Formation and growth of lipofuscin in the retinal pigment epithelium cells.

The kinetics of lipofuscin growth in diseased retinal pigment epithelium cells is investigated using Monte Carlo simulations and scaling theory on a cluster aggregation model. The model captures the essential physics of lipofuscin growth in the cells. A remarkable feature is that small particles may be removed from the cells while the larger ones become fixed and grow by aggregation. Model simulations are compared to the number of lipofuscin granules in eyes with early age-related degeneration.

Converting genetic network oscillations into somite spatial patterns.

The segmentation of vertebrate embryos, a process known as somitogenesis, depends on a complex genetic network that generates highly dynamic gene expression in an oscillatory manner. A recent proposal for the mechanism underlying these oscillations involves negative-feedback regulation at transcriptional translational levels, also known as the "delay model" [J. Lewis Curr. Biol. 13, 1398 (2003)]. In addition, in the zebrafish a longitudinal positional information signal in the form of an Fgf8 gradient constitutes a determination front that could be used to transform these coupled intracellular temporal oscillations into the observed spatial periodicity of somites. Here we consider an extension of the delay model by taking into account the interaction of the oscillation clock with the determination front. Comparison is made with the known properties of somite formation in the zebrafish embryo. We also show that the model can mimic the anomalies formed when progression of the determination wave front is perturbed and make an experimental prediction that can be used to test the model.

Effects of island disaggregation in growth models.

We introduced two point island models with island disaggregation. In the first one, particles can detach from islands with an odd number of particles and from those with two particles. In the second model, particles can detach from all islands with more than two particles. The scaling exponents are analytically obtained and verified with Monte Carlo simulations. Specially, the power-law scalings of the island and monomer densities are analyzed. Comparison with other models indicates that the models introduced here present different scaling behaviors.

Growth model with disaggregation of islands having an odd number of particles.

A simple model of deposition of particles and growth of point islands in a two-dimensional substrate is introduced and studied. The detachment of particles from islands with an odd number of particles can occur with a probability P. The power-law scalings of the island, monomer, and odd island densities are analytically obtained and verified by Monte Carlo simulations. The universality class of the model depends on P, and the island density exponent chi changes from chi=1/3 (for P=0 ) to chi=0 (for P>0 ).

Effects of the sticking probability on the scaling of the island density in a point island model.

The behavior of the island density exponent chi for a model of deposition, nucleation, and aggregation of particles, forming point islands with a sticking probability p in one dimension, is analyzed. Using Monte Carlo simulation we found that chi depends on p. For p=1 we obtain chi congruent with 1/4, the well-known result for perfect sticking and one-dimensional diffusion. Interestingly, as p is decreased, chi adopts higher values. Possible reasons for this behavior are addressed. The universal result for a one-dimensional diffusion, chi=1/4, is expected to be recovered, for all p, only in the asymptotic regime.