During the synthesis of integral membrane proteins (IMPs), the hydrophobic amino acids of the polypeptide sequence are partitioned mostly into the membrane interior and hydrophilic amino acids mostly into the aqueous exterior. Using a many-body statistical mechanics model, we analyze the minimum free energy state of polypeptide sequences partitioned into α-helical transmembrane (TM) segments and the role of thermal fluctuations. Results suggest that IMP TM segment partitioning shares important features with general theories of protein folding. For random polypeptide sequences, the minimum free energy state at room temperature is characterized by fluctuations in the number of TM segments with very long relaxation times. Moreover, simple assembly scenarios do not produce a unique number of TM segments due to jamming phenomena. On the other hand, for polypeptide sequences corresponding to actual IMPs, the minimum free energy structure with the wild-type number of segments is free of number fluctuations due to an anomalously large gap in the energy spectrum. Now, simple assembly scenarios do reproduce the minimum free energy state without jamming. Finally, we find a threshold number of random point mutations where the size of the anomalous gap is reduced to the point that the wild-type ground state is destabilized and number fluctuations reappear.
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