Application of quantum principles to living cells requires a new approximation of the full quantum mechanical description of intracellular dynamics. We discuss what principal elements any such good approximation should contain. As one such element, the notion of Catalytic force Cf is introduced. Cf is the effect of the molecular target of catalysis on the catalytic microenvironment that adjusts the microenvironment towards a state that facilitates the catalytic act. This phenomenon is experimentally testable and has an intriguing implication for biological organization and evolution, as it amounts to optimization without natural selection of replicators. Unlike the statistical-mechanical approaches to self-organization, the Cf principle does not encounter the problem of tradeoff between stability and complexity at the level of individual cell. Physically, the Cf is considered as a harmonic-like force of reaction, which keeps the state of the cell close to the ground state, defined here as a state where enzymatic acts work most efficiently. Ground state is subject to unitary evolution, and serves as a starting point in a general strategy of quantum description of intracellular processes, termed here Euclidean approach. The next step of this strategy is transition from the description of ground state to that one of growing state, and we suggest how it can be accomplished using arguments from the fluctuation-dissipation theorem. Finally, given that the most reliable and informative observable of an individual cell is the sequence of its genome, we propose that the non-classical correlations between individual molecular events at the single cell level could be easiest to detect using high throughput DNA sequencing.
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