TABLE 1.

Overview of the biological agents and processes in bone fracture healing and the way they can be captured in silico in continuous-time or discrete-time models. In keeping with the description in Section 3.1, the spatial scale (if present) is mentioned. Examples are provided of experimental setups to use during the calibration phase of in silico models. Units of quantitative parameters that can be extracted from experiments are in squared brackets. For those experiments that lead to qualitative observations, this is mentioned explicitly.

Type	Activity	Continuous-time models	Discrete-time models	Experimental techniques
Cells	Random motility	1) Fick’s second law, e.g. diffusion coefficient estimated from molecular weight or experimental dataa; 2) Haptokinetic process, e.g. influenced by total matrix density such that cells cannot move in absence or abundance of ECM densityb	Each agent moves in one of the empty surrounding positions chosen randomly by the algorithmi,j,m–q	Brightfield microscopy can quantify cell migration in organ-on-chip systemsr [cell velocity: distance/time]
	Chemotaxis	Receptor-ligand kinetics, e.g. maximum chemotactic response at certain growth factor concentrationc	The selection of the surrounding position during migration is not random but it is biased by the concentration of the chemotactic factori,o,q	Organ-on-chip systems facilitate the application of chemical gradientsr [diffusion of the leading edge of chemical: distance/time]
	Haptotaxis	Haptotactic process, e.g. based on a kinetic analysis of a model mechanism for the cell-surface-receptor-extracellular-ligand binding dynamicsb	The selection of the surrounding position during migration is not random but it is biased according to the composition and fiber orientation of ECMa,f,k	Organ-on-chip systems facilitate the application of density gradientsr [binding concentration: mass/volume]
	Differentiation	Concentration-dependent curve, e.g. Hill function regulated by the concentration of growth factorse or oxygenf up to a saturation level	The agent changes its phenotype status according to the surrounding environmental conditionsj,n,q	Analysis of cell surface markers (e.g. flow cytometry) [% of positive cells], gene expression profiles (e.g. qPCR and RNA-seq) [fold change in gene expression] and stainings (e.g. Alizarin Red for osteogenic differentiation)s [qualitative observation]
	Polarization/activation	Concentration-dependent curve, e.g. Hill function regulated by the concentration of cytokines up to a saturation levelg	The agent changes its activation status according to the surrounding environmental conditionsi,m,o,p	Analysis of cell surface markers (e.g. flow cytometry) (% of positive cells) and gene expression profiles (e.g. qPCR and RNA-seq) (qualitative observation)t
	Proliferation	Fisher equation and logistic growth function such that rate of cell division decreases linearly with cell density, e.g. regulated by ECM densityb or oxygen tensiond	A proliferative agent creates a copy of itself in one of the empty surrounding positions chosen randomly by the algorithmj,l–q	Proliferation assays based on DNA synthesis (e.g. EdU assay) [% of proliferating cells] or metabolic activity (e.g. MTT assay) (arbitrary units)s
	Apoptosis	1) Rate estimated from experimental datae; 2) Concentration-dependent curve, e.g. Hill function regulated by oxygen tension up to a saturation leveld	The apoptotic agent is removed from the modeli,j,l,m,o,p,q; nutrient-related survival conditions are applied by increasing the apoptosis ratio in undesired conditionsn	Depending on the apoptosis stage, fluorimetric assays detecting mito-chondrial degradation, caspase activation or DNA fragmentation [% of viable cells]
	Senescence	Cell differentiation as evolutionary process, e.g. cells gain properties of another cell type gradually over timeg	The senescent agent gradually reduces its cellular activity to zero (not performing actions, but not removed from the model)	Staining of SA-β-gal [qualitative observation]
Chemical agents (cytokines, growth factors, hormones, etc.)	Diffusion	Fick’s second law, e.g. diffusion coefficient estimated from molecular weight or experimental dataa	Discretized Fick’s first law: the amount of substance exchanged between two adjacent patches is proportional to concentration difference, diffusing from patch of higher concentration to patch of lower onei,p,q	The biomolecule distribution across an hydrogel can be quantified with immunoassays (e.g ELISA) [biomolecule concentration: mass/volume]r
	Production	1) Rate estimated from experimental dataa; 2) Concentration-dependent curve, e.g. Hill function to model a threshold-like behaviore	Substance concentration increases in function of the number of agents present in the patch according to a defined production ratioi,n,p,q	Immunoassays to quantify protein synthesis (e.g. ELISA)u [biomolecule concentration: mass/volume]
	Consumption	Michaelis-Menten kinetic law, e.g. oxygen consumption by cellsh	Substance concentration decreases in function of the number of agents present in the patch according to a defined consumption ratioq	Metabolites labeled with stable isotope tracers (e.g glucose consumption or fatty acid uptake) [normalized metabolite consumption: molarity/(time ⋅ mass)]t
	Denaturation	Rate estimated from experimental dataa	Substance decay within patch decreases by following a time-dependent exponential functioni,o,p,q	Biomolecule half-life estimation (e.g. pulse-chase analysis for cellular proteins) [time]
Extracellular matrix	Synthesis	Rate estimated from experimental datab	Matrix percentage increases within the patch where the cell is localized according to a synthesis ratioj,q	Cells/ECM growth can be evaluated with a Live-Dead viability/cytotoxicity staining [volume fraction: %]v
	Degradation	Rate estimated from experimental datab	Matrix percentage decreases within the patch where the cell is localized according to degradation ratioq	Level of biomolecules associated to degradation (e.g. hydroxyproline for collagen matrix) [biomolecule concentration: mass/volume]
Debris	Phagocytosis	Concentration-dependent curve, e.g. Hill function to model engulfing rateg	Phagocytic agent reduces the debris concentration within a defined radius of actionl,o	Phagocytes culture (e.g. macrophages) with cellular debris or pathogens [cytokine concentration: mass/volume]w
Angiogenesis	Vessel formation	Migration (random and directed)a and proliferationc of endothelial cells, finally producing vascular matrix	Development of vasculature according to tip endothelial cell movementa,f,k,n	Microscopy imaging, brightfieldx or confocaly, of an endothelial cell monolayer during sprouting [sprout displacement: length

References: ^a Anderson and Chaplain (1998), ^b Olsen et al. (1997), ^c Geris et al. (2008), ^d Carlier et al. (2015), ^e Bailón-Plaza and Van Der Meulen (2001), ^f Carlier et al. (2012), ^g Trejo et al. (2019), ^h Prokharau et al. (2012), ⁱ Mi et al. (2007), ^j Checa et al. (2011), ^k Peiffer et al. (2011), ^l Martínez et al. (2012), ^m Pennisi et al. (2013), ⁿ OReilly et al. (2016), ^o Shi et al. (2016), ^p Gong et al. (2017), ^q Borgiani et al. (2021), ^r Moreno-Arotzena et al. (2014), ^s Groeneveldt et al. (2020), ^t Vats et al. (2006), ^u Zhang et al. (2017), ^v Guyot et al. (2014), ^w Fraser et al. (2009), ^x Del Amo et al. (2016), ^y Vaeyens et al. (2020), Abbreviations: SA-β-gal, senescence-associated β-galactosidase; ELISA, enzyme-linked immunosorbent assay; qPCR, quantitative polymerase chain reaction; ECM, extracellular matrix; RNA-seq, RNA-sequencing.