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

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