Full title: A Multi-cell, Multi-scale Model of Vertebrate Segmentation and Somite Formation Date: 18.08.2023 Authors: Susann D. Hester, Julio M. Belmonte, J. Scott Gens, Sherry G. Clendenon, James A. Glazier Curators: Justin Buerger, Lutz Brusch Software: Morpheus (open source). Download from: https://morpheus.gitlab.io Model ID: https://identifiers.org/morpheus/M6696 Units: [time] = 0.015 min [space] = 1.43 µm This model reproduces the model and results obtained with CompuCell3D in the original publication. Reference: Susann D. Hester, Julio M. Belmonte, J. Scott Gens, Sherry G. Clendenon, James A. Glazier: A Multi-cell, Multi-scale Model of Vertebrate Segmentation and Somite Formation. PLoS Comput. Biol. 7(10): e1002155, 2011. https://doi.org/10.1371/journal.pcbi.1002155

4 cell.volume >= 2*tV Cell Division: as soon as the source cell reaches double its default target volume tV tS MediumNeighbor == 0 if((targetVolume < 3*tV), (targetVolume+gR), targetVolume) if((targetVolume < 3*tV), 5*sqrt(targetVolume), targetSurface)

if(PSM_Neighbors != 0, Sum_DL_mExt/PSM_Neighbors, 0) eps*(mu_sN-mu_dN*N/(K_dN+N)-(k_c*N*(K_IF^2/(K_IF^2 + F^2))*((DL_mExt/(K_DL +DL_mExt))/(K_aDL + (DL_mExt/(K_DL +DL_mExt)))))) eps*((k_c*N*(K_IF^2/(K_IF^2 + F^2))*((DL_mExt/(K_DL +DL_mExt))/(K_aDL + (DL_mExt/(K_DL +DL_mExt)))))-mu_dNa*N_a/(K_dNa +N_a)-(k_t1*N_a-k_t2*N_an)) eps*((k_t1*N_a-k_t2*N_an)-mu_dNan*N_an/(K_dNan + N_an)) eps*(mu_sF*(N_an-(mu_Nap*N_an*K/(K_pN+K)))^2/(KA^2 +(N_an-(mu_Nap*N_an*K/(K_pN+K)))^2)-mu_mF*MF/(K_dmF+MF)) eps*(k_sF*MF -mu_dF*F/(K_dF+F)) eps*(mu_s0MDMF*(N_an-(mu_Nap*N_an*K/(K_pN+K)))^2/(K_aNDMF^2+(N_an-(mu_Nap*N_an*K/(K_pN+K)))^2) - mu_dmDMF*MDMF/(K_dmDMF +MDMF)) eps*(k_sDMF*MDMF - mu_dDMF*DMF/(K_dDMF + DMF)) eps*(k_sDL*MDL*(N_an -(mu_Nap*N_an*K/(K_pN+K)))/(K_Nan +(N_an-(mu_Nap*N_an*K/(K_pN+K)))) -k_tDL*DL_c - mu_dDLc*DL_c/(K_dDLc + DL_c)) eps*(k_tDL*DL_c - mu_dDLm*DL_m/(K_dDLm + DL_m)) ODEs for the Notch Loop eta*(V_MaRas*((FGF_center^2/(K_aFgf^2 + FGF_center^2))*((Ras_t-Ras_a)/(K_aRas + (Ras_t-Ras_a)))-V_MdRas*(Ras_a/(K_dRas+Ras_a)))) eta*(V_MaErk*(Ras_a/Ras_t)*(ERK_t-ERK_a)/(K_aErk + (ERK_t-ERK_a))-K_cDusp*Dusp*ERK_a/(K_dErk+ERK_a)) eta*(V_MaX*ERK_a/ERK_t*(X_t-X_a)/(K_aX +(X_t-X_a))-V_MdX*X_a/(K_dX + X_a)) eta*(V_MsMDusp*(X_a^2/(K_aMDusp^2 + X_a^2))*(mu_DuspDMF*K_IMDusp/(K_IMDusp +DMF) +mu_DuspX) - V_MdMDusp*MDusp/(K_dMDusp +MDusp)) eta*(K_sDusp*MDusp-V_dDusp*Dusp/(K_dDusp + Dusp)) ODEs for the FGF Loop teta*(d_1*(K_t-K)-a_1*A*K) teta*(mu_sB-(V_MK*K_ID/(K_ID+Wnt)*B/(K_1+B))*(K_t-K)/K_t+(V_MP*B_p/(K_2+B_p))+(k_t4*B_n-k_t3*B)-k_d1*B) teta*((V_MK*K_ID/(K_ID+Wnt)*B/(K_1+B))*(K_t-K)/K_t-(V_MP*B_p/(K_2+B_p))-k_d2*B_p) -teta*(k_t4*B_n-k_t3*B) teta*(mu_0+mu_MB*B_n^2/(K_aB^2+B_n^2)+mu_MXa*X_a^2/(K_aXa^2+X_a^2)-mu_md*MAx/(K_md+MAx)) teta*(k_sAx*MAx-mu_dAx*A/(K_dAx+A)+(d_1*(K_t-K)-a_1*A*K)) ODEs for the Wnt Loop cell.center.y < cD 1 (cell.center.y >= wallDeath +5) + (cell.center.y < cD)*(wallDeath < 1.5*cD) 1 ticker-1 ticker <= 0

-k_fgf_cell*mFgf C_12w*mFgf ticker < 1 cell.center.y ticker-1

if(PSM_Neighbors != 0, Sum_DL_mExt/PSM_Neighbors, 0) -k_fgf_cell*mFgf C_12w*mFgf ticker < 1 cell.center.y ticker-1

if(PSM_Neighbors != 0, Sum_DL_mExt/PSM_Neighbors, 0) -k_fgf_cell*mFgf C_12w*mFgf ticker < 1 cell.center.y ticker-1

if(PSM_Neighbors != 0, Sum_DL_mExt/PSM_Neighbors, 0) eps*(mu_sN-mu_dN*N/(K_dN+N)-(k_c*N*(K_IF^2/(K_IF^2 + F^2))*((DL_mExt/(K_DL +DL_mExt))/(K_aDL + (DL_mExt/(K_DL +DL_mExt)))))) eps*((k_c*N*(K_IF^2/(K_IF^2 + F^2))*((DL_mExt/(K_DL +DL_mExt))/(K_aDL + (DL_mExt/(K_DL +DL_mExt)))))-mu_dNa*N_a/(K_dNa +N_a)-(k_t1*N_a-k_t2*N_an)) eps*((k_t1*N_a-k_t2*N_an)-mu_dNan*N_an/(K_dNan + N_an)) eps*(mu_sF*(N_an-(mu_Nap*N_an*K/(K_pN+K)))^2/(KA^2 +(N_an-(mu_Nap*N_an*K/(K_pN+K)))^2)-mu_mF*MF/(K_dmF+MF)) eps*(k_sF*MF -mu_dF*F/(K_dF+F)) eps*(mu_s0MDMF*(N_an-(mu_Nap*N_an*K/(K_pN+K)))^2/(K_aNDMF^2+(N_an-(mu_Nap*N_an*K/(K_pN+K)))^2) - mu_dmDMF*MDMF/(K_dmDMF +MDMF)) eps*(k_sDMF*MDMF - mu_dDMF*DMF/(K_dDMF + DMF)) eps*(k_sDL*MDL*(N_an -(mu_Nap*N_an*K/(K_pN+K)))/(K_Nan +(N_an-(mu_Nap*N_an*K/(K_pN+K)))) -k_tDL*DL_c - mu_dDLc*DL_c/(K_dDLc + DL_c)) eps*(k_tDL*DL_c - mu_dDLm*DL_m/(K_dDLm + DL_m)) ODEs for the Notch Loop eta*(V_MaRas*((FGF_center^2/(K_aFgf^2 + FGF_center^2))*((Ras_t-Ras_a)/(K_aRas + (Ras_t-Ras_a)))-V_MdRas*(Ras_a/(K_dRas+Ras_a)))) eta*(V_MaErk*(Ras_a/Ras_t)*(ERK_t-ERK_a)/(K_aErk + (ERK_t-ERK_a))-K_cDusp*Dusp*ERK_a/(K_dErk+ERK_a)) eta*(V_MaX*ERK_a/ERK_t*(X_t-X_a)/(K_aX +(X_t-X_a))-V_MdX*X_a/(K_dX + X_a)) eta*(V_MsMDusp*(X_a^2/(K_aMDusp^2 + X_a^2))*(mu_DuspDMF*K_IMDusp/(K_IMDusp +DMF) +mu_DuspX) - V_MdMDusp*MDusp/(K_dMDusp +MDusp)) eta*(K_sDusp*MDusp-V_dDusp*Dusp/(K_dDusp + Dusp)) -k_fgf_cell*mFgf ODEs for the FGF Loop teta*(d_1*(K_t-K)-a_1*A*K) teta*(mu_sB-(V_MK*K_ID/(K_ID+Wnt)*B/(K_1+B))*(K_t-K)/K_t+(V_MP*B_p/(K_2+B_p))+(k_t4*B_n-k_t3*B)-k_d1*B) teta*((V_MK*K_ID/(K_ID+Wnt)*B/(K_1+B))*(K_t-K)/K_t-(V_MP*B_p/(K_2+B_p))-k_d2*B_p) -teta*(k_t4*B_n-k_t3*B) teta*(mu_0+mu_MB*B_n^2/(K_aB^2+B_n^2)+mu_MXa*X_a^2/(K_aXa^2+X_a^2)-mu_md*MAx/(K_md+MAx)) teta*(k_sAx*MAx-mu_dAx*A/(K_dAx+A)+(d_1*(K_t-K)-a_1*A*K)) ODEs for the Wnt Loop C_12w*mFgf Equation for Wnt degredation

(FGF_center < fdTh)*(FGF_center > 0.000001)*(B>bdTh) Change cell type as soon as a threshold of fgf concentration is reached. If the beta catenenin concentration is above another threshold, the PSM cell differentiates to a pre_core cell. (FGF_center < fdTh)*(FGF_center > 0.000001)*(B<=bdTh)*(F<=A*aPre) Change cell type as soon as a threshold of fgf concentration is reached. If the beta catenenin concentration is below another threshold, and the Axin2 concentration times a factor is bigger or equal to the Lfng concentrentration the PSM cell differentiates to a pre_EphrinBB2 cell. (FGF_center < fdTh)*(FGF_center > 0.000001)*(B<=bdTh)*(F>A*aPre) Change cell type as soon as a threshold of fgf concentration is reached. If the beta catenenin concentration is below another threshold, and the Axin2 concentration times a factor is smaller than the Lfng concentrentration the PSM cell differentiates to a pre_EphA4 cell. 2 4 Default cell diameter Default target surface Default weight for CPM surface constraint, termed lambda_s in Hester et al. 2011 Default weight for CPM volume constraint, termed lambda_v in Hester et al. 2011 Number of empty lattice nodes between wall cells and lattice boundary Width of the two columns made by Wall cells Initial slope of FGF8 gradient (used for initializing FGF field) computed as the value of FGF (from Hester et al. 2011, page 13 bottom right) at the posterior end (45nM) minus the value of FGF at the fourth cell layer (39.6 nM) divided by the thickness of 4 cell layers. Initialization of FGF8 gradient and diffusion term (units were rescaled from µm^2/min to pixel^2/MCS) as defined in Hester et al., 2011 -k_FGF_global*FGF + s_FGF*mFgf Rates (and time scale of diffusion coefficient) were given in 1/min and need to be rescaled into 1/MCS using "1 MCS=mpm min -> 1 min=1/mpm MCS and 1/min = mpm 1/MCS" hence rates have been multiplied by mpm. System-wide variable that specifies where somites have already formed, i.e. where the wall can disappear. Initialized with value outside of the lattice to maintain wall initially. As specified in the code in Hester's Dissertation ("Grow=0.120" on page 129)