(390h) 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.