answer 3:4 - Wrong answer: negative cooperativity and molecular heterogeneity cause a broader rather than a steeper ligand binding isotherm

As shown in the preceding tutorial #2, the ligand binding isotherm of a negatively cooperative protein or of a chemically heterogeneous mixture of isoforms, is broader than that of a monomeric protein. In the present case the ligand binding isotherm is steeper than that of a monomeric protein, thus it is incompatible with chemical heterogeneity and with negative cooperativity.

We may express the same concept using the Hill coefficients:
Characteristics of the system Ligand binding isotherm Hill coefficient
negative cooperativity
chemical heterogeneity:
      hetero-oligomeric protein
      mixture of isoforms
broader than for a monomeric protein       < 1
absence of cooperativity:
      monomeric proteins
      non-cooperative oligomers
Y = [X] / (1 + [X])       = 1
positively cooperative oligomeric proteins steeper than for a monomeric protein       > 1

The Hill coefficient n=1.43 obtained for this ligand binding isoterm is compatible with the hypothesis of a homodimeric or homooligomeric positively cooperative protein, ruling out negative cooperativity or absence of cooperativity. Chemical heterogeneity of the sample, due to the presence of isoforms or heterooligomers, cannot be excluded because positive cooperativity may overcome the broadening of the ligand binding isotherm caused by these conditions.

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