In many cases, transcriptional regulation involves the binding of transcription factors at sites on the DNA that are not immediately adjacent to the promoter of interest. This action at a distance is often mediated by the formation of DNA loops: Binding at two or more sites on the DNA results in the formation of a loop, which can bring the transcription factor into the immediate neighborhood of the relevant promoter. These processes are important in settings ranging from the historic bacterial examples (bacterial metabolism and the lytic-lysogeny decision in bacteriophage), to the modern concept of gene regulation to regulatory processes central to pattern formation during development of multicellular organisms. Though there have been a variety of insights into the combinatorial aspects of transcriptional control, the mechanism of DNA looping as an agent of combinatorial control in both prokaryotes and eukaryotes remains unclear. We use single-molecule techniques to dissect DNA looping in the lac operon. In particular, we measure the propensity for DNA looping by the Lac repressor as a function of the concentration of repressor protein and as a function of the distance between repressor binding sites. As with earlier single-molecule studies, we find (at least) two distinct looped states and demonstrate that the presence of these two states depends both upon the concentration of repressor protein and the distance between the two repressor binding sites. We find that loops form even at interoperator spacings considerably shorter than the DNA persistence length, without the intervention of any other proteins to prebend the DNA. The concentration measurements also permit us to use a simple statistical mechanical model of DNA loop formation to determine the free energy of DNA looping, or equivalently, the for looping.

We calculate the probability of DNA loop formation mediated by regulatory proteins such as Lac repressor (LacI), using a mathematical model of DNA elasticity. Our model is adapted to calculating quantities directly observable in tethered particle motion (TPM) experiments, and it accounts for all the entropic forces present in such experiments. Our model has no free parameters; it characterizes DNA elasticity using information obtained in other kinds of experiments. It assumes a harmonic elastic energy function (or wormlike chain type elasticity), but our Monte Carlo calculation scheme is flexible enough to accommodate arbitrary elastic energy functions. We show how to compute both the ‘looping J factor’ (or equivalently, the looping free energy) for various DNA construct geometries and LacI concentrations, as well as the detailed probability density function of bead excursions. We also show how to extract the same quantities from recent experimental data on TPM, and then compare to our model’s predictions. In particular, we present a new method to correct observed data for finite camera shutter time and other experimental effects. Although the currently available experimental data give large uncertainties, our first-principles predictions for the looping free energy change are confirmed to within about 1 kBT, for loops of length around 300 basepairs. More significantly, our model successfully reproduces the detailed distributions of bead excursion, including their surprising three-peak structure, without any fit parameters and without invoking any alternative conformation of the LacI tetramer. Indeed, the model qualitatively reproduces the observed dependence of these distributions on tether length (e.g., phasing) and on LacI concentration (titration). However, for short DNA loops (around 95 basepairs) the experiments show more looping than is predicted by the harmonic-elasticity model, echoing other recent experimental results. Because the experiments we study are done in vitro, this anomalously high looping cannot be rationalized as resulting from the presence of DNA-bending proteins or other cellular machinery. We also show that it is unlikely to be the result of a hypothetical ‘open’ conformation of the LacI tetramer.

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The heterogeneity of cell membranes, specifically the presence of lipid rafts, has been hypothesized to play a role in a large number of cellular processes. Although extensive work has been carried out to show the function of lipid rafts in these processes, the characterization of lipid rafts has proven to be extremely difficult. It is known that raft size is relevant to the function of cellular processes and that raft coalescence may be a driving factor for these processes; however, it remains unclear what factors influence raft size and coalescence in natural cell membranes. In this work, we study two ternary model phospholipid and cholesterol systems using two steady-state fluorescent techniques to detect and characterize membrane domains. Domain size is determined through the use of a model to relate experimental Förster resonance energy transfer (FRET) measurements to domain size. Domains in the range of 3-15 nm were detected in a dioleoylphosphatidylcholine-dipalmitoylphosphatidylcholine-cholesterol (DOPC-DPPC-Chol) system, while only a very small region containing domains was detected in a 1-palmitoyl-2-oleoyl-phosphatidylcholine-dipamitoylphosphatidylcholine-cholesterol (POPC-DPPC-Chol) system. In addition, the polarity-dependent emission maximum shift of the acceptor 1-myristoyl-2-[12-[(5-dimethylamino-1-naphthalenesulfonyl)amino]dodecanoyl]-sn-glycero-3-phosphocholine (DAN-PC) was used to detect the type of liquid phase(s) present in the membrane. It was found that, even in the case in which no two-phase coexistence was observed (POPC-DPPC-Chol), two liquid phases are present, although not necessarily in coexistence. These steady-state fluorescent techniques provide a method for detecting the presence of very small domains in model membranes and provide previously inaccessible detail about the phase behavior of these two systems.

This work applied two steady-state fluorescence techniques to detect nanoscopic membrane domains in a binary dimyristoylphosphocholine (DMPC)-cholesterol system and a ternary dioleoylphosphocholine (DOPC)-dipalmitoylphosphocholine (DPPC)-cholesterol system. A polarity-induced spectral shift in the emission spectra of 1-myristoyl-2-[12-[(5-dimethylamino-1-naphthalenesulfonyl)amino]dodecanoyl]-sn-glycero-3-phosphocholine (DAN-PC) in combination with a Förster resonance energy transfer (FRET) assay agreed with the phase diagrams that have been published for these systems and were observed to be useful tools in the detection of membrane heterogeneities. The DAN-PC/dehydroergosterol (DHE) FRET pair was found to be best suited for use with these steady-state techniques because of their differential partitioning between phases, although a high acceptor concentration was needed to obtain accurate measurements. In the binary system, this high probe concentration was found to be perturbing, but in more representative ternary systems, the high probe concentration no longer disrupted the phase behavior of the system. This FRET pair allowed for the calculation of nanometer-scale domain sizes in model ternary systems, using the two steady-state fluorescence techniques along with a clear and straightforward model.