Table 2 Definitions of factors and feedback loops

Initial population

The identity, location, and state of all cells present at the start of an experiment or simulation.

Initial chemical environment

The concentration profiles of all chemicals initially present in the environment at the start of an experiment or simulation.

Initial physical environment

The initial state of the physical environment, including boundary conditions, flow profiles, etc. at the start of an experiment or simulation.

Growth

The rate at which cells divide and form new biomass.

Movement

The rate and direction in which cells move either due to active movement or passive movement in response to external forces.

Chemical environment

The type, concentration, and distribution of all chemicals that are present in a cell’s environment as well as their fluxes. It includes the concentrations of nutrients, toxins, signaling molecules, matrix components, and surfactants.

Physical environment

The set of all physical factors that exert a force or physical constraint on cells or that otherwise affect cell growth and movement. It includes the thermodynamic state (e.g., temperature), geometry (e.g., dimensionality, boundaries), surface properties (e.g., viscosity, roughness), and hydrodynamic properties (e.g., water activity and flow rate) of the environment. Cells themselves are part of the physical environment as well, because cell crowding can lead to significant friction and pressure.

Coupling between chemical and physical environment

A single factor (e.g., surfactant production) can simultaneously affect the chemical and physical environment.

Coupling between growth and movement

Cell growth often leads to movement (e.g., as cells increase in volume they push around their neighbors), while movement affects cell growth by moving a cell to a different local environment (e.g., moving to an area with more favorable environmental conditions).

Chemical environment-growth feedback

The chemical environment influences cell growth by determining a cell’s metabolic activity and growth. In turn, cellular metabolism changes the chemical environment, as growth can cause depletion of nutrients and accumulation of byproducts.

Physical environment-movement feedback

The physical environment influences cell movement by imposing forces and constraints (e.g., cell movement is constrained by cell crowding or boundaries of a growth chamber). In turn, cell movement changes the physical environment (e.g., movement to a new region increases cell density and crowding in that region)

Chemical environment-movement feedback

The chemical environment influences cell movement through chemotaxis. In turn, movement can change chemical gradients, as a cell can move to a new area and secrete chemicals locally.

Physical environment-growth feedback

The physical environment influences cell growth directly through temperature and pressure. Physical features such as flow can also influence chemical distribution, thereby influencing growth indirectly. In turn, cell growth contributes to physical effects, such as pressure from cell crowding.

Metabolic interactions

Metabolic interactions emerge as neighboring cells become coupled through their shared chemical microenvironment.

Physical interactions

Physical interactions emerge as neighboring cells become coupled through their shared physical microenvironment.