Typical prototype for a model describing the spread of an infectious disease.

<p>S, I, and R describe pools of susceptible, infected, and recovered individuals. Susceptible individuals only become sick as the result of contact with an infected person.</p

Diagram of a typical Michaelis-Menten reaction, in which an enzyme, E, catalyzes the conversion of a substrate, S, into a product, P, via the formation of an intermediate complex, ES.

<p>The indexed quantities, <i>k</i>, denote reaction rates.</p

Generic pathway with one activating and two inhibitory signals.

<p>Subscripted <i>X</i>'s are metabolites, while subscripted <i>v</i>'s are processes.</p

Understanding the Melanocyte Distribution in Human Epidermis: An Agent-Based Computational Model Approach

<div><p>The strikingly even color of human skin is maintained by the uniform distribution of melanocytes among keratinocytes in the basal layer of the human epidermis. In this work, we investigated three possible hypotheses on the mechanism by which the melanocytes and keratinocytes organize themselves to generate this pattern. We let the melanocyte migration be aided by (1) negative chemotaxis due to a substance produced by the melanocytes themselves, or (2) positive chemotaxis due to a substance produced by keratinocytes lacking direct physical contact with a melanocyte, or (3) positive chemotaxis due to a substance produced by keratinocytes in a distance-to-melanocytes dependent manner. The three hypotheses were implemented in an agent-based computational model of cellular interactions in the basal layer of the human epidermis. We found that they generate mutually exclusive predictions that can be tested by existing experimental protocols. This model forms a basis for further understanding of the communication between melanocytes and other skin cells in skin homeostasis.</p></div

Melanocyte density under different parameter settings.

<p>The three mechanisms for guiding melanocyte growth and migration were tested for their ability to establish a uniform melanocyte distribution at 5%, 10%, 25%, and 40% melanocyte densities. The temporal developments of the melanocyte density throughout the 10 days of simulation are shown. The simulations were repeated 12 times for each of the four parameter settings.</p

Melanocyte uniformity measurements.

<p>As quantitative measurements of the three different mechanisms’ ability to distribute melanocytes evenly, we counted the number of melanocytes with three or more melanocyte neighbors (top), and the relative standard deviation of the distance from all melanocytes to the nearest other melanocyte (bottom). All measurements are given as mean and standard deviation of 12 repetitions. A Kolmogorov–Smirnov test was performed to test for significant differences between the hypotheses at each parameter setting of which the results are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0040377#pone-0040377-t001" target="_blank"><b>Table 1</b></a>.</p

The observation area of the virtual dish after ended simulations.

<p>Simulations were performed with parameters set to establish four different melanocyte densities as indicated, for all three mechanisms proposed. All simulations were performed in 12 replicates; one representative image is shown for each parameter setting and mechanism.</p

Strength of exclusivity: Kolmogorov–Smirnov test on the data plotted in Figure 4.

<p>Strength of exclusivity: Kolmogorov–Smirnov test on the data plotted in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0040377#pone-0040377-g004" target="_blank">Figure 4</a>.</p

Signal gradient as produced by our diffusion model.

<p>Two different views of three different virtual cell cultures are shown. In the left panels the cells are colored according to cell type; keratinocytes blue and melanocytes red, while in the right panels cells are colored according to strength of signal (lighter color equals higher concentration). The signal substance diffuses from cell to cell and degrades according to our diffusion model. In these simulations, we have restricted the melanocytes to reside at the outer rim of the dish in order to visualize the global gradient towards the middle. In A, the cells are colored according to the concentration of signal substance R that is produced by all melanocytes at a constant rate. In B and C, the cells are colored according to the concentration of the attracting signal substance A. The gradient in B is generated by production of signal in all keratinocytes not in contact with a melanocyte (A, binary), while in C the gradient is set up by production of signal in all keratinocytes as a function of the strength of the signal R (A, R-dependent).</p

Effect of Regulatory Architecture on Broad versus Narrow Sense Heritability

<div><p>Additive genetic variance (<i>V_A</i>) and total genetic variance (<i>V_G</i>) are core concepts in biomedical, evolutionary and production-biology genetics. What determines the large variation in reported <i>V_A</i>/<i>V_G</i> ratios from line-cross experiments is not well understood. Here we report how the <i>V_A</i>/<i>V_G</i> ratio, and thus the ratio between narrow and broad sense heritability (<i>h²</i>/<i>H²</i>), varies as a function of the regulatory architecture underlying genotype-to-phenotype (GP) maps. We studied five dynamic models (of the cAMP pathway, the glycolysis, the circadian rhythms, the cell cycle, and heart cell dynamics). We assumed genetic variation to be reflected in model parameters and extracted phenotypes summarizing the system dynamics. Even when imposing purely linear genotype to parameter maps and no environmental variation, we observed quite low <i>V_A</i>/<i>V_G</i> ratios. In particular, systems with positive feedback and cyclic dynamics gave more non-monotone genotype-phenotype maps and much lower <i>V_A</i>/<i>V_G</i> ratios than those without. The results show that some regulatory architectures consistently maintain a transparent genotype-to-phenotype relationship, whereas other architectures generate more subtle patterns. Our approach can be used to elucidate these relationships across a whole range of biological systems in a systematic fashion.</p></div