness, invariance and interaction order of a force field can be encoded into corresponding kernel properties. A range of kernels is then proposed, possessing all the required properties and an adjustable parameter $n$ governing the interaction order modelled. The order $n$ best suited to describe a given system can be found automatically within the Bayesian framework by maximisation of the marginal likelihood. The procedure is first tested on a toy model of known interaction and later applied to two real materials described at the DFT level of accuracy. The models automatically selected for the two materials were found to be in agreement with physical intuition. More in general, it was found that lower order (simpler) models should be chosen when the data are not sufficient to resolve more complex interactions. Low $n$ GPs can be further sped up by orders of magnitude by constructing the corresponding tabulated force field, here named "MFF".Comment: 31 pages, 11 figures, book chapte

The influence of technology on the mathematical modelling of physical phenomena

A study is presented in which students are asked to model two physical phenomena using applications on electronic tablets : a bounce of a ball and the extension of a spring. The analysis focusses on (a) the influence of characteristics of the applications on the tablets on the decisions that groups of 16-year-old students made during the modelling phases in which reality and mathematics are related, (b) mathematisation of the phenomena and (c) interpretation of the models. The phenomena were recorded using an app that requests users establish a set of references during the mathematisation process, which makes students focus on the way the references have been set to interpret the model properly. Our findings indicated inconsistences between student decisions made during mathematisation and their considerations during interpretation of the model. To conclude we suggest reasons students experience problems in working without a pre-defined reference syste

Expression patterns of protein C inhibitor in mouse development

Proteolysis of extracellular matrix is an important requirement for embryonic development and is instrumental in processes such as morphogenesis, angiogenesis, and cell migration. Efficient remodeling requires controlled spatio-temporal expression of both the proteases and their inhibitors. Protein C inhibitor (PCI) effectively blocks a range of serine proteases, and recently has been suggested to play a role in cell differentiation and angiogenesis. In this study, we mapped the expression pattern of PCI throughout mouse development using in situ hybridization and immunohistochemistry. We detected a wide-spread, yet distinct expression pattern with prominent PCI levels in skin including vibrissae, and in fore- and hindgut. Further sites of PCI expression were choroid plexus of brain ventricles, heart, skeletal muscles, urogenital tract, and cartilages. A strong and stage-dependent PCI expression was observed in the developing lung. In the pseudoglandular stage, PCI expression was present in distal branching tubules whereas proximal tubules did not express PCI. Later in development, in the saccular stage, PCI expression was restricted to distal bronchioli whereas sacculi did not express PCI. PCI expression declined in postnatal stages and was not detected in adult lungs. In general, embryonic PCI expression indicates multifunctional roles of PCI during mouse development. The expression pattern of PCI during lung development suggests its possible involvement in lung morphogenesis and angiogenesis

A statistical approach to estimating the strength of cell-cell interactions under the differential adhesion hypothesis

International audienceBACKGROUND: The Differential Adhesion Hypothesis (DAH) is a theory of the organization of cells within a tissue which has been validated by several biological experiments and tested against several alternative computational models. RESULTS: In this study, a statistical approach was developed for the estimation of the strength of adhesion, incorporating earlier discrete lattice models into a continuous marked point process framework. This framework allows to describe an ergodic Markov Chain Monte Carlo algorithm that can simulate the model and reproduce empirical biological patterns. The estimation procedure, based on a pseudo-likelihood approximation, is validated with simulations, and a brief application to medulloblastoma stained by beta-catenin markers is given. CONCLUSION: Our model includes the strength of cell-cell adhesion as a statistical parameter. The estimation procedure for this parameter is consistent with experimental data and would be useful for high-throughput cancer studies

Modulation of ATP/ADP Concentration at the Endothelial Cell Surface by Flow: Effect of Cell Topography

Determining how flow affects the concentration of the adenine nucleotides ATP and ADP at the vascular endothelial cell (EC) surface is essential for understanding flow-induced mobilization of intracellular calcium. Previously, mathematical models were formulated to describe the ATP/ADP concentration at the EC surface; however, all previous models assumed the endothelium to be flat. In the present study we investigate the effect of surface undulations on ATP/ADP concentration at the EC surface. The results demonstrate that under certain geometric and flow conditions, the ATP + ADP concentration at the EC surface is considerably lower for a wavy cell surface than for a flat surface. Because ECs in regions of disturbed arterial flow are expected to have larger undulations than cells in non-disturbed flow zones, our findings suggest that ECs in regions of flow disturbance would exhibit lower ATP + ADP concentrations at their surfaces, which may lead to impaired calcium signaling. If validated experimentally, the present results may contribute to our understanding of endothelial cell dysfunction observed in regions of disturbed flow

Cell-Cell Contact Preserves Cell Viability via Plakoglobin

Control over cell viability is a fundamental property underlying numerous physiological processes. Cell spreading on a substrate was previously demonstrated to be a major factor in determining the viability of individual cells. In multicellular organisms, cell-cell contact is likely to play a significant role in regulating cell vitality, but its function is easily masked by cell-substrate interactions, thus remains incompletely characterized. In this study, we show that suspended immortalized human keratinocyte sheets with persisting intercellular contacts exhibited significant contraction, junctional actin localization, and reinforcement of cell-cell adhesion strength. Further, cells within these sheets remain viable, in contrast to trypsinized cells suspended without either cell-cell or cell-substrate contact, which underwent apoptosis at high rates. Suppression of plakoglobin weakened cell-cell adhesion in cell sheets and suppressed apoptosis in suspended, trypsinized cells. These results demonstrate that cell-cell contact may be a fundamental control mechanism governing cell viability and that the junctional protein plakoglobin is a key regulator of this process. Given the near-ubiquity of plakoglobin in multicellular organisms, these findings could have significant implications for understanding cell adhesion, modeling disease progression, developing therapeutics and improving the viability of tissue engineering protocols

Approach to canine paroxysmal dyskinesias

The term ‘paroxysmal dyskinesia’ (PD) describes a manifestation of involuntary movement or muscle tone, which by definition is episodic in nature and self-limiting. The PDs remain poorly understood and frequently under-recognised conditions in veterinary patients. The purpose of this article is to review the basic classification and principles of recognition and diagnosis of PDs. This article introduces some of the breed-specific PDs, as well as the treatment/management options available and expected outcomes