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Membrane protein homo-oligomers named higher-order transient structures (HOTS) are formed through cohesive self-interactions in the range of a few $k_{B}T$. The small magnitude of these interactions underlies the rapid reversibility of HOTS on the timescale of membrane signaling processes, permitting the dynamic modulation of signals. At the same time, weak interactions present an apparent paradox: HOTS should form only if the concentration of a particular protein is sufficiently high to produce oligomerization by mass action. And yet, HOTS are observed experimentally with membrane proteins present in cell membranes at concentrations of only a few per $\mathrm{\mu }{\mathrm{m}}^2$. In this study, we employ principles of statistical thermodynamics to explain how cells can alter the configurational entropy of the oligomerization reaction, thereby achieving HOTS formation at low concentrations of the protein in the membrane. We propose that this modification of the configurational entropy, a process we call configurational length scaling, is an important aspect of HOTS formation in cell membranes and possibly other cellular compartments.