Table 2.

Common modeling formalisms in QSP

Modeling approach	Mathematical form	Strengths	Potential drawbacks	Example & software/language
Statistical data‐driven	Algebraic + probabilistic equations	• Data‐driven biology	• Less mechanistic • Best for coordinated measurement of numerous variables	Apoptosis signaling32
Logic‐based	Rule‐based interactions	• Intuitive rules	• Less kinetic richness • Best for coordinated measurement of numerous variables	Kinase pathway crosstalk56 (MATLAB Fuzzy Logic toolboxa); Myeloma cell‐line pharmacodynamics53 (MATLAB ODEfy54)
Differential equations	Temporal ODEs or SDEs	• Continuous temporal dynamics • Random effects, if SDEs	• Potential stiffness • Requires rich kinetic data	NGF signaling pathway and targets16 (MATLAB Simbiologya)
	Spatiotemporal PDEs or SDEs	• Continuous spatial and temporal dynamics • Random effects, if stochastic SDEs	• Computational expense • Spatial information needed	Ocular drug dissolution and distribution55 (ANSYSb)
Cellular automata & agent‐based models	Interaction and evolution rules for collection of “agents”	• Intuitive rules • Spatial and temporal dynamics • Random effects & emergent behaviors	• Computational expense • Spatial information needed • Link to higher level behaviors	TB granuloma & inhaled treatment response56 (C++)

ODEs, ordinary differential equations; PDEs, partial differential equations; QSP, quantitative systems pharmacology; SDEs, stochastic differential equations.

^aMathworks, Natick, MA. ^bANSYS, Canonsburg, PA.