Cell cycle regulates proliferative cell capacity under normal or pathologic conditions, and in general it governs all in vivo/in vitro cell growth and proliferation processes. Mathematical simulation by means of reliable and predictive models represents an important tool to interpret experiment results, to facilitate the definition of the optimal operating conditions for in vitro cultivation, or to predict the effect of a specific drug in normal/pathologic mammalian cells. Along these lines, a novel model of cell cycle progression is proposed in this work. Specifically, it is based on a population balance (PB) approach that allows one to quantitatively describe cell cycle progression through the different phases experienced by each cell of the entire population during its own life. The transition between two consecutive cell cycle phases is simulated by taking advantage of the biochemical kinetic model developed by Gérard and Goldbeter (2009) which involves cyclin-dependent kinases (CDKs) whose regulation is achieved through a variety of mechanisms that include association with cyclins and protein inhibitors, phosphorylation–dephosphorylation, and cyclin synthesis or degradation. This biochemical model properly describes the entire cell cycle of mammalian cells by maintaining a sufficient level of detail useful to identify check point for transition and to estimate phase duration required by PB. Specific examples are discussed to illustrate the ability of the proposed model to simulate the effect of drugs for in vitro trials of interest in oncology, regenerative medicine and tissue engineering. Superficial area in the Petri dish effectively available for adhesion of proliferating cells at time t, μm2 Superficial area in the Petri dish available for adhesion of proliferating cells at time t, μm2 Superficial area in the Petri dish roofed by proliferating adherent cells at time t, μm2 Superficial area in the Petri dish roofed by proliferating adherent cells in G1 at time t, μm2 Superficial area in the Petri dish, μm2 Division probability density function, 1/μm3 Proportionality constant in the expression of the rate rv (Eq. (20)), 1/h Number of total cell, dimensionless Number of initial total cell, dimensionless Number of total cell for the generic P phase, dimensionless 2D number density distribution of cells for the generic P phase, μm−3 1D number density distribution of cells for the generic P phase in the volume variable v, μm−3 1D number density distribution of cells for the generic P phase in the age variable, ξ, dimensionless Generic phase, G1, G0, S, G2, M Partitioning function, μm−3 Coefficient appearing in the symmetric beta function, dimensionless Time rate of change of v, μm3 h−1 Time rate of change of ξ, h−1 Time, h Single cell volume, μm3 Mother cell volume, μm3 Maximum value for cell volume, μm3 Minimum value for cell volume, μm3 Shape factor of the Weibull distribution function, dimensionless Constant parameter appearing in the definition of A EF, dimensionless Symmetric beta function, dimensionless Gamma function, dimensionless Rate of transition G1 → G0, h−1 Scale factor of the Weibull distribution function, μm3 Mean of bivariate normal Gaussian distribution for v variable, μm3 Mean of bivariate normal Gaussian distribution for ξ variable, dimensionless Age, dimensionless Phase maturation time for transition P→P+1, h Geometric limiting factor, dimensionless Standard deviation of bivariate normal Gaussian distribution for v variable, μm3 Standard deviation of bivariate normal Gaussian distribution for ξ variable, dimensionless 
A novel quantitative model of cell cycle progression based on cyclin-dependent kinases activity and population balances