A statistical thermodynamic model has been developed In prokaryotes, genes are commonly switched on and off by the interactions of regulatory proteins with specific DNA sequences. A particularly complex example of such a switch is found at the right operator (OR) ofbacteriophage A: this operator consists of three tandem DNA sites that are recognized by two phage-encoded regulatory proteins (the A repressor and cro protein). When phage A is in the "lysogenic state," the A repressor (cI gene product) is synthesized and occupies sites OR1 and OR2 In this configuration of OR, the cro gene is repressed and the ci gene is transcribed.The phage switches into the "lytic state" when the repressor protein is cleaved in half by the recA protein, an action initiated by DNA damage. As repressor is destroyed, the cro gene is derepressed and the cro protein is made and occupies site OR3, turning off transcription of the cl gene, yet allowing its own synthesis. In this fashion, the phage can switch from one state (lysogeny) to another (lytic growth) in response to an external signal (for review, see ref. 1).In this paper, we consider the lysogenic state (repressor on, cro off) in an attempt to understand the physical principles that govern the ways in which the protein-DNA and protein-protein interactions operate in concert to produce the known physiological behavior. We show that a model based on statistical thermodynamic assumptions is sufficient to account for some of the known physiological properties of the repressor-operator regulatory system. A brief summary of certain aspects of this work has been presented elsewhere (1).Models for interactions at the lac operon have been developed to include effects of inducer and nonspecific DNA on the binding of lac repressor (2-4). The systems of A and other inducible phages differ from lac by using multiple operator binding sites that have cooperative interactions between bound repressors (1). This requires a more elaborate theoretical approach to the protein-DNA binding problem-one that has not previously been developed. The mathematical model we present here incorporates a set of rules and assumptions derived from previous genetic, biochemical, and structural studies. Combination of this information with statistical thermodynamic assumptions generates a quantitative formulation that incorporates salient features of the qualitative description developed over the last several years (1,(5)(6)(7)(8)(9)). This quantitative model has the following significance. (i) It provides a way to test assumptions regarding the physical bases for operation of the system. Thus, it predicts quantitatively the activities of the two OR-controlled promoters (PR and PRM) as a function of repressor concentration, and these predictions can then be compared with known.physiological properties of the system. (ii) It points out features of the A operator system that were not obvious (or at least fully appreciated) from previous experiments. (iii) It incorporates a theory for interpreting cooperati...

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Although tetrameric hemoglobin has been studied extensively as a prototype for understanding mechanisms of allosteric regulation, the functional and structural properties of its eight intermediate ligation forms have remained elusive. Recent experiments on the energetics of cooperativity of these intermediates, along with assignments of their quaternary structures, have revealed that the allosteric mechanism is controlled by a previously unrecognized symmetry feature: quaternary switching from form T to form R occurs whenever heme-site binding creates a tetramer with at least one ligated subunit on each dimeric half-molecule. This "symmetry rule" translates the configurational isomers of heme-site ligation into six observed switchpoints of quaternary transition. Cooperativity arises from both "concerted" quaternary switching and "sequential" modulation of binding within each quaternary form, T and R. Binding affinity is regulated through a hierarchical code of tertiary-quaternary coupling that includes the classical allosteric models as limiting cases.

In a lysogen, most genes of phage lambda are repressed; in response to a transient induction signal, they are efficiently switched on. The switch, which consists in part of a tripartite operator to which two regulatory proteins bind, depends not only on DNA--protein interactions, but also on effects transmitted from one DNA-bound protein to another. lambda Exemplifies a strategy that facilitates efficient switching between two physiological states in response to a transient signal.