Macroscopic limits of individual-based models for motile cell populations with volume exclusion

Partial differential equation models are ubiquitous in studies of motile cell populations, giving a phenomenological description of events which can be analyzed and simulated using a wide range of existing tools. However, these models are seldom derived from individual cell behaviors and so it is difficult to accurately include biological hypotheses on this spatial scale. Moreover, studies which do attempt to link individual- and population-level behavior generally employ lattice-based frameworks in which the artifacts of lattice choice at the population level are unclear. In this work we derive limiting population-level descriptions of a motile cell population from an off-lattice, individual-based model (IBM) and investigate the effects of volume exclusion on the population-level dynamics. While motility with excluded volume in on-lattice IBMs can be accurately described by Fickian diffusion, we demonstrate that this is not the case off lattice. We show that the balance between two key parameters in the IBM (the distance moved in one step and the radius of an individual) determines whether volume exclusion results in enhanced or slowed diffusion. The magnitude of this effect is shown to increase with the number of cells and the rate of their movement. The method we describe is extendable to higher-dimensional and more complex systems and thereby provides a framework for deriving biologically realistic, continuum descriptions of motile populations

Nickel-catalyzed transamidation of aliphatic amide derivatives.

Transamidation, or the conversion of one amide to another, is a long-standing challenge in organic synthesis. Although notable progress has been made in the transamidation of primary amides, the transamidation of secondary amides has remained underdeveloped, especially when considering aliphatic substrates. Herein, we report a two-step approach to achieve the transamidation of secondary aliphatic amides, which relies on non-precious metal catalysis. The method involves initial Boc-functionalization of secondary amide substrates to weaken the amide C-N bond. Subsequent treatment with a nickel catalyst, in the presence of an appropriate amine coupling partner, then delivers the net transamidated products. The transformation proceeds in synthetically useful yields across a range of substrates. A series of competition experiments delineate selectivity patterns that should influence future synthetic design. Moreover, the transamidation of Boc-activated secondary amide derivatives bearing epimerizable stereocenters underscores the mildness and synthetic utility of this methodology. This study provides the most general solution to the classic problem of secondary amide transamidation reported to date

Conference on Automated Decision-Making and Problem Solving, the Third Day: Issues Discussed

A conference held at Langley Research Center in May of 1980 brought together university experts from the fields of Control Theory, Operations Research, and Artificial Intelligence to explore current research in automation from both the perspective of their own particular disciplines and from that of interdisciplinary considerations. Informal discussions from the final day of the those day conference are summarized

MULTIPAC, a multiple pool processor and computer for a spacecraft central data system, phase 2 Final report

MULTIPAC, multiple pool processor and computer for deep space probe central data syste

Non-linear effects on Turing patterns: time oscillations and chaos.

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space, produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, Turing patterns oscillate in time, a phenomenon which is expected to occur only in a three morphogen system. When varying a single parameter, a series of bifurcations lead to period doubling, quasi-periodic and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examined the Turing conditions for obtaining a diffusion driven instability and discovered that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. All this results demonstrates the limitations of the linear analysis for reaction-diffusion systems

Swelling and shrinking kinetics of a lamellar gel phase

We investigate the swelling and shrinking of L_beta lamellar gel phases composed of surfactant and fatty alcohol after contact with aqueous poly(ethylene-glycol) solutions. The height change $\Delta h(t)$ is diffusion-like with a swelling coefficient, S: $\Delta h = S \sqrt{t}$. On increasing polymer concentration we observe sequentially slower swelling, absence of swelling, and finally shrinking of the lamellar phase. This behavior is summarized in a non-equilibrium diagram and the composition dependence of S quantitatively described by a generic model. We find a diffusion coefficient, the only free parameter, consistent with previous measurements.Comment: 3 pages, 4 figures to appear in Applied Physics Letter