We study collections of self-propelled rods (SPR) moving in two dimensions for packing fractions less than or equal to 0.3. We find that in the thermodynamical limit the SPR undergo a phase transition between a disordered gas and a novel phase-separa
ted system state. Interestingly, (global) orientational order patterns -- contrary to what has been suggested -- vanish in this limit. In the found novel state, the SPR self-organize into a highly dynamical, high-density, compact region - which we call aggregate - which is surrounded by a disordered gas. Active stresses build inside aggregates as result of the combined effect of local orientational order and active forces. This leads to the most distinctive feature of these aggregates: constant ejection of polar clusters of SPR. This novel phase-separated state represents a novel state of matter characterized by large fluctuations in volume and shape, related to mass ejection, and exhibits positional as well as orientational local order. SPR systems display new physics unseen in other active matter systems due to the coupling between density, active stresses, and orientational order (such coupling cannot be reduced simply to a coupling between speed and density).
Multipotent differentiation, where cells adopt one of several cell fates, is a determinate and orchestrated procedure that often incorporates stochastic mechanisms in order to diversify cell types. How these stochastic phenomena interact to govern ce
ll fate are poorly understood. Nonetheless, cell fate decision making procedure is mainly regulated through the activation of differentiation waves and associated signaling pathways. In the current work, we focus on the Notch/Delta signaling pathway which is not only known to trigger such waves but also is used to achieve the principle of lateral inhibition, i.e. a competition for exclusive fates through cross-signaling between neighboring cells. Such a process ensures unambiguous stochastic decisions influenced by intrinsic noise sources, e.g.~as ones found in the regulation of signaling pathways, and extrinsic stochastic fluctuations, attributed to micro-environmental factors. However, the effect of intrinsic and extrinsic noise on cell fate determination is an open problem. Our goal is to elucidate how the induction of extrinsic noise affects cell fate specification in a lateral inhibition mechanism. Using a stochastic Cellular Automaton with continuous state space, we show that extrinsic noise results in the emergence of steady-state furrow patterns of cells in a frustrated/transient phenotypic state.
We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node is empty. H
ere we show that such effects lead to a surprisingly rich variety of self-organized spatial patterns. As particles exhibit an increasingly higher tendency to align to neighbors, they first self-segregate into disordered particle aggregates. Aggregates turn into traffic jams. Traffic jams evolve toward gliders, triangular high density regions that migrate in a well-defined direction. Maximum order is achieved by the formation of elongated high density regions - bands - that transverse the entire system. Numerical evidence suggests that below the percolation density the phase transition associated to orientational order is of first-order, while at full occupancy it is of second-order. The model highlights the (pattern formation) importance of a coupling between local density, orientation, and local speed.
The growth of world population, limitation of resources, economic problems and environmental issues force engineers to develop increasingly efficient solutions for logistic systems. Pure optimization for efficiency, however, has often led to technica
l solutions that are vulnerable to variations in supply and demand, and to perturbations. In contrast, nature already provides a large variety of efficient, flexible and robust logistic solutions. Can we utilize biological principles to design systems, which can flexibly adapt to hardly predictable, fluctuating conditions? We propose a bio-inspired BioLogistics approach to deduce dynamic organization processes and principles of adaptive self-control from biological systems, and to transfer them to man-made logistics (including nanologistics), using principles of modularity, self-assembly, self-organization, and decentralized coordination. Conversely, logistic models can help revealing the logic of biological processes at the systems level.
Environmental and genetic mutations can transform the cells in a co-operating healthy tissue into an ecosystem of individualistic tumour cells that compete for space and resources. Various selection forces are responsible for driving the evolution of
cells in a tumour towards more malignant and aggressive phenotypes that tend to have a fitness advantage over the older populations. Although the evolutionary nature of cancer has been recognised for more than three decades (ever since the seminal work of Nowell) it has been only recently that tools traditionally used by ecological and evolutionary researchers have been adopted to study the evolution of cancer phenotypes in populations of individuals capable of co-operation and competition. In this chapter we will describe game theory as an important tool to study the emergence of cell phenotypes in a tumour and will critically review some of its applications in cancer research. These applications demonstrate that game theory can be used to understand the dynamics of somatic cancer evolution and suggest new therapies in which this knowledge could be applied to gain some control over the evolution of the tumour.
Tumour cells have to acquire a number of capabilities if a neoplasm is to become a cancer. One of these key capabilities is increased motility which is needed for invasion of other tissues and metastasis. This paper presents a qualitative mathematica
l model based on game theory and computer simulations using cellular automata. With this model we study the circumstances under which mutations that confer increased motility to cells can spread through a tumour made of rapidly proliferating cells. The analysis suggests therapies that could help prevent the progression towards malignancy and invasiveness of benign tumours.
A mean-field approach (MFA) is proposed for the analysis of orientational order in a two-dimensional system of stochastic self-propelled particles interacting by local velocity alignment mechanism. The treatment is applied to the cases of ferromagnet
ic (F) and liquid-crystal (LC) alignment. In both cases, MFA yields a second order phase transition for a critical noise strength and a scaling exponent of 1/2 for the respective order parameters. We find that the critical noise amplitude $eta_c$ at which orientational order emerges in the LC case is smaller than in the F-alignment case, i.e. $eta^{LC}_{C}<eta^{F}_{C}$. A comparison with simulations of individual-based models with F- resp. LC-alignment shows that the predictions about the critical behavior and the qualitative relation between the respective critical noise amplitudes are correct.
