Glassy dynamics in bacterial growth rate temperature dependence

An empirical expression for the temperature dependence of bacterial growth rate, k=b(T−T0), where k is the intrinsic growth rate, T is the ambient temperature, T0 is the hypothetical temperature, and b is the regression coefficient, has been exemplified for practical bacterial growth. Although this relationship has been popularly used as the standard evaluation of the bacterial growth rate, its scientific foundation is not clear. We propose a new relation, k = k0 exp[−Ea/kB(T − Tc)], where k0 is a constant, Ea is the activation energy (eV), kB is the Boltzmann constant, T is the absolute temperature (K), and Tc is the characteristic (frozen-in) temperature (K). The present equation resembles that for temperature-dependent fluidity (inverse viscosity) originally found for glass-forming liquids in inorganic materials. This commonality is attributed to the glass-like properties of the bacterial cytoplasm in accordance with the recent findings of glassy dynamics in active or lived matter.