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Concentration and length dependence of DNA looping in transcriptional regulation.

Han L, Garcia HG, Blumberg S, Towles KB, Beausang JF, Nelson PC, Phillips R - PLoS ONE (2009)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Physics, California Institute of Technology, Pasadena, California, United States of America.

ABSTRACT
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.

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Schematic showing the different looping topologies associated with binding of Lac repressor.(A) Orientation of the two operators on the DNA. Choice of labeling orientation is arbitrary. (B)–(E) two parallel (P1 and P2) and antiparallel (A1 and A2) orientations of the DNA when subjected to Lac repressor mediated looping. We adopted the naming conventions given in refs. [36], [37].
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pone-0005621-g005: Schematic showing the different looping topologies associated with binding of Lac repressor.(A) Orientation of the two operators on the DNA. Choice of labeling orientation is arbitrary. (B)–(E) two parallel (P1 and P2) and antiparallel (A1 and A2) orientations of the DNA when subjected to Lac repressor mediated looping. We adopted the naming conventions given in refs. [36], [37].

Mentions: It is convenient to describe the probability of the various states using both the language of microscopic binding energies (and looping free energies) and the language of equilibrium constants (and ). From a microscopic perspective, the key parameters that show up in the model are the standard free energy changes for repressor binding to the two operators, and , the looping free energy and the concentration of repressor . The binding energy here contains two components. One is the standard positional free energy required for bringing one Lac repressor molecule to its DNA binding site at 1 M concentration of Lac repressor. The other is the rotational entropy loss times , plus the interaction free energy due to the physical contact upon protein binding [42], [43], [63]. The associated free energy with each configuration gives the statistical weights of the equilibrium probability (listed in the middle column of fig. 2). For example, to obtain the probability of the looped state, we construct the ratio of state (v) in the figure to the sum over all five states, as given by(1)where and the temperature is in degrees Kelvin. As detailed in the Supporting Information S1 and can be read off from the right column in fig. 2, this microscopic description is conveniently rewritten in terms of the equilibrium constants and for looping as(2)Here is the average of the individual factors corresponding to different loop topologies. These topologies can be classified according to the orientation of each one of the operators with respect to the two Lac repressor binding heads as shown in fig. 5. We define the state variables and that describe the orientation of and , respectively, and that can adopt a value of either 1 or 2. The average is then(3)An alternative to this scheme is to construct the ratio . In the limit where the strongest operator, , is always occupied, this ratio takes the simple, linear form(4)This permits the determination of the as the slope of a linear fit of the form without necessarily a need to obtain . Below we discuss the validity of this particular model. For the remaining data points at loop lengths other than 306 bp, where no titration was done, we can use the relation(5)Just like in the titration case, this relation allows to obtain without knowing , as long as we know at least one value of and its corresponding .


Concentration and length dependence of DNA looping in transcriptional regulation.

Han L, Garcia HG, Blumberg S, Towles KB, Beausang JF, Nelson PC, Phillips R - PLoS ONE (2009)

Schematic showing the different looping topologies associated with binding of Lac repressor.(A) Orientation of the two operators on the DNA. Choice of labeling orientation is arbitrary. (B)–(E) two parallel (P1 and P2) and antiparallel (A1 and A2) orientations of the DNA when subjected to Lac repressor mediated looping. We adopted the naming conventions given in refs. [36], [37].
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2682762&req=5

pone-0005621-g005: Schematic showing the different looping topologies associated with binding of Lac repressor.(A) Orientation of the two operators on the DNA. Choice of labeling orientation is arbitrary. (B)–(E) two parallel (P1 and P2) and antiparallel (A1 and A2) orientations of the DNA when subjected to Lac repressor mediated looping. We adopted the naming conventions given in refs. [36], [37].
Mentions: It is convenient to describe the probability of the various states using both the language of microscopic binding energies (and looping free energies) and the language of equilibrium constants (and ). From a microscopic perspective, the key parameters that show up in the model are the standard free energy changes for repressor binding to the two operators, and , the looping free energy and the concentration of repressor . The binding energy here contains two components. One is the standard positional free energy required for bringing one Lac repressor molecule to its DNA binding site at 1 M concentration of Lac repressor. The other is the rotational entropy loss times , plus the interaction free energy due to the physical contact upon protein binding [42], [43], [63]. The associated free energy with each configuration gives the statistical weights of the equilibrium probability (listed in the middle column of fig. 2). For example, to obtain the probability of the looped state, we construct the ratio of state (v) in the figure to the sum over all five states, as given by(1)where and the temperature is in degrees Kelvin. As detailed in the Supporting Information S1 and can be read off from the right column in fig. 2, this microscopic description is conveniently rewritten in terms of the equilibrium constants and for looping as(2)Here is the average of the individual factors corresponding to different loop topologies. These topologies can be classified according to the orientation of each one of the operators with respect to the two Lac repressor binding heads as shown in fig. 5. We define the state variables and that describe the orientation of and , respectively, and that can adopt a value of either 1 or 2. The average is then(3)An alternative to this scheme is to construct the ratio . In the limit where the strongest operator, , is always occupied, this ratio takes the simple, linear form(4)This permits the determination of the as the slope of a linear fit of the form without necessarily a need to obtain . Below we discuss the validity of this particular model. For the remaining data points at loop lengths other than 306 bp, where no titration was done, we can use the relation(5)Just like in the titration case, this relation allows to obtain without knowing , as long as we know at least one value of and its corresponding .

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Physics, California Institute of Technology, Pasadena, California, United States of America.

ABSTRACT
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.

Show MeSH