Partner: Yongtao Zhang

University of Notre Dame (US)

Ostatnie publikacje
1.Newman S.A., Christley S., Glimm T., Hentschel H.G., Kaźmierczak B., Zhang Y.T., Zhu J., Alber M., Multiscale models for vertebrate limb development, CURRENT TOPICS IN DEVELOPMENTAL BIOLOGY, ISSN: 0070-2153, Vol.81, pp.311-340, 2008

Streszczenie:

Dynamical systems in which geometrically extended model cells produce and interact with diffusible (morphogen) and nondiffusible (extracellular matrix) chemical fields have proved very useful as models for developmental processes. The embryonic vertebrate limb is an apt system for such mathematical and computational modeling since it has been the subject of hundreds of experimental studies, and its normal and variant morphologies and spatiotemporal organization of expressed genes are well known. Because of its stereotypical proximodistally generated increase in the number of parallel skeletal elements, the limb lends itself to being modeled by Turing-type systems which are capable of producing periodic, or quasiperiodic, arrangements of spot- and stripe-like elements. This chapter describes several such models, including, (i) a system of partial differential equations in which changing cell density enters into the dynamics explicitly, (ii) a model for morphogen dynamics alone, derived from the latter system in the “morphostatic limit” where cell movement relaxes on a much slower time-scale than cell differentiation, (iii) a discrete stochastic model for the simplified pattern formation that occurs when limb cells are placed in planar culture, and (iv) several hybrid models in which continuum morphogen systems interact with cells represented as energy-minimizing mesoscopic entities. Progress in devising computational methods for handling 3D, multiscale, multimodel simulations of organogenesis is discussed, as well as for simulating reaction–diffusion dynamics in domains of irregular shape.

Afiliacje autorów:

Newman S.A.-New York Medical College (US)
Christley S.-University of Chicago (US)
Glimm T.-Western Washington University (US)
Hentschel H.G.-Emory University (US)
Kaźmierczak B.-IPPT PAN
Zhang Y.T.-University of Notre Dame (US)
Zhu J.-University of Notre Dame (US)
Alber M.-University of Notre Dame (US)
2.Alber M., Glimm T., Hentschel H.G., Kaźmierczak B., Zhang Y.T., Zhu J., Newman S.A., The morphostatic limit for a model of skeletal pattern formation in the vertebrate limb, BULLETIN OF MATHEMATICAL BIOLOGY, ISSN: 0092-8240, DOI: 10.1007/s11538-007-9264-3, Vol.70, pp.460-483, 2007

Streszczenie:

A recently proposed mathematical model of a “core” set of cellular and molecular interactions present in the developing vertebrate limb was shown to exhibit pattern-forming instabilities and limb skeleton-like patterns under certain restrictive conditions, suggesting that it may authentically represent the underlying embryonic process (Hentschel et al., Proc. R. Soc. B 271, 1713–1722, 2004). The model, an eight-equation system of partial differential equations, incorporates the behavior of mesenchymal cells as “reactors,” both participating in the generation of morphogen patterns and changing their state and position in response to them. The full system, which has smooth solutions that exist globally in time, is nonetheless highly complex and difficult to handle analytically or numerically. According to a recent classification of developmental mechanisms (Salazar-Ciudad et al., Development 130, 2027–2037, 2003), the limb model of Hentschel et al. is “morphodynamic,” since differentiation of new cell types occurs simultaneously with cell rearrangement. This contrasts with “morphostatic” mechanisms, in which cell identity becomes established independently of cell rearrangement. Under the hypothesis that development of some vertebrate limbs employs the core mechanism in a morphostatic fashion, we derive in an analytically rigorous fashion a pair of equations representing the spatiotemporal evolution of the morphogen fields under the assumption that cell differentiation relaxes faster than the evolution of the overall cell density (i.e., the morphostatic limit of the full system). This simple reaction–diffusion system is unique in having been derived analytically from a substantially more complex system involving multiple morphogens, extracellular matrix deposition, haptotaxis, and cell translocation. We identify regions in the parameter space of the reduced system where Turing-type pattern formation is possible, which we refer to as its “Turing space.” Obtained values of the parameters are used in numerical simulations of the reduced system, using a new Galerkin finite element method, in tissue domains with nonstandard geometry. The reduced system exhibits patterns of spots and stripes like those seen in developing limbs, indicating its potential utility in hybrid continuum-discrete stochastic modeling of limb development. Lastly, we discuss the possible role in limb evolution of selection for increasingly morphostatic developmental mechanisms.

Słowa kluczowe:

Limb development, Chondrogenesis, Mesenchymal condensation, Reaction–diffusion model

Afiliacje autorów:

Alber M.-University of Notre Dame (US)
Glimm T.-Western Washington University (US)
Hentschel H.G.-Emory University (US)
Kaźmierczak B.-IPPT PAN
Zhang Y.T.-University of Notre Dame (US)
Zhu J.-University of Notre Dame (US)
Newman S.A.-New York Medical College (US)