/* * Distinct modes of collagen type I proteolysis by matrix metalloproteinase * (MMP) 2 and membrane type I MMP during the migration of a tip * endothelial cell: insights from a computational model * * Model Status * * This version of the model has been checked in COR and PCEnv * and it runs - possibly replicating the published results. The * units have been checked and they are consistent. * * Model Structure * * The formation of new biological vessels requires the coordinated * assembly of a proliferating syncytium of endothelial cells (EC) * at different developmental stages. Angiogenesis may also be * an essential mechanism of blood vessel remodelling which occurs * during a diverse range of physiological processes; including * tissue regeneration following injury and new vessel formation * during muscle exercise. It can also occur under pathological * conditions such as atherosclerosis and the vascularisation of * cancerous tumours. * * Matrix metalloproteinases (MMPs) are a family of enzymes responsible * for the proteolytic processing of extracellular matrix (ECM) * structural proteins. During angiogenesis MMPs are expressed * by a single endothelial cell at the tip of the new vessel. These * enzymes manifest a proteolytic activity that allows the cells * of the new vessle to penetrate the ECM. In the mathematical * model presented here, Karagiannis and Popel investigate the * proteolytic potential of such a tip endothelial cell. The model * authors suggest this model provides a foundation for future * quantitative studies of angiogenesis in ECMs of different compositions. * The model is described in more detail in the figure below: * * The complete original paper reference is cited below: * * Distinct modes of collagen type I proteolysis by matrix metalloproteinase * (MMP) 2 and membrane type I MMP during the migration of a tip * endothelial cell: insights from a computational model, Emmanouil * D. Karagiannis and Aleksander S. Popel, 2006, The Journal of * Theoretical Biology, 238, 124-145. PubMed ID: 16005020 * * model diagram * * [[Image file: karagiannis_2006.png]] * * A schematic diagram of the signalling pathway. */ import nsrunit; unit conversion on; unit s=1 second^1; //Warning: unit um_ renamed from um, as the latter is predefined in JSim with different fundamental units. unit um_=1E-3 meter^(-3)*mole^1; unit flux=1E-3 meter^(-3)*second^(-1)*mole^1; unit first_order_rate_constant=1 second^(-1); unit M=1E3 meter^(-3)*mole^1; unit second_order_rate_constant=1E3 meter^3*second^(-1)*mole^(-1); math main { realDomain t s; t.min=0; extern t.max; extern t.delta; real kM2T2_on second_order_rate_constant; kM2T2_on=5900000; real kM2T2_off first_order_rate_constant; kM2T2_off=6.3; real kM2T2_iso first_order_rate_constant; kM2T2_iso=33; real kM2T2_negativeiso first_order_rate_constant; kM2T2_negativeiso=0.00000002; real kM2C1_on second_order_rate_constant; kM2C1_on=2600; real kM2C1_off first_order_rate_constant; kM2C1_off=0.0021; real kM2C1_cat first_order_rate_constant; kM2C1_cat=0.0045; real kMT1T2_on second_order_rate_constant; kMT1T2_on=2980000; real kMT1T2_off first_order_rate_constant; kMT1T2_off=0.202; real kMT1T2M2pro_on second_order_rate_constant; kMT1T2M2pro_on=140000; real kMT1T2M2pro_off first_order_rate_constant; kMT1T2M2pro_off=0.0047; real kM2_act first_order_rate_constant; kM2_act=0.02; real kMT1_shedeff second_order_rate_constant; kMT1_shedeff=2800; real kMT1C1_cat first_order_rate_constant; kMT1C1_cat=0.00197; real kMT1C1_on second_order_rate_constant; kMT1C1_on=1000; real kMT1C1_off first_order_rate_constant; kMT1C1_off=1; real kMT1T2M2proMT1_on second_order_rate_constant; kMT1T2M2proMT1_on=3000; real kMT1T2M2proMT1_off first_order_rate_constant; kMT1T2M2proMT1_off=0.0009; real M2T2(t) M; when(t=t.min) M2T2=0.0000000072; real M2C1(t) M; when(t=t.min) M2C1=0.0000085; real MT1T2(t) M; when(t=t.min) MT1T2=0.00000000139; real MT1T2M2proMT1(t) M; when(t=t.min) MT1T2M2proMT1=0.00000000056; real MT1C1(t) M; when(t=t.min) MT1C1=0.0000029; real M2(t) M; when(t=t.min) M2=0; real MT1(t) M; when(t=t.min) MT1=0; real M2_p(t) M; when(t=t.min) M2_p=0; real T2(t) M; when(t=t.min) T2=0; real C1_D(t) M; when(t=t.min) C1_D=0; real C1(t) M; when(t=t.min) C1=0; real MT1_cat(t) M; when(t=t.min) MT1_cat=0; real MT1_t(t) M; when(t=t.min) MT1_t=0; real MT1T2M2pro(t) M; when(t=t.min) MT1T2M2pro=0; real qMT1 flux; qMT1=0; real qT2 flux; qT2=0; real qpro flux; qpro=0; real MT1T2_star(t) um_; when(t=t.min) MT1T2_star=0; real M2T2_star(t) um_; when(t=t.min) M2T2_star=0; // // M2:t=((-1)*kM2T2_on*M2*T2+kM2T2_off*M2T2-kM2C1_on*M2*C1+(kM2C1_off+kM2C1_cat)*M2C1+kM2_act*MT1T2M2proMT1); MT1:t=(qMT1-kMT1_shedeff*MT1*MT1-kMT1T2_on*MT1*T2+kMT1T2_off*MT1T2-kMT1C1_on*MT1*C1+(kMT1C1_off+kMT1C1_cat)*MT1C1-kMT1T2M2proMT1_on*MT1*MT1T2M2pro+kMT1T2M2proMT1_off*MT1T2M2proMT1+kM2_act*MT1T2M2proMT1); MT1_t:t=(kMT1_shedeff*MT1*MT1); MT1C1:t=(kMT1C1_on*MT1*C1-(kMT1C1_off+kMT1C1_cat)*MT1C1); MT1T2:t=(kMT1T2_on*MT1*T2-kMT1T2_off*MT1T2-kMT1T2M2pro_on*MT1T2*M2_p+kMT1T2M2pro_off*MT1T2M2pro); MT1T2M2pro:t=(kMT1T2M2pro_on*MT1T2*M2_p-kMT1T2M2pro_off*MT1T2M2pro-kMT1T2M2proMT1_on*MT1*MT1T2M2pro+kMT1T2M2proMT1_off*MT1T2M2proMT1); MT1T2M2proMT1:t=(kMT1T2M2proMT1_on*MT1*MT1T2M2pro-kMT1T2M2proMT1_off*MT1T2M2proMT1-kM2_act*MT1T2M2proMT1); C1:t=((-1)*kMT1C1_on*MT1*C1+kMT1C1_off*MT1C1-kM2C1_on*M2*C1+kM2C1_off*M2C1); C1_D:t=(kM2C1_cat*M2C1+kMT1C1_cat*MT1C1); MT1_cat:t=(kMT1_shedeff*MT1*MT1); T2:t=((-1)*kM2T2_on*M2*T2+kM2T2_off*M2T2+qT2-kMT1T2_on*MT1*T2+kMT1T2_off*MT1T2); M2_p:t=(qpro-kMT1T2M2pro_on*MT1T2*M2_p+kMT1T2M2pro_off*MT1T2M2pro); M2T2:t=(kM2T2_on*M2*T2-kM2T2_off*M2T2-kM2T2_iso*M2T2+kM2T2_negativeiso*M2T2_star); M2T2_star:t=(kM2T2_iso*M2T2-kM2T2_negativeiso*M2T2_star); M2C1:t=(kM2C1_on*M2*C1-(kM2C1_off+kM2C1_cat)*M2C1); MT1T2_star:t=(kM2_act*MT1T2M2proMT1); }