  In order to grow in any given environment, bacteria need to collect
information about the medium composition and implement suitable growth
strategies by adjusting their regulatory and metabolic degrees of freedom. In
the standard sense, optimal strategy selection is achieved when bacteria grow
at the fastest rate possible in that medium. While this view of optimality is
well suited for cells that have perfect knowledge about their surroundings
(e.g. nutrient levels), things are more involved in uncertain or fluctuating
conditions, especially when changes occur over timescales comparable to (or
faster than) those required to organize a response. Information theory however
provides recipes for how cells can choose the optimal growth strategy under
uncertainty about the stress levels they will face. Here we analyse the
theoretically optimal scenarios for a coarse-grained, experiment-inspired model
of bacterial metabolism for growth in a medium described by the (static)
probability density of a single variable (the `stress level'). We show that
heterogeneity in growth rates consistently emerges as the optimal response when
the environment is sufficiently complex and/or when perfect adjustment of
metabolic degrees of freedom is not possible (e.g. due to limited resources).
In addition, outcomes close to those achievable with unlimited resources are
often attained effectively with a modest amount of fine tuning. In other terms,
heterogeneous population structures in complex media may be rather robust with
respect to the resources available to probe the environment and adjust reaction
rates.
