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- Christine Sample, Stanislav Y Shvartsman
- Proceedings of the National Academy of Sciences…
- 2010

We developed a multiscale approach for the computationally efficient modeling of morphogen gradients in the syncytial Drosophila embryo, a single cell with multiple dividing nuclei. By using a homogenization technique, we derived a coarse-grained model with parameters that are explicitly related to the geometry of the syncytium and kinetics of… (More)

- Alexander M Berezhkovskii, Christine Sample, Stanislav Y Shvartsman
- Biophysical journal
- 2010

A morphogen gradient is defined as a concentration field of a molecule that acts as a dose-dependent regulator of cell differentiation. One of the key questions in studies of morphogen gradients is whether they reach steady states on timescales relevant for developmental patterning. We propose a systematic approach for addressing this question and… (More)

- Alexander M Berezhkovskii, Christine Sample, Stanislav Y Shvartsman
- Physical review. E, Statistical, nonlinear, and…
- 2011

Spatial regulation of cell differentiation in embryos can be provided by morphogen gradients, which are defined as the concentration fields of molecules that control gene expression. For example, a cell can use its surface receptors to measure the local concentration of an extracellular ligand and convert this information into a corresponding change in its… (More)

- Peter V Gordon, Christine Sample, Alexander M Berezhkovskii, Cyrill B Muratov, Stanislav Y Shvartsman
- Proceedings of the National Academy of Sciences…
- 2011

Some aspects of pattern formation in developing embryos can be described by nonlinear reaction-diffusion equations. An important class of these models accounts for diffusion and degradation of a locally produced single chemical species. At long times, solutions of such models approach a steady state in which the concentration decays with distance from the… (More)

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