The Fibonacci sequence is also called the "rabbit sequence" 12. The earliest model problem is as follows: Suppose there is a pair of young rabbits that grow up after one month, and then they can breed a pair of young rabbits every month. The young rabbits will also grow up after one month of growth and join the ranks of young breeding rabbits. Assuming that no rabbits will die, ask how many pairs of rabbits there are in month X.According to the calculation, the specific values are 1 pair in the first month, 2 pairs in the second month, 3 pairs in the third month, 5 pairs in the fourth month, 8 pairs in the fifth month, 13 pairs in the sixth month, 21 pairs in the seventh month, 34 pairs in the eighth month and 55 pairs in the ninth month, …. Since then, scholars have found that the processes of several aspects of many species in nature follow the Fibonacci sequence, such as the emergence of large branches, which is as follows: the thickest trunk is 1, the upward branches are 2, and then the upward branches are 3, 5, 8, .... For example, the emergence of some plant leaves and the number of petals are consistent with the numbers of the sequence. Why does this phenomenon occur? Scientists have found through experiments that breeding processes in line with the Fibonacci sequence are the fastest way,as the energy in animals and plants is constant this way 2,3 13.
When knee OA occurs, the proliferation ability of chondrocytes in articular cartilage tissue decreases, which leads to a decrease in both chondrocytes and extracellular matrix secreted by chondrocytes,ultimately leading to a decrease in cartilage tissue quantity.Therefore, the proliferation ability of chondrocytes is an important direction to study the development of knee OA 14,15.The division and proliferation of chondrocytes are affected by many factors.When we cultured chondrocytes in vitro, we found that the process of chondrocyte division and proliferation did not follow the mode of 1–2,2–4,4–8; in other words, it was not a 2n series mode.Instead, we found that when a chondrocyte population divides and proliferates, there are always some chondrocytes in the division stage and the other chondrocytes in the resting stage.As shown by the red arrow in Fig. 1F, 3 out of 5 chondrocytes are in the cell division stage (the nucleus is about to divide).
To observe the change in the proliferation number of normal chondrocytes,we added Gottingen pig knee chondrocytes to culture bottles at very low density,and because of the "ameba" movement of chondrocytes, when we selected chondrocytes for observation, we selected isolated chondrocytes without other cells around the microscope field of vision.After 42 days of observation, we found that the proliferation of normal chondrocytes conformed to the Fibonacci sequence. Sixteen of the 30 observed chondrocyte colonies essentially conformed to the sequence.The proliferation number of the other remaining chondrocytes was lower than that of the Fibonacci sequence, and no chondrocyte colony presenting numbers exceeding those corresponding to this sequence was observed.Moreover, the chondrocytes in the OA group essentially did not have chondrocyte colonies whose growth followed a pattern similar to that of the Fibonacci sequence, and the number of chondrocyte colonies that proliferated in the end was significantly less than that in the normal group.By comparing the average norm of chondrocyte number and Fibonacci number at the same time point between the two groups, we found that the average norm of the OA group was significantly larger than that of the normal group.This shows that the proliferation number of chondrocytes in the OA group deviated from thenumbers of the Fibonacci sequence more than that in the normal group did.Therefore, we believe that in the process of the proliferation of Gottingen pig knee chondrocytes, the change in chondrocyte number is close to the numbers in the Fibonacci sequence under normal circumstances, and when there are interferingfactors such as cell ageing and the proliferation ability decreases, the number deviates from and becomes lower than corresponding numbers of the Fibonacci sequence.We even speculate that the fastest of all cell proliferation methods may be closely aligned to the Fibonacci sequence, but the time differences in changes in cell numbers are different, which eventually leads to the inconsistency of the cell proliferation rate after 24 hours.