Dissecting Gene Regulation Through DNA Loop Formation Using Statistical Mechanical Models and Experiments

Testing our understanding of genetic circuits requires models which make quantitative predictions that can be experimentally validated.  A common motif of gene regulation involves the interactions between transcription factors, RNA polymerase, and DNA.  Although many examples of gene regulation through such interactions are well known, our understanding of even the simplest such systems is often qualitative, at the level of biological “cartoons”.  These cartoons only predict whether interactions between the regulatory components increase, decrease, or have no effect on gene expression.   Such models fail to make quantitative predictions about specific realizations of such genetic circuits, even for well-studied systems such as the lac operon. 

Our approach has been to construct models of gene expression based on equilibrium statistical mechanics.  The models require only a few input parameters.  The model parameters include binding energies of proteins, copy numbers of components, and the mechanical properties of DNA.  These parameters are measured in simple control experiments.  Once these inputs have been determined, the models contain no free parameters and make quantitative predictions about the level of gene expression over a wide range of parameter space.  We have constructed and experimentally validated such models to test our understanding of the lac operon.

In the lac operon, a dimeric transcription factor, lac repressor, can bind to three different binding sites on DNA, called operators.  Gene expression is reduced by repressor binding to the center operator just adjacent to the promoter.  It is thought that binding to the outer, auxiliary sites alone cannot directly influence gene expression.  Instead, the auxiliary sites can participate in loop formation, in which one dimeric repressor can simultaneously bind to both the center and an auxiliary operator, bending the intervening DNA into a loop.  The looped state leads to enhancement of repression due to the loop locking in the repressor on the center operator.

We use this genetic circuit to make predictions about how the specifics features of the lac operon lead to a specific level of gene expression.  The model we developed for the lac operon has six states, with the probability of each state weighted by a Boltzmann factor calculated from the change in free energy associated with each state.  Some of the states lead to repression while others enable binding of the RNA polymerase and transcription of the gene.  Using the model, we make quantitative predictions about how the level of gene expression is modulated by each component of the system.  We model and test how changes in the binding energies of the repressor to the operators, the number of repressors per cell, the length of the DNA loop, and the flexibility of the DNA in the loop alter the level of gene expression.

The models were tested experimentally by creating genetic circuits containing the gene regulatory components of the lac operon.  These circuits were incorporated into the genome of E. coli.  Fluorescent reporters were used to quantify the level of gene expression in each circuit.  The readout of the experiments was the absolute level of fluorescent protein.  Using this approach, the predictions of the thermodynamic equilibrium models were experimentally tested for many genetic circuits containing different combinations of the regulatory elements of the lac operon.

The experiments reveal that the standard model described above does not hold.  There is a contribution from the downstream auxiliary operator to repression, even in the absence of loop formation.  This result shows that binding events downstream of the promoter can still interfere with the activity of RNA polymerase, and do so in a manner which is dependent upon the orientation of the promoter and operator.  Additionally, the intrinsic flexibility of the looping DNA has no effect on the level of repression.  DNA sequences that have previously been shown to easily form loops in vitro do not lead to increased repression.  The apparent lack of dependence of repression on the flexibility of the looping DNA suggests that other in vivo factors such as DNA bending proteins are dominant in determining the probability of the looping in vivo.  These results highlight the ability of quantitative models of gene expression, such as the zero free parameter thermodynamic equilibrium model applied here, to test and expand our understanding of gene regulatory mechanisms.  This approach should lead to both mechanistic insights into gene regulation in vivo, and also enable the construction of synthetic genetic circuits with fine-tuned control of gene expression.