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Royal Society Open Science RSS feed -- recent Mathematics articles2054-5703Royal Society Open Science<![CDATA[Influences of transversely isotropic rheology and translational diffusion on the stability of active suspensions]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/5/8/180456?rss=1
Suspensions of self-motile, elongated particles are a topic of significant current interest, exemplifying a form of ‘active matter’. Examples include self-propelling bacteria, algae and sperm, and artificial swimmers. Ericksen's model of a transversely isotropic fluid (Ericksen 1960 Colloid Polym. Sci.173, 117–122 (doi:10.1007/bf01502416)) treats suspensions of non-motile particles as a continuum with an evolving preferred direction; this model describes fibrous materials as diverse as extracellular matrix, textile tufts and plant cell walls. Director-dependent effects are incorporated through a modified stress tensor with four viscosity-like parameters. By making fundamental connections with recent models for active suspensions, we propose a modification to Ericksen's model, mainly the inclusion of self-motility; this can be considered the simplest description of an oriented suspension including transversely isotropic effects. Motivated by the fact that transversely isotropic fluids exhibit modified flow stability, we conduct a linear stability analysis of two distinct cases, aligned and isotropic suspensions of elongated active particles. Novel aspects include the anisotropic rheology and translational diffusion. In general, anisotropic effects increase the instability of small perturbations, while translational diffusion stabilizes a range of wave-directions and, in some cases, a finite range of wavenumbers, thus emphasizing that both anisotropy and translational diffusion can have important effects in these systems.
]]>2018-08-15T00:55:35-07:00info:doi/10.1098/rsos.180456hwp:master-id:royopensci;rsos.1804562018-08-15Mathematics58180456180456<![CDATA[A mathematical understanding of how cytoplasmic dynein walks on microtubules]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/5/8/171568?rss=1
Cytoplasmic dynein 1 (hereafter referred to simply as dynein) is a dimeric motor protein that walks and transports intracellular cargos towards the minus end of microtubules. In this article, we formulate, based on physical principles, a mechanical model to describe the stepping behaviour of cytoplasmic dynein walking on microtubules from the cell membrane towards the nucleus. Unlike previous studies on physical models of this nature, we base our formulation on the whole structure of dynein to include the temporal dynamics of the individual subunits such as the cargo (for example, an endosome, vesicle or bead), two rings of six ATPase domains associated with diverse cellular activities (AAA+ rings) and the microtubule-binding domains which allow dynein to bind to microtubules. This mathematical framework allows us to examine experimental observations on dynein across a wide range of different species, as well as being able to make predictions on the temporal behaviour of the individual components of dynein not currently experimentally measured. Furthermore, we extend the model framework to include backward stepping, variable step size and dwelling. The power of our model is in its predictive nature; first it reflects recent experimental observations that dynein walks on microtubules using a weakly coordinated stepping pattern with predominantly not passing steps. Second, the model predicts that interhead coordination in the ATP cycle of cytoplasmic dynein is important in order to obtain the alternating stepping patterns and long run lengths seen in experiments.
]]>2018-08-08T00:05:56-07:00info:doi/10.1098/rsos.171568hwp:master-id:royopensci;rsos.1715682018-08-08Mathematics58171568171568<![CDATA[Advancing risk assessment: mechanistic dose-response modelling of Listeria monocytogenes infection in human populations]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/5/8/180343?rss=1
The utility of characterizing the effects of strain variation and individual/subgroup susceptibility on dose–response outcomes has motivated the search for new approaches beyond the popular use of the exponential dose–response model for listeriosis. While descriptive models can account for such variation, they have limited power to extrapolate beyond the details of particular outbreaks. By contrast, this study exhibits dose–response relationships from a mechanistic basis, quantifying key biological factors involved in pathogen–host dynamics. An efficient computational algorithm and geometric interpretation of the infection pathway are developed to connect dose–response relationships with the underlying bistable dynamics of the model. Relying on in vitro experiments as well as outbreak data, we estimate plausible parameters for the human context. Despite the presence of uncertainty in such parameters, sensitivity analysis reveals that the host response is most influenced by the pathogen–immune system interaction. In particular, we show how variation in this interaction across a subgroup of the population dictates the shape of dose–response curves. Finally, in terms of future experimentation, our model results provide guidelines and highlight vital aspects of the interplay between immune cells and particular strains of Listeria monocytogenes that should be examined.
]]>2018-08-01T00:05:39-07:00info:doi/10.1098/rsos.180343hwp:master-id:royopensci;rsos.1803432018-08-01Mathematics58180343180343<![CDATA[The auxiliary region method: a hybrid method for coupling PDE- and Brownian-based dynamics for reaction-diffusion systems]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/5/8/180920?rss=1
Reaction–diffusion systems are used to represent many biological and physical phenomena. They model the random motion of particles (diffusion) and interactions between them (reactions). Such systems can be modelled at multiple scales with varying degrees of accuracy and computational efficiency. When representing genuinely multiscale phenomena, fine-scale models can be prohibitively expensive, whereas coarser models, although cheaper, often lack sufficient detail to accurately represent the phenomenon at hand. Spatial hybrid methods couple two or more of these representations in order to improve efficiency without compromising accuracy. In this paper, we present a novel spatial hybrid method, which we call the auxiliary region method (ARM), which couples PDE- and Brownian-based representations of reaction–diffusion systems. Numerical PDE solutions on one side of an interface are coupled to Brownian-based dynamics on the other side using compartment-based ‘auxiliary regions’. We demonstrate that the hybrid method is able to simulate reaction–diffusion dynamics for a number of different test problems with high accuracy. Furthermore, we undertake error analysis on the ARM which demonstrates that it is robust to changes in the free parameters in the model, where previous coupling algorithms are not. In particular, we envisage that the method will be applicable for a wide range of spatial multi-scales problems including filopodial dynamics, intracellular signalling, embryogenesis and travelling wave phenomena.
]]>2018-08-01T00:05:39-07:00info:doi/10.1098/rsos.180920hwp:master-id:royopensci;rsos.1809202018-08-01Mathematics58180920180920<![CDATA[Bistable fully developed mixed convection flow with viscous dissipation in a vertical channel]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/5/7/171880?rss=1
It is shown that unstable dual solutions in fully developed mixed convection flow in a vertical channel disappear in the presence of relatively strong thermal radiation. In this case, we have a unique stable flow at each pressure gradient. When the effect of thermal radiation is weak another branch of stable solutions is created, resulting in bistable flows. In this case, the flow exhibits hysteresis with variation of the pressure gradient. Optically, a thin radiation model is used.
]]>2018-07-11T00:09:56-07:00info:doi/10.1098/rsos.171880hwp:master-id:royopensci;rsos.1718802018-07-11Mathematics57171880171880<![CDATA[Technology networks: the autocatalytic origins of innovation]]>
http://rsos.royalsocietypublishing.org/cgi/content/short/5/6/172445?rss=1
We analyse the autocatalytic structure of technological networks and evaluate its significance for the dynamics of innovation patenting. To this aim, we define a directed network of technological fields based on the International Patents Classification, in which a source node is connected to a receiver node via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random. We show that the evolution of the technology network is compatible with the presence of a growing autocatalytic structure, i.e. a portion of the network in which technological fields mutually benefit from being connected to one another. We further show that technological fields in the core of the autocatalytic set display greater fitness, i.e. they tend to appear in a greater number of patents, thus suggesting the presence of positive spillovers as well as positive reinforcement. Finally, we observe that core shifts take place whereby different groups of technology fields alternate within the autocatalytic structure; this points to the importance of recombinant innovation taking place between close as well as distant fields of the hierarchical classification of technological fields.
]]>2018-06-27T06:04:49-07:00info:doi/10.1098/rsos.172445hwp:master-id:royopensci;rsos.1724452018-06-27Mathematics56172445172445