DNA molecules containing repetitive motifs are prone to expand in their lengths. Once there appear a head to tail tandem of two identical DNA sequences in the system, they can propagate indefinitely by the mechanism involving cycles of staggered annealing of complementary DNA strands of variable lengths and polymerase mediated filling-in of the generated overhangs. Microgene Polymerization Reaction (MPR) is an experimental model for expansion of short repetitive DNA to longer lengths. The testable kinetic model of (MPR) was formulated and solved numerically by Itsko et al. in Kinetics of Repeat Propagation in the Microgene Polymerization Reaction (2009). Here, the simple cases of MPR were solved analytically using modified Smoluchowski coagulation equation. It was found that the repeats propagate according to Gumbel probability density function when the distribution of lengths of obtained polymers follows inverted Gumbel probability density function.

包含重复基序的DNA分子容易扩展长度。一旦在系统中出现两个相同的DNA序列从头到尾的串联，它们可以通过涉及可变长度的互补DNA链交错退火和聚合酶介导的所产生突出端的填充循环的机制无限期传播。微基因聚合反应（MPR）是将短重复DNA扩增到更长长度的实验模型。（MPR）的可测试动力学模型是由Itsko等人建立并用数值方法求解的。在在Microgene聚合反应重复传播动力学（2009）。在这里，使用改进的Smoluchowski凝血方程解析地解决了MPR的简单情况。发现当所获得的聚合物的长度的分布遵循倒Gumbel概率密度函数时，重复根据Gumbel概率密度函数传播。