Swapping in lattice-based cell migration models.

Cell migration is frequently modeled using on-lattice agent-based models (ABMs) that employ the excluded volume interaction. However, cells are also capable of exhibiting more complex cell-cell interactions, such as adhesion, repulsion, pulling, pushing, and swapping. Although the first four of these have already been incorporated into mathematical models for cell migration, swapping has not been well studied in this context. In this paper, we develop an ABM for cell movement in which an active agent can "swap" its position with another agent in its neighborhood with a given swapping probability. We consider a two-species system for which we derive the corresponding macroscopic model and compare it with the average behavior of the ABM. We see good agreement between the ABM and the macroscopic density. We also analyze the movement of agents at an individual level in the single-species as well as two-species scenarios to quantify the effects of swapping on an agent's motility.

A suitable anaesthetic protocol for metamorphic zebrafish.

Zebrafish are frequently used as a means to investigate development. These studies increasingly require repeated anaesthesia of zebrafish during juvenile (i.e. metamorphic) stages. The effects of anaesthesia during this time remain poorly studied. The aim of this study was to develop a reliable method that can be used for frequently repeated anaesthesia during juvenile stages. Initially, we assessed different concentrations of MS-222, the most commonly used fish anaesthetic, for 30 minute anaesthesia with recovery. We showed that suitable MS-222 doses could be identified for the smallest (7mm) and largest (20mm) fish. However, we found that juvenile fish within a specific metamorphic window (sized between 8-16 mm) were vulnerable to MS-222 and no standard concentration of MS-222 provided reliable anaesthesia under these conditions. Hence we focussed our efforts on identifying a protocol for these stages. We tested six different published anaesthesia protocols P1-P6 where P1, P2 corresponds to 0.01% MS-222, P3, P4: 0.085% 2-phenoxyethanol and P5, P6: 0.00025%/0.0050% Propofol/Lidocaine. In protocols P1, P3, P5 fish were maintained by immersion, whilst in P2, P4 and P6: fish were maintained on an anaesthetic-doused cotton-pad. We assessed reliable anaesthesia using 10 fish for 10 minutes, with full recovery. Our data allowed us to eliminate two of these protocols as unsuitable for short term anaesthesia with recovery of juvenile fish. Extending these studies to explore repeated anaesthesia at 4 day intervals for 20 days under the remaining four protocols, we showed that P1 and P4 were both suitable for repeated anaesthesia, and that P4 was most suitable for imaging. We confirmed that P4 remained suitable when the frequency of anaesthesia was increased to every 2 days. We conclude that this protocol provides a refinement to the current protocol for repeated anaesthesia with recovery of juvenile zebrafish in the vulnerable metamorphic window.

A quantitative modelling approach to zebrafish pigment pattern formation.

Pattern formation is a key aspect of development. Adult zebrafish exhibit a striking striped pattern generated through the self-organisation of three different chromatophores. Numerous investigations have revealed a multitude of individual cell-cell interactions important for this self-organisation, but it has remained unclear whether these known biological rules were sufficient to explain pattern formation. To test this, we present an individual-based mathematical model incorporating all the important cell-types and known interactions. The model qualitatively and quantitatively reproduces wild type and mutant pigment pattern development. We use it to resolve a number of outstanding biological uncertainties, including the roles of domain growth and the initial iridophore stripe, and to generate hypotheses about the functions of leopard. We conclude that our rule-set is sufficient to recapitulate wild-type and mutant patterns. Our work now leads the way for further in silico exploration of the developmental and evolutionary implications of this pigment patterning system.

Pair correlation functions for identifying spatial correlation in discrete domains.

Identifying and quantifying spatial correlation are important aspects of studying the collective behavior of multiagent systems. Pair correlation functions (PCFs) are powerful statistical tools that can provide qualitative and quantitative information about correlation between pairs of agents. Despite the numerous PCFs defined for off-lattice domains, only a few recent studies have considered a PCF for discrete domains. Our work extends the study of spatial correlation in discrete domains by defining a new set of PCFs using two natural and intuitive definitions of distance for a square lattice: the taxicab and uniform metric. We show how these PCFs improve upon previous attempts and compare between the quantitative data acquired. We also extend our definitions of the PCF to other types of regular tessellation that have not been studied before, including hexagonal, triangular, and cuboidal. Finally, we provide a comprehensive PCF for any tessellation and metric, allowing investigation of spatial correlation in irregular lattices for which recognizing correlation is less intuitive.

Zebrafish adult pigment stem cells are multipotent and form pigment cells by a progressive fate restriction process: Clonal analysis identifies shared origin of all pigment cell types.

Skin pigment pattern formation is a paradigmatic example of pattern formation. In zebrafish, the adult body stripes are generated by coordinated rearrangement of three distinct pigment cell-types, black melanocytes, shiny iridophores and yellow xanthophores. A stem cell origin of melanocytes and iridophores has been proposed although the potency of those stem cells has remained unclear. Xanthophores, however, seemed to originate predominantly from proliferation of embryonic xanthophores. Now, data from Singh et al. shows that all three cell-types derive from shared stem cells, and that these cells generate peripheral neural cell-types too. Furthermore, clonal compositions are best explained by a progressive fate restriction model generating the individual cell-types. The numbers of adult pigment stem cells associated with the dorsal root ganglia remain low, but progenitor numbers increase significantly during larval development up to metamorphosis, likely via production of partially restricted progenitors on the spinal nerves.