Continuous macroscopic limit of a discrete stochastic model for interaction of living cells

In the development of multiscale biological models it is crucial to establish a connection between discrete microscopic or mesoscopic stochastic models and macroscopic continuous descriptions based on cellular density. In this paper a continuous limit of a two-dimensional Cellular Potts Model (CPM) with excluded volume is derived, describing cells moving in a medium and reacting to each other through both direct contact and long range chemotaxis. The continuous macroscopic model is obtained as a Fokker-Planck equation describing evolution of the cell probability density function. All coefficients of the general macroscopic model are derived from parameters of the CPM and a very good agreement is demonstrated between CPM Monte Carlo simulations and numerical solution of the macroscopic model. It is also shown that in the absence of contact cell-cell interactions, the obtained model reduces to the classical macroscopic Keller-Segel model. General multiscale approach is demonstrated by simulating spongy bone formation from loosely packed mesenchyme via the intramembranous route suggesting that self-organizing physical mechanisms can account for this developmental process.Comment: 4 pages, 3 figure

A modernized approach to meet diversified earth observing system (EOS) AM-1 mission requirements

From a flight dynamics perspective, the EOS AM-1 mission design and maneuver operations present a number of interesting challenges. The mission design itself is relatively complex for a low Earth mission, requiring a frozen, Sun-synchronous, polar orbit with a repeating ground track. Beyond the need to design an orbit that meets these requirements, the recent focus on low-cost, 'lights out' operations has encouraged a shift to more automated ground support. Flight dynamics activities previously performed in special facilities created solely for that purpose and staffed by personnel with years of design experience are now being shifted to the mission operations centers (MOCs) staffed by flight operations team (FOT) operators. These operators' responsibilities include flight dynamics as a small subset of their work; therefore, FOT personnel often do not have the experience to make critical maneuver design decisions. Thus, streamlining the analysis and planning work required for such a complicated orbit design and preparing FOT personnel to take on the routine operation of such a spacecraft both necessitated increasing the automation level of the flight dynamics functionality. The FreeFlyer(TM) software developed by AI Solutions provides a means to achieve both of these goals. The graphic interface enables users to interactively perform analyses that previously required many parametric studies and much data reduction to achieve the same result In addition, the fuzzy logic engine enables the simultaneous evaluation of multiple conflicting constraints, removing the analyst from the loop and allowing the FOT to perform more of the operations without much background in orbit design. Modernized techniques were implemented for EOS AM-1 flight dynamics support in several areas, including launch window determination, orbit maintenance maneuver control strategies, and maneuver design and calibration automation. The benefits of implementing these techniques include increased fuel available for on-orbit maneuvering, a simplified orbit maintenance process to minimize science data downtime, and an automated routine maneuver planning process. This paper provides an examination of the modernized techniques implemented for EOS AM-1 to achieve these benefits

Patterns of Mesenchymal Condensation in a Multiscale, Discrete Stochastic Model

Cells of the embryonic vertebrate limb in high-density culture undergo chondrogenic pattern formation, which results in the production of regularly spaced “islands” of cartilage similar to the cartilage primordia of the developing limb skeleton. The first step in this process, in vitro and in vivo, is the generation of “cell condensations,” in which the precartilage cells become more tightly packed at the sites at which cartilage will form. In this paper we describe a discrete, stochastic model for the behavior of limb bud precartilage mesenchymal cells in vitro. The model uses a biologically motivated reaction–diffusion process and cell-matrix adhesion (haptotaxis) as the bases of chondrogenic pattern formation, whereby the biochemically distinct condensing cells, as well as the size, number, and arrangement of the multicellular condensations, are generated in a self-organizing fashion. Improving on an earlier lattice-gas representation of the same process, it is multiscale (i.e., cell and molecular dynamics occur on distinct scales), and the cells are represented as spatially extended objects that can change their shape. The authors calibrate the model using experimental data and study sensitivity to changes in key parameters. The simulations have disclosed two distinct dynamic regimes for pattern self-organization involving transient or stationary inductive patterns of morphogens. The authors discuss these modes of pattern formation in relation to available experimental evidence for the in vitro system, as well as their implications for understanding limb skeletal patterning during embryonic development

Communicability across evolving networks

Many natural and technological applications generate time ordered sequences of networks, defined over a fixed set of nodes; for example time-stamped information about ‘who phoned who’ or ‘who came into contact with who’ arise naturally in studies of communication and the spread of disease. Concepts and algorithms for static networks do not immediately carry through to this dynamic setting. For example, suppose A and B interact in the morning, and then B and C interact in the afternoon. Information, or disease, may then pass from A to C, but not vice versa. This subtlety is lost if we simply summarize using the daily aggregate network given by the chain A-B-C. However, using a natural definition of a walk on an evolving network, we show that classic centrality measures from the static setting can be extended in a computationally convenient manner. In particular, communicability indices can be computed to summarize the ability of each node to broadcast and receive information. The computations involve basic operations in linear algebra, and the asymmetry caused by time’s arrow is captured naturally through the non-mutativity of matrix-matrix multiplication. Illustrative examples are given for both synthetic and real-world communication data sets. We also discuss the use of the new centrality measures for real-time monitoring and prediction

Predicting population coverage of T-cell epitope-based diagnostics and vaccines

BACKGROUND: T cells recognize a complex between a specific major histocompatibility complex (MHC) molecule and a particular pathogen-derived epitope. A given epitope will elicit a response only in individuals that express an MHC molecule capable of binding that particular epitope. MHC molecules are extremely polymorphic and over a thousand different human MHC (HLA) alleles are known. A disproportionate amount of MHC polymorphism occurs in positions constituting the peptide-binding region, and as a result, MHC molecules exhibit a widely varying binding specificity. In the design of peptide-based vaccines and diagnostics, the issue of population coverage in relation to MHC polymorphism is further complicated by the fact that different HLA types are expressed at dramatically different frequencies in different ethnicities. Thus, without careful consideration, a vaccine or diagnostic with ethnically biased population coverage could result. RESULTS: To address this issue, an algorithm was developed to calculate, on the basis of HLA genotypic frequencies, the fraction of individuals expected to respond to a given epitope set, diagnostic or vaccine. The population coverage estimates are based on MHC binding and/or T cell restriction data, although the tool can be utilized in a more general fashion. The algorithm was implemented as a web-application available at . CONCLUSION: We have developed a web-based tool to predict population coverage of T-cell epitope-based diagnostics and vaccines based on MHC binding and/or T cell restriction data. Accordingly, epitope-based vaccines or diagnostics can be designed to maximize population coverage, while minimizing complexity (that is, the number of different epitopes included in the diagnostic or vaccine), and also minimizing the variability of coverage obtained or projected in different ethnic groups

A compact roller-gear pitch-yaw joint module: Design and control issues

Robotic systems have been proposed as a means of accomplishing assembly and maintenance tasks in space. The desirable characteristics of these systems include compact size, low mass, high load capacity, and programmable compliance to improve assembly performance. In addition, the mechanical system must transmit power in such a way as to allow high performance control of the system. Efficiency, linearity, low backlash, low torque ripple, and low friction are all desirable characteristics. This work presents a pitch-yaw joint module designed and built to address these issues. Its effectiveness as a two degree-of-freedom manipulator using natural admittance control, a method of force control, is demonstrated