A novel density control devicefor the study of cancer cell autocrine effect
Wei Yang1，2, Zhaojun Li2 ,Weilin Zhang3, Chunxiong Luo*1,2,Qi Ouyang, *1,2,3, Gen Yang4, Yugang Wang4
1The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, People’s Republic of China.
2Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, People’s Republic of China.
3Peking-Tsinghua Center for Life Sciences，Peking University, Beijing 100871, People’s Republic of China.
4State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, People’s Republic of China.
*To whom correspondence should be addressed:
ChunxiongLuo, Email: , Tel: +86-10-62754743
Qi Ouyang, Email: , Tel: +86-10-62756943
Supplementary Information
We conducted a simple model to learn the effect of autocrine factors and external FBS concentration on cell growth in cell-loading cavity. Our model is based on the assumption that both FBS level and autocrine factors concentration influence the cell’s growth rate,with no regard toinsufficient nutrient supply and crowding effect.
(1)
(2)
Corresponding to experiment, there were two kinds of boundary conditions. For cases where cells grew in micro-cavities, communication with external environment through the inlets and parallel palisading channel were considered.For the case of cells in Petri dishes, cell growth environment was assumed as a closed cube with the side length of 5000μm and cells stay at the bottom of the cube.
Equation (1) is the diffusion equation of autocrine factors. Where Cc is the concentration of autocrine factors; D is the diffusion coefficient of the secreted molecules; k1and k2 are constant ratesat which autocrine factors are secreted and degraded by every cell;V is the volume of cell; ri is cell location andis dirac delta function. According to some known growth factors’ molecular weight, we settle the value of diffusion coefficient D around 100μm2s-1. The adjustment of k1 value showed that the concentration of autocrine factor increases as k1 increasing, but the ratio of the concentration between different sizes of micro-cavities is unchanged. However, k2is quite sensitive. When k2is around10-3s-1, the ratio of concentration around cells in different size of micro-cavities has obvious distinction. Since our focus is distinguishing the live/death decision making in different environment, we chose secreted rate k1 as 10000a.u.μm3s-1to keep autocrine factors concentration in reasonable range, and self-degradation rate k2 as 0.00125s-1to illustrate the difference between different cases.In this simulation, space was segmented into lattice with 20μm long and time step was set as 0.01s, without consideringany small molecules are absorbed into PDMS.
In equation (2), N is the cell number in loading-cavity. For the functions g(Cc) and f(Cf), we use Hill function for simplification at current stage. The explicit forms of functions are:and.Where the average Cc over the whole chamber volume was used, and in quasi-static assumption this value is linearly related to the number of cells exists in the cell-loading cavity;Cf is the FBS concentration added in culture media;kc, Kc, kf and Kf are corresponding constants in the function; Kd is the death rate of the cell. All the unmeasured parameters in this equationcome out of fitting by MultiStart routine (Matlab, the Mathworks Inc., according to cell growth experiments with different FBS levelsin micro-chambers with the side length of 200μm and 500μm(Table 1 and Table 2).Finally, kcis 0.0214s-1, Kc is 1.75a.u., kf is 0.02s-1, Kf is 0.03 a.u.and Kdis 0.0106s-1.It conforms well to the experiment results (Fig.s1) and can be used for prediction to some extent.If we set equation (2) to be zeroat fixed FBS level, it is possible that there may be a threshold of the autocrine factors concentration or the cell number to keep the cells alive. But considering the inevitable cell-cell variation among small amount of cells under observation, it is difficult to quantify the exact cell number and FBS level of the liminal value.
Fig.s1 Cell growthexperiment data and fitting curves with different FBS levelsin micro-chambers with the side length of 200μm (left)and 500μm(right).
Table 1. Cell growth experiments in 200μm*200μm micro-chambers during 3 days, 40-50 data for every FBS level.
Table 2. Cell growth experiments in 500μm*500μm micro-chambersduring 3 days, 40-50 data for every FBS level.