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We propose a general mathematical and computational approach to study cellular transport driven by a group of kinesin motors. It is a framework for multi-scale modeling that integrates kinetic models of single kinesin motors, including detachment and reattachment events, to study group behaviors of several motors. By formulating the problem as a semi-Markov process and applying a central limit theorem, asymptotic velocity and diffusivity can be readily calculated, which offers considerable computational advantage over Monte Carlo simulations in tasks such as parameter sensitivity analysis and model selection. We demonstrate the method with some examples. The importance of incorporating the intrinsic microscopic-level dynamics of individual motors is illustrated by showing how changes at the microscopic level propagate to the motor-cargo complex at a mesoscopic level. Particularly, we showcase an example in which changes in the second moment of single-motor characteristics gives rise to different first moment characteristics of the motor group. [ABSTRACT FROM AUTHOR]

Multiscale modeling of marine and aerial plankton has traditionally been difficult to address holistically due to the challenge of resolving individual locomotion dynamics while being carried with larger-scale flows. However, such problems are of paramount importance, e.g., dispersal of marine larval plankton is critical for the health of coral reefs, and aerial plankton (tiny arthropods) can be used as effective agricultural biocontrol agents. Here we introduce the open-source, agent-based modeling software Planktos targeted at 2D and 3D fluid environments in Python. Agents in this modeling framework are relatively tiny organisms in sufficiently low densities that their effect on the surrounding fluid motion can be considered negligible. This library can be used for scientific exploration and quantification of collective and emergent behavior, including interaction with immersed structures. In this paper, we detail the implementation and functionality of the library along with some illustrative examples. Functionality includes arbitrary agent behavior obeying either ordinary differential equations, stochastic differential equations, or coded movement algorithms, all under the influence of time-dependent fluid velocity fields generated by computational fluid dynamics, experiments, or analytical models in domains with static immersed mesh structures with sliding or sticky collisions. In addition, data visualization tools provide images or animations with kernel density estimation and velocity field analysis with respect to deterministic agent behavior via the finite-time Lyapunov exponent. [ABSTRACT FROM AUTHOR]

A difficulty in using diffusion models to predict large scale animal population dispersal is that individuals move differently based on local information (as opposed to gradients) in differing habitat types. This can be accommodated by using ecological diffusion. However, real environments are often spatially complex, limiting application of a direct approach. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion and apply it to a simple model for chronic wasting disease in mule deer. Homogenization allows us to determine the impact of small scale (10-100 m) habitat variability on large scale (10-100 km) movement. The procedure generates asymptotic equations for solutions on the large scale with parameters defined by small-scale variation. The simplicity of this homogenization procedure is striking when compared to the multi-dimensional homogenization procedure for Fickian diffusion,and the method will be equally straightforward for more complex models. [ABSTRACT FROM AUTHOR]

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller-Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated. [ABSTRACT FROM AUTHOR]