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. 2020 Oct 6;82(10):132. doi: 10.1007/s11538-020-00810-2

Table 2.

Parameter values for a fixed relaxation time t0 of 1 h after cell division

Parameter Description Value
μcubic Spring stiffness, cubic force 5.7
μR Repulsive spring stiffness, pw. quad. force 9.1
m Ratio of adhesive to repulsive spring stiffness, pw. quad. force 0.21
μA Adhesive spring stiffness, pw. quad. force 1.91
rR Repulsive interaction distance, pw. quad. force 1.18
μGLS Spring stiffness, GLS force 1.95
α(1) Breadth of exponential, GLS force (strategy #1) 7.51
α(2) Breadth of exponential, GLS force (strategy #2) 13.76

Free parameters are printed in bold. The spring stiffness values μcubic, μR and μGLS and the ratio m have been determined numerically by minimizing the difference between the separation distance r and 99% of the rest length s at t0, i.e. minμr(t0;μ)-0.99s. Here, the minimization was done using the minimize function of the scipy.optimize library (Virtanen et al. 2020; The SciPy Community 2018), where the separation distance was evaluated for different spring stiffness values μ using our CBMOS simulation code. For the cubic and the GLS forces the BFGS algorithm (Nocedal and Wright 2006) and the Nelder–Mead algorithm (Nelder and Mead 1965; Wright 1996) were used, respectively. For the piecewise quadratic force, the minimization was done jointly over μR and the ratio m using the L-BFGS-B algorithm (Byrd et al. 1995; Zhu et al. 1997). Values were rounded to two decimal values, except for the ratio where they were rounded to three decimal values. The truncated values were used in the calculation of the remaining parameters and all subsequent numerical experiments. The adhesive spring stiffness was chosen as μA=m·μR. The value for rR was chosen according to Eq. (12). The value for α(1) was determined by fitting the GLS force to the cubic force in magnitude over the adhesive regime with all other parameters fixed as listed in the table (strategy #1). The alternative value, α(2), was chosen according to Eq. (14)(strategy #2). The values for rR and α(2) are stated here rounded; however, the exact values were used in the numerical experiments