Table 1.

Summary of major stem cell modeling approaches surveyed, the insights they provide and their pros and cons.

Modeling approach	Insights gained on:	Pros and cons
	Ranges of ligand concentration and duration of stem cell exposure to trigger a particular response (e.g. self-renewal or differentiation).	Pros: Numerical treatment is typically straightforward (systems of ODEs).
Signal transduction network (typically single-cell) models	Identifying network intermediates exerting more/less control over stem cell response(s) to given signals.	Cons: Require extensions of single-cell model to reflect population behavior.
	Deconvolving synergistic effects from the action of multiple factors.
	Interactions among key genes influencing stem cell fate decisions. Kinetics of gene expression related to stem cell phenotype adoption.	Pros: Multiple approaches are available (e.g. Boolean, Bayesian, ODEs etc.) for GRN analysis.
		Pertinent numerical methods are typically well-defined.
Gene regulatory network (typically single-cell) models		Stochastic gene expression can be described.
		Cons: Require extension of single-cell model to reflect population-level behavior.
		Source of stem cell heterogeneity is limited to noise in gene expression.
	Effects of variability in gene expression and other subcellular processes (e.g. signaling, metabolism etc.) on stem cell population diversity.	Pros: Applicable numerical methods are straightforward to implement.
Cell ensemble models	Linking adjustable bioprocess variables (e.g. factor and/or nutrient concentration) to property profiles of the population.	High-dimensional state vectors can be accommodated. GRNs can be directly included.
		Multiple scales can be modeled (typically with steady-state assumptions).
		Cons: Incorporation of cell division, differentiation and apoptosis is demanding.
Population balance models	How processes at different scales (e.g. fluctuating gene expression, stochastic partitioning of cellular material at mitosis, etc.) synergize to bring about a particular property distribution on the stem cell population.	Pros: Multiple scales can be accommodated. Allow incorporation of GRNs with noise (stochastic PBEs).
	Describing stem cell population heterogeneity. Linking adjustable bioprocess variables to desirable state vector distributions.	Cons: Achieving numerical solutions is not trivial and computational complexity increases with the state vector dimensionality.
		Single-cell functions (especially agent-dependent) for differentiation, death and growth under different states (e.g. self-renewing or committed) are challenging to obtain.