Glossary - Cellular Potts Models: Multiscale Extensions and Biological Applications - page 211

contrast to the logistic function in which both asymptotes are approached
by the curve symmetrically. Its general formula is
y(t) = ae be ct ;
where a is the upper asymptote, since
ae be 1 = ae 0 = a;
and b and c are negative numbers. In particular, b sets the x displacement
and c sets the growth rate (x scaling). Examples of uses for Gompertz
curves include modeling of growth of populations in a confined space, as
birth rates first increase and then slow as resource limits are reached. In
the 1960s, A.K. Laird for the first time successfully used the Gompertz
curve to fit data of growth of tumors. In fact, tumors are cellular popu-
lations growing in a confined space where the availability of nutrients is
limited.
Hamiltonian: Functional describing the effective energy of the system.
Haptotaxis: A directional motility or outgrowth of cells, e.g., in the case of
axonal outgrowth, up a gradient of cellular adhesion sites or substrate-
bound chemical sources. These gradients are naturally present in the ex-
tracellular matrix (ECM) of the body during processes such as angiogen-
esis or artificially present in biomaterials where gradients are established
by altering the concentration of adhesion sites on a polymer substrate.
Hepatocyte growth factor (HGF)/ scatter factor (SF): Growth fac-
tor eliciting multiple processes, such as mitogenesis, motility, morpho-
genesis, cell dissociation, migration through the extracellular matrix, ac-
quisition of polarity, and tubule formation.
Internal state vector: Vector characterizing an object whose components
represent the internal factors (i.e., nutrients, proteins, growth factors, gene
expressions, . . . ) influencing its properties and behavior.
Lattice: Regular repeated graph R d formed by identical d-dimensional
closed grid sites, where d = 1; 2; 3.
Matrigel: Gelatinous protein mixture that resembles the complex extracel-
lular environment found in many tissues and is used by cell biologists as
a substrate for cell cultures. The ability of Matrigel to stimulate complex
cell behavior is a consequence of its heterogeneous composition. The chief
components of Matrigel are structural proteins such as laminin, entactin,
and collagen, which present cultured cells with the adhesive peptide se-
quences that they would encounter in their natural environment. Also
present are growth factors that promote differentiation and proliferation
of many cell types. Matrigel contains numerous other proteins in small
amounts, and its exact composition can vary from in each case.