Refining self-propelled particle models for collective behaviour

Swarming, schooling, flocking and herding are all names given to the wide variety of collective behaviours exhibited by groups of animals, bacteria and even individual cells. More generally, the term swarming describes the behaviour of an aggregate of agents (not necessarily biological) of similar size and shape which exhibit some emergent property such as directed migration or group cohesion. In this paper we review various individual-based models of collective behaviour and discuss their merits and drawbacks. We further analyse some one-dimensional models in the context of locust swarming. In specific models, in both one and two dimensions, we demonstrate how varying the parameters relating to how much attention individuals pay to their neighbours can dramatically change the behaviour of the group. We also introduce leader individuals to these models with the ability to guide the swarm to a greater or lesser degree as we vary the parameters of the model. We consider evolutionary scenarios for models with leaders in which individuals are allowed to evolve the degree of influence neighbouring individuals have on their subsequent motion

Reconciling transport models across scales: the role of volume exclusion

Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the role of volume exclusion, which can significantly alter diffusive transport, particularly within biological systems where the diffusing particles might occupy a significant fraction of the available space. In this work we use a random walk approach to provide a means to reconcile models that incorporate crowding effects on different spatial scales. Our work demonstrates that coarse-grained models incorporating simplified descriptions of excluded volume can be used in many circumstances, but that care must be taken in pushing the coarse-graining process too far

Efficient parameter sensitivity computation for spatially extended reaction networks

Reaction-diffusion models are widely used to study spatially-extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for computing parametric sensitivities are required. In this work, we focus on stochastic models of spatially-extended chemical reaction systems that involve partitioning the computational domain into voxels. Parametric sensitivities are often calculated using Monte Carlo techniques that are typically computationally expensive; however, variance reduction techniques can decrease the number of Monte Carlo simulations required. By exploiting the characteristic dynamics of spatially-extended reaction networks, we are able to adapt existing finite difference schemes to robustly estimate parametric sensitivities in a spatially-extended network. We show that algorithmic performance depends on the dynamics of the given network and the choice of summary statistics. We then describe a hybrid technique that dynamically chooses the most appropriate simulation method for the network of interest. Our method is tested for functionality and accuracy in a range of different scenarios

Variable species densities are induced by volume exclusion interactions upon domain growth.

In this work we study the effect of domain growth on spatial correlations in agent populations containing multiple species. This is important as heterogenous cell populations are ubiquitous during the embryonic development of many species. We have previously shown that the long term behaviour of an agent population depends on the way in which domain growth is implemented. We extend this work to show that, depending on the way in which domain growth is implemented, different species dominate in multispecies simulations. Continuum approximations of the lattice-based model that ignore spatial correlations cannot capture this behaviour, while those that explicitly account for spatial correlations can. The results presented here show that the precise mechanism of domain growth can determine the long term behaviour of multispecies populations, and in certain circumstances, establish spatially varying species densities

Extending the multi-level method for the simulation of stochastic biological systems

The multi-level method for discrete state systems, first introduced by Anderson and Higham [Multiscale Model. Simul. 10:146--179, 2012], is a highly efficient simulation technique that can be used to elucidate statistical characteristics of biochemical reaction networks. A single point estimator is produced in a cost-effective manner by combining a number of estimators of differing accuracy in a telescoping sum, and, as such, the method has the potential to revolutionise the field of stochastic simulation. The first term in the sum is calculated using an approximate simulation algorithm, and can be calculated quickly but is of significant bias. Subsequent terms successively correct this bias by combining estimators from approximate stochastic simulations algorithms of increasing accuracy, until a desired level of accuracy is reached. In this paper we present several refinements of the multi-level method which render it easier to understand and implement, and also more efficient. Given the substantial and complex nature of the multi-level method, the first part of this work (Sections 2 - 5) is written as a tutorial, with the aim of providing a practical guide to its use. The second part (Sections 6 - 8) takes on a form akin to a research article, thereby providing the means for a deft implementation of the technique, and concludes with a discussion of a number of open problems.Comment: 38 page

The effect of sacubitril/valsartan compared to olmesartan on cardiovascular remodelling in subjects with essential hypertension: the results of a randomized, double-blind, active-controlled study

Aims: Progressive aortic stiffening eventually leads to left ventricular (LV) hypertrophy and heart failure if left untreated. Anti-hypertensive agents have been shown to reverse this to some extent. The effects of sacubitril/valsartan (LCZ696), a dual-action angiotensin receptor blocker (ARB), and neprilysin inhibitor, on arterial stiffness and LV remodelling have not been investigated. Methods and results: This was a randomized, multi-centre, double-blind, double-dummy, active-controlled, parallel group, study to compare the effects on cardiovascular remodelling of sacubitril/valsartan with those of olmesartan in patients with hypertension and elevated pulse pressure. Magnetic resonance imaging scans were used to assess LV mass and local aortic distensibility, at baseline and at 12 and 52 weeks after initiation of treatment. Central pulse and systolic pressure were determined using a SphymoCor® XCEL device at each time point. A total of 114 patients were included, with 57 in each treatment group. The mean age was 59.8 years, and 67.5% were male. Demographic characteristics did not vary between the two sets of patients. Left ventricular mass index decreased to a greater extent in the sacubitril/valsartan group compared to the olmesartan group from baseline to 12 weeks (−6.36 vs. −2.32 g/m2; P = 0.039) and from baseline to 52 weeks (−6.83 vs. −3.55 g/m2; P = 0.029). These differences remained significant after adjustment for systolic blood pressure (SBP) at follow-up (P = 0.036 and 0.019 at 12 and 52 weeks, respectively) and similar signals (though formally non-significant) were observed after adjusting for changes in SBP (P = 0.0612 and P = 0.0529, respectively). There were no significant differences in local distensibility changes from baseline to 12 or 52 weeks between the two groups; however, there was a larger reduction in central pulse pressure for the sacubitril/valsartan group compared to the olmesartan group (P = 0.010). Conclusion: Since LV mass change correlates with cardiovascular prognosis, the greater reductions in LV mass indicate valuable advantages of sacubitril/valsartan compared to olmesartan. The finding that LV mass index decrease might be to some extent independent of SBP suggests that the effect of the dual-acting agent may go beyond those due to its BP-lowering ability

Using approximate Bayesian computation to quantify cell-cell adhesion parameters in a cell migratory process

In this work we implement approximate Bayesian computational methods to improve the design of a wound-healing assay used to quantify cell-cell interactions. This is important as cell-cell interactions, such as adhesion and repulsion, have been shown to play a role in cell migration. Initially, we demonstrate with a model of an unrealistic experiment that we are able to identify model parameters that describe agent motility and adhesion, given we choose appropriate summary statistics for our model data. Following this, we replace our model of an unrealistic experiment with a model representative of a practically realisable experiment. We demonstrate that, given the current (and commonly used) experimental set-up, our model parameters cannot be accurately identified using approximate Bayesian computation methods. We compare new experimental designs through simulation, and show more accurate identification of model parameters is possible by expanding the size of the domain upon which the experiment is performed, as opposed to increasing the number of experimental replicates. The results presented in this work therefore describe time and cost-saving alterations for a commonly performed experiment for identifying cell motility parameters. Moreover, this work will be of interest to those concerned with performing experiments that allow for the accurate identification of parameters governing cell migratory processes, especially cell migratory processes in which cell-cell adhesion or repulsion are known to play a significant role

The effect of domain growth on spatial correlations

Mathematical models describing cell movement and proliferation are important tools in developmental biology research. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations between agent locations in a continuum approximation of a one-dimensional lattice-based model of cell motility and proliferation. This is important as the inclusion of spatial correlations in continuum models of cell motility and proliferation without domain growth has previously been shown to be essential for their accuracy in certain scenarios. We include the effect of spatial correlations by deriving a system of ordinary differential equations that describe the expected evolution of individual and pair density functions for agents on a growing domain. We then demonstrate how to simplify this system of ordinary differential equations by using an appropriate approximation. This simplification allows domain growth to be included in models describing the evolution of spatial correlations between agents in a tractable manner