Department of Mathematics, University of California Irvine, Irvine, CA 92697, USA.
J Theor Biol. 2012 Dec 7;314:84-94. doi: 10.1016/j.jtbi.2012.08.015. Epub 2012 Aug 23.
Neutral mutations play an important role in many biological processes including cancer initiation and progression, the generation of drug resistance in bacterial and viral diseases as well as cancers, and the development of organs in multicellular organisms. In this paper we study how neutral mutants are accumulated in nonlinearly growing colonies of cells subject to growth constraints such as crowding or lack of resources. We investigate different types of growth control which range from "division-controlled" to "death-controlled" growth (and various mixtures of both). In division-controlled growth, the burden of handling overcrowding lies with the process of cell-divisions, the divisions slow down as the carrying capacity is approached. In death-controlled growth, it is death rate that increases to slow down expansion. We show that division-controlled growth minimizes the number of accumulated mutations, and death-controlled growth corresponds to the maximum number of mutants. We check that these results hold in both deterministic and stochastic settings. We further develop a general (deterministic) theory of neutral mutations and achieve an analytical understanding of the mutant accumulation in colonies of a given size in the absence of back-mutations. The long-term dynamics of mutants in the presence of back-mutations is also addressed. In particular, with equal forward- and back-mutation rates, if division-controlled and a death-controlled types are competing for space and nutrients, cells obeying division-controlled growth will dominate the population.
中性突变在许多生物学过程中起着重要作用，包括癌症的发生和发展、细菌和病毒疾病以及癌症中耐药性的产生，以及多细胞生物器官的发育。在本文中，我们研究了在受到生长限制（如拥挤或缺乏资源）的非线性生长细胞菌落中，中性突变体是如何积累的。我们研究了不同类型的生长控制，从“分裂控制”到“死亡控制”生长（以及两者的各种混合）。在分裂控制的生长中，处理拥挤的负担在于细胞分裂的过程，随着承载能力的接近，分裂速度会减慢。在死亡控制的生长中，死亡率的增加会减缓扩张。我们表明，分裂控制的生长使积累的突变数量最小化，而死亡控制的生长对应于最大数量的突变体。我们检查了这些结果在确定性和随机性设置中的有效性。我们进一步发展了中性突变的一般（确定性）理论，并在不存在反向突变的情况下，对给定大小的菌落中突变体的积累获得了分析理解。还解决了存在反向突变时突变体的长期动力学问题。特别是，如果分裂控制和死亡控制类型在争夺空间和营养，且正向突变和反向突变的速率相等，那么遵循分裂控制生长的细胞将主导种群。
