We describe a 'reactor-diffusion' mechanism for precartilage condensation based on recent experiments chondrogenesis in the early vertebrate limb and additional hypotheses. Cellular differentiation of mesenchymal cells into subtypes with different fibroblast growth factor (FGF) receptors occurs presence spatio-temporal variations FGFs transforming factor-betas (TGF-betas). One class differentiated produces elevated quantities extracellular matrix protein fibronectin, which initiates...

In this paper we present the foundation of a unified, object-oriented, three-dimensional biomodelling environment, which allows us to integrate multiple submodels at scales from subcellular those tissues and organs. Our current implementation combines modified discrete model statistical mechanics, Cellular Potts Model, with continuum reaction–diffusion state automaton well-defined conditions for cell differentiation transitions genetic regulation. This environment rapidly compactly create...

We present COMPUCELL3D, a software framework for three-dimensional simulation of morphogenesis in different organisms. COMPUCELL3D employs biologically relevant models cell clustering, growth, and interaction with chemical fields. uses design patterns speed, efficient memory management, extensibility, flexibility to allow an almost unlimited variety simulations. have verified by building model growth skeletal pattern formation the avian (chicken) limb bud. Binaries source code are available,...

The Cellular Potts Model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. In this paper, we derive continuous limit discrete one dimensional CPM with chemotactic interactions between cells form a Fokker-Planck equation evolution cell probability density function. This is then reduced to...

To gain performance, developers often build scientific applications in procedural languages, such as C or Fortran, which unfortunately reduces flexibility. address this imbalance, the authors present CompuCell3D, a multitiered, flexible, and scalable problem-solving environment for morphogenesis simulations that's written C++ using object-oriented design patterns.

This review discusses concepts of how agency, defined here as organism-initiated behavior (both species-characteristic and individually idiosyncratic), was aligned at the cellular integrated in multicellular levels during evolution. We consider agency relation to autonomy purposiveness cells organisms. While extant forms (and inferred single-cell antecedents) is assumed our analysis, we do not speculate on its origins. attempt discern role generation form function social bacteria amoebae,...

It is shown that the problem of designing a two-reflector system transforming plane wave front with given intensity into an output prescribed can be formulated and solved as Monge-Kantorovich mass transfer 1 .

Abstract We present a model of systems cells with intracellular oscillators (‘clocks’). This is motivated by examples from developmental biology and the behavior organisms on threshold to multicellularity. Cells undergo random motion adhere each other. The adhesion strength between neighbors depends their clock phases in addition constant baseline strength. are linked via Kuramoto-type local interactions. an advection-diffusion partial differential equation nonlocal advection terms....

Genotypic variation, environmental and their interaction may produce variation in the developmental process cause phenotypic differences among individuals. Developmental noise, which arises during development from stochasticity cellular molecular processes when genotype environment are fixed, also contributes to variation. While evolutionary biology has long focused on teasing apart relative contribution of genes our understanding role noise lagged due technical difficulties directly...

A multiscale network of two galectins Galectin-1 (Gal-1) and Galectin-8 (Gal-8) patterns the avian limb skeleton. Among vertebrates with paired appendages, chondrichthyan fins typically have one or more cartilage plates many repeating parallel endoskeletal elements, actinopterygian varied nodules, bars plates, while tetrapod limbs exhibit tandem arrays few, proximodistally increasing numbers elements. We applied a comparative genomic protein evolution approach to understand origin galectin...

The stability of Turing patterns in an n-dimensional cube (0, π)n is studied, where n ≥ 2. It shown by using a generalization classical result Ermentrout concerning spots and stripes two dimensions that under appropriate assumptions only sheet-like or nodule-like structures can be stable cube. Other also regions comprising products lower-dimensional cubes intervals length. Stability results are applied to new model skeletal pattern formation the vertebrate limb.

Ovarian cancer is amongst the most morbid of gynecological malignancies due to its diagnosis at an advanced stage, a transcoelomic mode metastasis, and rapid transition chemotherapeutic resistance. Like all other malignancies, progression ovarian may be interpreted as emergent outcome conflict between metastasizing cells natural defense mounted by microenvironmental barriers such migration. Here, we asked whether senescence in coelom-lining mesothelia, brought about drug exposure, affects...

We consider the following geometric optics problem: construct a system of two reflectors which transforms spherical wavefront generated by point source into beam parallel rays. This has prescribed intensity distribution. give rigorous analysis this problem. The we are (parts of) boundaries convex sets. prove existence solutions for large class input data and uniqueness result. To author's knowledge, is first time that mathematical problem given. approach based on optimal transportation...

We investigate a simple generic model of reaction–diffusion system consisting an activator and inhibitor molecule in the presence linear morphogen gradient. assume that this gradient is established independently acts by increasing production proportional to concentration. The motivated several existing models developmental biology which Turing patterning mechanism proposed various chemical gradients are known be important for development. Mathematically, leads equations with explicit spatial...

The mesenchymal tissue of the developing vertebrate limb bud is an excitable medium that sustains both spatial and temporal periodic phenomena. first these outcome general Turing-type reaction-diffusion dynamics generate standing waves cell condensations. These condensations are transformed into nodules rods cartilaginous, eventually (in most species) bony, endoskeleton. In second, periodicity results from intracellular regulatory oscillations in expression one or more gene whose products...

Animal color patterns are widely studied in ecology, evolution, and through mathematical modeling. Patterns may vary among distinct body parts such as the head, trunk or tail. As large amounts of photographic data is becoming more easily available, there a growing need for general quantitative methods capturing analyzing full complexity details pattern variation. Detailed information on variation elements necessary to understand how produced established during development, which evolutionary...