BIO-LGCA: A cellular automaton modelling class for analysing collective cell migration

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics—understood as population behaviour arising from the interplay of the constituting discrete cells—can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments.     

A particle model analysing the behavioural rules underlying the collective flight of a bee swarm towards the new nest

The swarming of a bee colony is guided by a small group of scout individuals, which are informed of the target destination (the new nest). However, little is known on the underlying mechanisms, i.e. on how the information is passed within the population. In this respect, we here present a discrete mathematical model to investigate these aspects. In particular, each bee, represented by a material point, is assigned its status within the colony and set to move according to individual strategies and social interactions. More specifically, we propose alternative assumptions on the flight synchronization mechanism of uninformed individuals and on the characteristic dynamics of the scout insects. Numerical realizations then point out the combinations of behavioural hypotheses resulting in collective productive movement. An analysis of the role of the scout bee percentage and of the phenomenology of the swarm in domains with structural elements is finally performed.     

Soft tissue modelling for applications in virtual surgery and surgical robotics

Soft tissue modelling has gained a great deal of importance, for a large part due to its application in surgical training simulators for minimally invasive surgery (MIS). This article provides a structured overview of different continuum-mechanical models that have been developed over the years. It aims at facilitating model choice for specific soft tissue modelling applications. According to the complexity of the model, different features of soft biological tissue will be incorporated, i.e. nonlinearity, viscoelasticity, anisotropy, heterogeneity and finally, tissue damage during deformation. A brief summary of experimental methods for material characterisation and an introduction to methods for geometric modelling are also provided.

The overview is non-exhaustive, focusing on the most important general models and models with specific biological applications. A trade-off in complexity must be made for enabling real-time simulation, but still maintaining realistic representation of the organ deformation. Depending on the organ and tissue types, different models with emphasis on certain features will prove to be more appropriate, meaning the optimal model choice is organ and tissue-dependent.     

Soft tissue modelling for applications in virtual surgery and surgical robotics

Soft tissue modelling has gained a great deal of importance, for a large part due to its application in surgical training simulators for minimally invasive surgery (MIS). This article provides a structured overview of different continuum-mechanical models that have been developed over the years. It aims at facilitating model choice for specific soft tissue modelling applications. According to the complexity of the model, different features of soft biological tissue will be incorporated, i.e. nonlinearity, viscoelasticity, anisotropy, heterogeneity and finally, tissue damage during deformation. A brief summary of experimental methods for material characterisation and an introduction to methods for geometric modelling are also provided. The overview is non-exhaustive, focusing on the most important general models and models with specific biological applications. A trade-off in complexity must be made for enabling real-time simulation, but still maintaining realistic representation of the organ deformation. Depending on the organ and tissue types, different models with emphasis on certain features will prove to be more appropriate, meaning the optimal model choice is organ and tissue-dependent.     

A framework for modelling and analysing conspecific brood parasitism

Recently several papers that model parasitic egg-laying by birds in the nests of others of their own species have been published. Whilst these papers are concerned with answering different questions, they approach the problem in a similar way and have a lot of common features. In this paper a framework is developed which unifies these models, in the sense that they all become special cases of a more general model. This is useful for two main reasons; firstly in order to aid clarity, in that the assumptions and conclusions of each of the models are easier to compare. Secondly it provides a base for further similar models to start from. The basic assumptions for this framework are outlined and a method for finding the ESSs of such models is introduced. Some mathematical results for the general, and more specific, models are considered and their implications discussed. In addition we explore the biological consequences of the results that we have obtained and suggest possible questions which could be investigated using models within or very closely related to our framework.M. Broom is also a member of the Centre for the Study of Evolution at the University of Sussex.     

On the collective nature of phytochrome photoactivation

The red/far-red-sensing biological photoreceptor phytochrome is a paradigmatic two-state signaling system. The two thermally stable states are interconverted via a photoreaction of the covalently bound tetrapyrrole chromophore. Applying recently developed solid-state nuclear magnetic resonance, we study both the chromophore and its protein pocket in the Pr (red-absorbing) and Pfr (far-red-absorbing) states. The observations show that the phototransformation combines local chemical reactions with a mesoscopic transition of order. Both the chromophore and its binding pocket are quasi-liquid and disordered in Pr, yet quasi-solid and ordered in Pfr. Possible biochemical implications are discussed.     

On the topological evidences for modelling lipophilicity

Topological evidences for modelling lipophilicity of a large series of diversed compounds have been provided on the basis of distance-based topological indices. A pool of topological indices along with indicator parameters related to the type of the compounds present in the set of 140 compounds were used for this purpose. The results have shown that topology as well as the type of compounds are the responsible parameters for modelling lipophilicity.     

Follow the straggler: zebrafish use a simple heuristic for collective decision-making

Animal groups often make decisions sequentially, from the front to the back of the group. In such cases, individuals can use the choices made by earlier ranks, a form of social information, to inform their own choice. The optimal strategy for such decisions has been explored in models which differ on, for example, whether or not agents take into account the sequence of observed choices. The models demonstrate that choices made later in a sequence are more informative, but it is not clear if animals use this information or rely instead on simpler heuristics, such as quorum rules. We show that a simple rule ‘copy the last observed choice'', gives similar predictions to those of optimal models for most likely sequences. We trained groups of zebrafish to choose one arm of a Y-maze and used them to demonstrate various sequences to naive fish. We show that the naive fish appear to use a simple rule, most often copying the choice of the last demonstrator, which results in near-optimal choices at a fraction of the computational cost.     

On the role of collective sensing and evolution in group formation

Collective sensing is an emergent phenomenon which enables individuals to estimate a hidden property of the environment through the observation of social interactions. Previous work on collective sensing shows that gregarious individuals obtain an evolutionary advantage by exploiting collective sensing when competing against solitary individuals. This work addresses the question of whether collective sensing allows for the emergence of groups from a population of individuals without predetermined behaviors. It is assumed that group membership does not lessen competition on the limited resources in the environment, e.g., groups do not improve foraging efficiency. Experiments are run in an agent-based evolutionary model of a foraging task, where the fitness of the agents depends on their foraging strategy. The foraging strategy of agents is determined by a neural network, which does not require explicit modeling of the environment and of the interactions between agents. Experiments demonstrate that gregarious behavior is not the evolutionary-fittest strategy if resources are abundant, thus invalidating previous findings in a specific region of the parameter space. In other words, resource scarcity makes gregarious behavior so valuable as to make up for the increased competition over the few available resources. Furthermore, it is shown that a population of solitary agents can evolve gregarious behavior in response to a sudden scarcity of resources, thus individuating a possible mechanism that leads to gregarious behavior in nature. The evolutionary process operates on the whole parameter space of the neural networks; hence, these behaviors are selected among an unconstrained set of behavioral models.     

The use of animated difference matrices for analysing protein molecular dynamics simulation data

A method for analysing molecular dynamics data is described which uses animation on a calligraphic system. Each conformation from the dynamics experiment is represented by a ‘frame’ of an interactive movie. The frames show upper triangles of distance matrices calculated from the conformations. Distance matrices enable researchers to recognise cooperative motions of the atoms. Difference distance matrices, which are calculated by subtracting the corresponding elements of a distance matrix from those in the previous one, are also used to analyse the motions. In this paper the technique is explained and an example is given where these tools are being used to analyse results from a dynamics simulation of a polypeptide.     

Optimality modelling and quantitative genetics as alternatives to study the evolution of foraging behaviours in insect herbivores.

Summary Although the evolution of large-scale dispersal has received considerable attention, we know very little about how natural selection influences foraging behaviours in herbivorous insects. Host-selection behaviours and within-habitat movements jointly determine foraging behaviours, since host selection affects the allocation of time spent on a particular host versus moving between these hosts. However, host selection is generally a labile trait, whose expression is influenced by the physiological state of the forager and hence, by characteristics of the habitat. We discuss how the quantitative genetic concepts can be used to study the evolution of such labile behaviours. Since host responses depend on the physiological state of the forager, it is argued that the state of the forager must be explicitly considered when estimating the additive genetic basis of host-selection behaviours. The lability of foraging behaviours increases the difficulty of measuring the fitness consequence of variation in the foraging phenotype in specific habitats. Therefore, it may be difficult to rely exclusively on quantitative genetic methods to test hypotheses about adaptive change in foraging behaviours across different habitats. We provide a novel approach based on optimality modelling to calculate the fitness consequence of variation in the foraging phenotype across different habitats. This method, in conjunction with quantitative genetics, can be used to test hypotheses concerning the evolution of foraging behaviours.     

Phylogenetic generalised dissimilarity modelling: a new approach to analysing and predicting spatial turnover in the phylogenetic composition of communities

Compared to species turnover, patterns of phylogenetic turnover provide extra information about the spatial structure of biodiversity, for example providing more informative comparisons between the biota of sites which share no species. To harness this information for broad‐scale spatial analysis, we present phylo‐GDM, a technique for interpolating the spatial structure of phylogenetic turnover between sampled locations in relation to environment, based on generalised dissimilarity modelling (GDM). Using a database of over 150 000 location records for 114 myobatrachid frog species in Australia, linked to a species‐level phylogeny inferred from 2467 base pairs of mitochondrial DNA, we calculated species and phylogenetic turnover between pairs of sites. We show how phylogenetic turnover extended the range of informative comparison of compositional turnover to more biologically and environmentally dissimilar sites. We generated GDM models which predict species and phylogenetic turnover across Australia, and tested the fit of models for different ages within the phylogeny to find the phylogenetic tree depth at which the relationship to current day environment is greatest. We also incorporated explanatory variables based on biogeographic patterns, to represent broad‐scale turnover resulting from divergent evolutionary histories. We found that while the predictive power of our models was lower for full phylogenetic turnover than for species turnover, models based on the more recent components of the phylogeny (closer to the tips) outperformed species models and full phylogenetic models. Phylo‐GDM has considerable potential as a method for incorporating phylogenetic relationships into biodiversity analyses in ways not previously possible. Because phylogenies do not require named taxa, phylo‐GDM may also provide a means of including lineages with poorly resolved taxonomy (e.g. from metagenomic sequencing) into biodiversity planning and phylogeographic analysis.     

Physiologically-based pharmacokinetic modelling for the reduction of animal use in the discovery of novel pharmaceuticals

The challenges of physiologically-based pharmacokinetic (PBPK) modelling and approaches to replacing the use of animals, in order to determine drug pharmacokinetics, are discussed. Reference is made to the limitations of in vivo animal studies in drug discovery. In particular, the ways in which animal studies contribute to drug attrition during the post-preclinical phase of testing are considered.     

Cooperative object transport with a swarm of e-puck robots: robustness and scalability of evolved collective strategies

Cooperative object transport in distributed multi-robot systems requires the coordination and synchronisation of pushing/pulling forces by a group of autonomous robots in order to transport items that cannot be transported by a single agent. The results of this study show that fairly robust and scalable collective transport strategies can be generated by robots equipped with a relatively simple sensory apparatus (i.e. no force sensors and no devices for direct communication). In the experiments described in this paper, homogeneous groups of physical e-puck robots are required to coordinate and synchronise their actions in order to transport a heavy rectangular cuboid object as far as possible from its starting position to an arbitrary direction. The robots are controlled by dynamic neural networks synthesised using evolutionary computation techniques. The best evolved controller demonstrates an effective group transport strategy that is robust to variability in the physical characteristics of the object (i.e. object mass and size of the longest object’s side) and scalable to different group sizes. To run these experiments, we designed, built, and mounted on the robots a new sensor that returns the agents’ displacement on a 2D plane. The study shows that the feedback generated by the robots’ sensors relative to the object’s movement is sufficient to allow the robots to coordinate their efforts and to sustain the transports for an extended period of time. By extensively analysing successful behavioural strategies, we illustrate the nature of the operational mechanisms underpinning the coordination and synchronisation of actions during group transport.