Cell fate determination by Lamarckian molecule-inheritance and chance
Single, isogenic cells can differ in their survival and adaptation capacity. This phenotypic diversity is generally due to stochastic molecular events. Since mother cells on average pass half of their molecular content on to their daughters, the states of progeny cells strongly correlate with that of mother cells (Lamarckian inheritance). Why a particular cell deviates qualitatively from others therefore requires consideration of chance events along its ancestral lineage. Here we develop theory to understand cellular heterogeneity in terms of stochastic ancestral events of molecule synthesis, molecule degradation and cell divisions. We find that cell growth stochasticity has profound consequences for molecular heterogeneity in isogenic populations of cells, especially for long-lived molecules such as proteins. For instance, the lower bound on noise in molecule copy numbers that has often been observed experimentally is shown to be solely determined by the probability distribution for the generation times of cells. Thus, copy-number noise is unavoidable, even in high-copy number circuits. Stochastic cell-fate and cell-differentiation decisions are therefore not necessarily due to noise in genetic circuits. We conclude that consideration of past chance events along cell lineages improves our understanding of how adaptive and mal-adaptive phenotypic heterogeneity arises in populations of isogenic cells.