Team:iHKU/modelling

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Generally, we can vary the parameters of cell growth and cell motility which, in experiments, are easy to  change, although there are lots of parameters in our model. So we list the results of varying several parameters in the cell growth part and cell motility  part. 1. Cell Growth In the cell growth term, we considered the growth rate was related to nutrient concentration. When the nutrient was consumed by the cell, the grow rate of the cell would decrease  (Fig. 7</a>). There was a maximum growth rate γ 0, when the nutrient was rich. The parameter κ described the sharp of this curve(Fig. 7</a>). The larger κ gave us more smooth increasing curve. And we made an assumption that one unit of nutrient would change to cell number with a ratio α. Also in the initial condition, the nutrient concentration ni can influence  the patterns. Therefore, the effects of all the four parameters were studied in our model. <p align="center" class="style26"><img src="/wiki/images/a/a7/Modelnew3.png" width="541" height="441" /> Above reuslts indicated that, the faster cell growth (larger γ0 and  smaller doubling time) formed a smaller and a little more unclear ring pattern. And the inner ring diameter would become a litter more large when the growth rate increased. <img src="/wiki/images/6/6d/Modelnew4.png" width="535" height="441" /> From above figures, it was found that the initial nutrient concentration ni had  little influence to the pattern, especially when it was large. The only effect we observed was that smaller initial nutrient concentration ni  made the ring slightly wider and more clear. <img src="/wiki/images/6/6c/Modelnew5.png" width="543" height="444" /> Here, the value of κ was related to the  initial nutrient concentration ni. When initial nutrient concentration ni was fixed, a smaller κ parameter gave us the similar results with that of faster cell  growth. <img src="/wiki/images/5/51/Modelnew6.png" width="545" height="447" /> When we increased the value of k, the  patterns did not change a lot, but only became a little more clearly. In conclusion, the simulation results showed that the parameters of maximum growth rate γ0 and κ had a more important role on the ring-like pattern. And the other two parameters k and ni did not influence the pattern much. 2. Cell Motility D ρ (h) </a>Forms of D ρ (h) As Dρ ( h ) was a decreasing function of h, the possible formed of it can be                            Click graph to see movie!~(Line 1 left to right a, b, c; Line 2 left to right d ,e ) </a>3. Funny Pattern With the initial conditions of two or more spots, we obtained the below funny patterns which are amazing similar with that of experiments(results)</a>. <img src="/wiki/images/8/85/Modelnew12.png" width="384" height="508" /> </a>Reference: <ul> [1] P.K.Pathria, Statistical Mechanics (Pergamon Press, Headington Hill Hall, Oxford; 1972)</li> [2] Howard C.Berg, Random Walks in Biology (Princeton University Press, Princeton, Hew Jersey; 1993)</li> [3] Nikhil Mittal, et al, Proc Natl Acad Sci 100, 13259 (2003)</li> [4] R. A. Fisher, Ann. Eugenics 7, 353 (1937)</li> [5] A.H.Bokhari, et al., Nonlinear Analysis (In Press)</li> </ul> [Back to Top]</a> -                           </a> </a>- </a>- </a>- </a>- <td width="10%">