DNA Looping and Physical Constraints on Transcription RegulationIntroductionRegulation With and Without LoopingRepression levelIncrease in the local concentrationDynamics and FluctuationsCell-to-Cell VariabilityConclusionsAcknowledgementsReferencesTransition RatesNon-specific Binding and DNA LoopingReferencesDNA Looping and Physical Constraints onTranscription RegulationJose´M. G. Vilar*and Stanislas LeiblerThe Rockefeller University1230 York Avenue, Box 34New York, NY 10021, USADNA looping participates in transcriptional regulation, for instance, byallowing distal binding sites to act synergistically. Here, we study thisprocess and compare different regulatory mechanisms based on repres-sion with and without looping. Within a simple mathematical model forthe lac operon, we show that regulation based on DNA looping, inaddition to increasing the repression level, can reduce the fluctuations oftranscription and, at the same time, decrease the sensitivity to changes inthe number of regulatory proteins. Looping is thus able to circumventsome of the constraints inherent to mechanisms based solely on bindingto a single operator site and provides a mechanism to regulate the averageproperties of transcription and its fluctuations.q 2003 Elsevier Ltd. All rights reserved.Keywords: gene expression; DNA looping; lac operon; computationalmodeling; regulation*Corresponding authorIntroductionCells use a wide variety of mechanisms to regu-late and perform their functions. Some of thesemechanisms are fairly simple. But, more often thatnot, there seems to be an unnecessary complexity.Consider for instance the lac operon, the systemwhere, together with l phage, gene regulation wasdiscovered.1–3It consists of a regulatory domainand three genes required for the uptake andcatabolism of lactose (see Figure 1). A regulatoryprotein, the lac repressor, can bind to the mainoperator O1and prevent the RNA polymerasefrom transcribing the genes. If it is not bound, tran-scription proceeds at a given rate. This simple ideaemerged as one of the milestones of gene regu-lation: there are DNA-binding proteins that canhinder or stimulate some of the steps leading totranscription. Regulation of transcription,however, is actually not so simple. In the case ofthe lac operon, besides O1there are two sites out-side the control region, the so-called auxiliaryoperators O2and O3, which closely resemble O1and where the repressor can also bind. At first,these two sites were considered to be justremnants of evolution without any specificfunction.2The reasons were diverse. They are faraway from the promoter, so that the repressor’sbinding to them cannot affect the RNA polymerasedirectly. They are much weaker than O1, O2isas much as ten times and O3is over 300 timesweaker. Moreover, elimination of either one ofthem leaves the repression level practicallyunchanged.The role of O2and O3, however, proved to be farfrom minor: simultaneous elimination of both ofthese operators reduced the repression level about100 times. Such a drastic effect was shown to bemediated by the DNA loops that the lac repressorcan induce by binding to two sites simultaneously.4Through looping, the auxiliary operators indirectlyincrease the probability for the repressor to bebound to the main operator.It is remarkable that, despite its apparentcomplexity, DNA looping is widely used in generegulation. It was first discovered in the araoperon5and subsequently, in other prokaryoticsystems like lac, deo, gal and gln.6It is a key elementin the regulation of the l phage7and it is at play ineukaryotic enhancers, allowing multiple proteinsfrom adjacent and distal sites to affect the RNApolymerase.6,8Here, we analyze how the dynamics of loopingaffects gene expression and compare it to differentalternative regulatory mechanisms. The results ofour model are in close agreement with the avail-able experimental data on the lac operon, whichspans over three orders of magnitude in the repres-sion level. In addition, the model shows that DNAlooping can be used to circumvent several of theshortcomings that are inherent to simplermechanisms.0022-2836/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.E-mail address of the corresponding author:[email protected]:10.1016/S0022-2836(03)00764-2 J. Mol. Biol. (2003) 331, 981–989Regulation With and Without LoopingIn Figure 2 we illustrate the main differences inthe mechanisms of regulation with and withoutlooping. The system with a single binding site canbe characterized by two states (Figure 2a). In thestate (i) the operator Omis not occupied and inthe state (ii) one of the N repressors of the cell isbound to Om: In principle, one might think of amore detailed description of the system, e.g.including states for the repressor bound non-specifically to DNA or freely diffusing in the cell.Such a detailed description would result at theend in an effective two-state description. Here,states are chosen to keep just the essentialelements.The DNA looping case is more complex andinteresting (Figure 2b). The major contribution oflooping to gene regulation comes from the syner-gistic effects of two operators. Thus, we considerthe two-operator case, for which there exist themost detailed experimental data.9Now, there arefive relevant states: (i) none of the operators isoccupied; (ii) a repressor is bound to just the mainoperator Om; (iii) to just the auxiliary operator Oa;(iv) to both of the operators by looping DNA; or(v) one repressor is bound to Omand the other toOaat the same time.Repression levelThe description based on states is suitable totackle, both qualitatively and quantitatively, theeffects of looping in gene regulation. Intuitively,looping increases repression because the system isdynamically trapped in the looped state (iv). Thesystem can only leave this state to either state (ii)or state (iii). In either of these two states, therepressor remains near the free operator. Therefore,the most likely event is that repressor is recapturedby the free operator to form the loop again. Thus,with high probability, the system comes back tostate (iv).This idea of the repressor being dynamicallytrapped is also a key element in a recently pro-posed mechanism for protein localization.10Proteins with two binding domains for each of theelements of an array will have a high probabilityof being attached to the array by one or both of itsdomains at any instant of time because, if theneighboring array elements are close
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