. Author manuscript; available in PMC: 2014 Aug 11.

Published in final edited form as: Nat Rev Mol Cell Biol. 2011 Mar 2;12(4):265–273. doi: 10.1038/nrm3079

Table 1.

Modelling methodologies:

Cell Circuit Dynamics	Describe the rates of change of interacting gene and signaling network components. Depending on the available information they are simulated in different ways:
1 Boolean^5, 18	Individual genes are described as ON/OFF; truth tables and state transition graphs describe gene regulatory rules. A very useful method to describe network dynamics with insufficient information (molecular mechanisms or data). However, one cannot obtain detailed dynamics of gene regulatory functions.
2. Differential Equations⁵	Gene regulation described by biophysically motivated rate laws, very often represented by Michaelis-Menten type of functions. Several analytical techniques are available for probing nonlinear network dynamics as well as for optimizing parameters. However, some parameters may have to be guessed.
3. Stochastic⁵	Simulations use probabilities based upon reaction rates to decide which chemical transitions occur. Novel phenomena due to inherent stochasticity of gene regulation and signaling illuminate new principles; however, for large networks, simulations can be prohibitively computationally intensive.
Mechanical Forces in Living Tissues	The forces within and between cells which ultimately are responsible for shaping the organ, are described by various frameworks:
1. Spring Models⁵	Cell walls are described by springs, which connect to other cells at vertices. Equilibrium is obtained by minimizing the total elastic energy. This simplified description of cells works well with cell division and growth, but it lacks resolution of finer cell wall details.
2. Finite Element Methods^{12, 56, 57}	Discretization of a tissue in terms of elements using various geometries, which then implement the rules of elasticity theory. This method provides a detailed description of the elastic properties of cells, but is computationally intensive and cannot easily be modified for growing and dividing cells.
3. Cellular Potts Methods⁴²	Cells are described as a collection of similar spins, which interact with each other and spins of neighboring cells. A Monte-Carlo scheme is employed to minimize the energy of the system and arrive at the equilibrium configuration. Used successfully in many biological cases; however, not adapted completely to plant systems, which require non-migrating cells.
4. Subcellular Element Method^{65, 66}	Coarse-grained description of cells in terms of interacting particles, which move by sensing forces from the neighboring particles. This method has excellent spatial resolution, but could be computationally intensive for multicellular systems.