Positive feedback produces broad distributions in maximum activation attained within a narrow time window in stochastic biochemical reactions

Abstract

How do single cell fate decisions induced by activation of key signaling proteins above threshold concentrations within a time interval are affected by stochastic fluctuations in biochemical reactions? We address this question using minimal models of stochastic chemical reactions commonly found in cell signaling and gene regulatory systems. Employing exact solutions and semi-analytical methods we calculate distributions of the maximum value ($N$) of activated species concentrations ($P_{max}(N)$) and the time ($t$) taken to reach the maximum value ($P_{max}(t)$) within a time window in the minimal models. We find, the presence of positive feedback interactions make $P_{max}(N)$ more spread out with a higher "peakedness" in $P_{max}(t)$. Thus positive feedback interactions may help single cells to respond sensitively to a stimulus when cell decision processes require upregulation of activated forms of key proteins to a threshold number within a time window.