Methods and measures for investigating microscale motility

Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks and theoretical methods, we can begin to probe the complex lives of microscopic motile organisms and answer the intertwining biological and physical questions of how these diverse lifeforms navigate their surroundings. Herein, we give an overview of different experimental, analytical, and mathematical methods used to study a suite of microscale motility mechanisms across different scales encompassing molecular-, individual- to population-level. We identify transferable techniques, pressing challenges, and future directions in the field. This review can serve as a starting point for researchers who are interested in exploring and quantifying the movements of organisms in the microscale world.Comment: 24 pages, 2 figure

Computing Interpretable Representations of Cell Morphodynamics

Shape changes (morphodynamics) are one of the principal ways cells interact with their environments and perform key intrinsic behaviours like division. These dynamics arise from a myriad of complex signalling pathways that often organise with emergent simplicity to carry out critical functions including predation, collaboration and migration. A powerful method for analysis can therefore be to quantify this emergent structure, bypassing the low-level complexity. Enormous image datasets are now available to mine. However, it can be difficult to uncover interpretable representations of the global organisation of these heterogeneous dynamic processes. Here, such representations were developed for interpreting morphodynamics in two key areas: mode of action (MoA) comparison for drug discovery (developed using the economically devastating Asian soybean rust crop pathogen) and 3D migration of immune system T cells through extracellular matrices (ECMs). For MoA comparison, population development over a 2D space of shapes (morphospace) was described using two models with condition-dependent parameters: a top-down model of diffusive development over Waddington-type landscapes, and a bottom-up model of tip growth. A variety of landscapes were discovered, describing phenotype transitions during growth, and possible perturbations in the tip growth machinery that cause this variation were identified. For interpreting T cell migration, a new 3D shape descriptor that incorporates key polarisation information was developed, revealing low-dimensionality of shape, and the distinct morphodynamics of run-and-stop modes that emerge at minute timescales were mapped. Periodically oscillating morphodynamics that include retrograde deformation flows were found to underlie active translocation (run mode). Overall, it was found that highly interpretable representations could be uncovered while still leveraging the enormous discovery power of deep learning algorithms. The results show that whole-cell morphodynamics can be a convenient and powerful place to search for structure, with potentially life-saving applications in medicine and biocide discovery as well as immunotherapeutics.Open Acces

Collective Phenomena in Active Systems

This dissertation investigates collective phenomena in active systems of biological relavance across length scales, ranging from intracellular actin systems to bird flocks. The study has been conducted via theoretical modeling and computer simulations using tools from soft condensed matter physics and non-equilibrium statistical mechanics. The work has been organized into two parts through five chapters. In part one (chapter 2 to 3), continuum theories have been utilized to study pattern formation in bacteria suspensions, actomyosin systems and bird flocks, whose dynamics is described generically within the framework of polar active fluids. The continuum field equations have been written down phenomenogically and derived rigorously through explicit coarse-graining of corresponding microscopic equations of motion. We have investigated the effects of alignment interaction, active motility, non-conserved density, and rotational inertia on pattern formation in active systems. In part two (chapter 4 to 5), computer simulations have been performed to study the self-organization and mechanical properties of dense active systems. A minimal self-propelled particle (SPP) model has been utilized to understand the aggregation and segregation of active systems under confinement (Chapter 4), where an active pressure has been defined for the first time to characterize the mechanical state of the active system. The same model is utilized in Chapter 5 to understand the self-assembly of passive particles in an active bath

Influences on the formation and evolution of Physarum polycephalum inspired emergent transport networks

The single-celled organism Physarum polycephalum efficiently constructs and minimises dynamical nutrient transport networks resembling proximity graphs in the Toussaint hierarchy. We present a particle model which collectively approximates the behaviour of Physarum. We demonstrate spontaneous transport network formation and complex network evolution using the model and show that the model collectively exhibits quasi-physical emergent properties, allowing it to be considered as a virtual computing material. This material is used as an unconventional method to approximate spatially represented geometry problems by representing network nodes as nutrient sources. We demonstrate three different methods for the construction, evolution and minimisation of Physarum-like transport networks which approximate Steiner trees, relative neighbourhood graphs, convex hulls and concave hulls. We extend the model to adapt population size in response to nutrient availability and show how network evolution is dependent on relative node position (specifically inter-node angle), sensor scaling and nutrient concentration. We track network evolution using a real-time method to record transport network topology in response to global differences in nutrient concentration. We show how Steiner nodes are utilised at low nutrient concentrations whereas direct connections to nutrients are favoured when nutrient concentration is high. The results suggest that the foraging and minimising behaviour of Physarum-like transport networks reflect complex interplay between nutrient concentration, nutrient location, maximising foraging area coverage and minimising transport distance. The properties and behaviour of the synthetic virtual plasmodium may be useful in future physical instances of distributed unconventional computing devices, and may also provide clues to the generation of emergent computation behaviour by Physarum. © Springer Science+Business Media B.V. 2010

Mathematical Biology

This years meeting on Mathematical Biology focussed on the mathematical modeling and analysis of some specific bio-medical questions, where quite detailed experimental findings are available. A main aim for this decision was to further deepen the exchange between the fields, on the long run in a similar manner as known e.g. from mathematics and physics. Talks by mathematicians and talks by experimentalists on related scientific questions were put back to back, wherever possible

Nonlocal Models in Biology and Life Sciences: Sources, Developments, and Applications

Nonlocality is important in realistic mathematical models of physical and biological systems at small-length scales. It characterizes the properties of two individuals located in different locations. This review illustrates different nonlocal mathematical models applied to biology and life sciences. The major focus has been given to sources, developments, and applications of such models. Among other things, a systematic discussion has been provided for the conditions of pattern formations in biological systems of population dynamics. Special attention has also been given to nonlocal interactions on networks, network coupling and integration, including models for brain dynamics that provide us with an important tool to better understand neurodegenerative diseases. In addition, we have discussed nonlocal modelling approaches for cancer stem cells and tumor cells that are widely applied in the cell migration processes, growth, and avascular tumors in any organ. Furthermore, the discussed nonlocal continuum models can go sufficiently smaller scales applied to nanotechnology to build biosensors to sense biomaterial and its concentration. Piezoelectric and other smart materials are among them, and these devices are becoming increasingly important in the digital and physical world that is intrinsically interconnected with biological systems. Additionally, we have reviewed a nonlocal theory of peridynamics, which deals with continuous and discrete media and applies to model the relationship between fracture and healing in cortical bone, tissue growth and shrinkage, and other areas increasingly important in biomedical and bioengineering applications. Finally, we provided a comprehensive summary of emerging trends and highlighted future directions in this rapidly expanding field.Comment: 71 page

Differential Equations arising from Organising Principles in Biology

This workshop brought together experts in modeling and analysis of organising principles of multiscale biological systems such as cell assemblies, tissues and populations. We focused on questions arising in systems biology and medicine which are related to emergence, function and control of spatial and inter-individual heterogeneity in population dynamics. There were three main areas represented of differential equation models in mathematical biology. The first area involved the mathematical description of structured populations. The second area concerned invasion, pattern formation and collective dynamics. The third area treated the evolution and adaptation of populations, following the Darwinian paradigm. These problems led to differential equations, which frequently are non-trivial extensions of classical problems. The examples included but were not limited to transport-type equations with nonlocal boundary conditions, mixed ODE-reaction-diffusion models, nonlocal diffusion and cross-diffusion problems or kinetic equations