Plasticity of the cis-Regulatory Input Function of a Gene

The transcription rate of a gene is often controlled by several regulators that bind specific sites in the gene's cis-regulatory region. The combined effect of these regulators is described by a cis-regulatory input function. What determines the form of an input function, and how variable is it with respect to mutations? To address this, we employ the well-characterized lac operon of Escherichia coli, which has an elaborate input function, intermediate between Boolean AND-gate and OR-gate logic. We mapped in detail the input function of 12 variants of the lac promoter, each with different point mutations in the regulator binding sites, by means of accurate expression measurements from living cells. We find that even a few mutations can significantly change the input function, resulting in functions that resemble Pure AND gates, OR gates, or single-input switches. Other types of gates were not found. The variant input functions can be described in a unified manner by a mathematical model. The model also lets us predict which functions cannot be reached by point mutations. The input function that we studied thus appears to be plastic, in the sense that many of the mutations do not ruin the regulation completely but rather result in new ways to integrate the inputs

Parameter Space and Phenotype Space of the <i>lac</i> CRIFs

<p>(A) Parameter space is the space of the three parameters <i>a, c,</i> and <i>d</i> that describe the relative binding affinity of RNAp, LacI, and CRP to their sites in the <i>lac</i> CRR; 5,000 points log-uniformly distributed in this space are shown. (B) Phenotype space, whose axes correspond to the ratio of plateaus I, II, III to plateau IV in the input function (see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0040045#pbio-0040045-g003" target="_blank">Figure 3</a>C for definition of these plateaus). The phenotypes of the points in (A) are shown; corresponding points in parameter and phenotype space have the same color. Also plotted are the input functions that correspond to the eight extreme corners of phenotype space. Input functions marked with a star cannot be reached with point mutations in the regulator binding sites according to the model. In the case of the (1, 1, 1) vertex, all plateaus are equal (either to 1 or 0). We depict this situation by the FALSE gate. (C) Phenotype space: the experimentally observed input functions are indicated in green dots and that of the wild type promoter region in a red dot; black dots are the phenotypes of points shown in (A). </p

The Wild-Type <i>lac</i> Promoter Region and the Point Mutations Used in This Study

<p>Locations of point mutations are indicated by dots, where a red indicates mutations used in all variants, black means change to A or T with equal probability, and white means change to A, C, or T with equal probability. Also shown are the positions of the two LacI sites O1 and O3, the CRP site, and the RNAp site (−10 and −35 regions). Note that the promoter region is displayed in this figure in two parts: the sequence in the top part ends just downstream of the beginning of the sequence in the bottom part. The black arrow indicates the transcription start site of the <i>lacZ</i> gene. </p

All 16 Possible Two-Input Boolean Logic Gates

<p>The gates are functions of two inputs, <i>x</i> and <i>y,</i> each of which can be 0 or 1. The top left gate, for example, is an AND gate whose output is 1 only when both <i>x</i> = 1 and <i>y</i> = 1, and zero otherwise. The AND gate is represented by a high plateau when <i>x</i> = 1 and <i>y</i> = 1, and by three low plateaus for the other combinations of <i>x</i> and <i>y.</i> The six gates with a shaded background are realizable by the model of the <i>lac</i> input function, whereas the ten gates with a white background are not (forbidden gates). </p

Input Function of the Wild-Type <i>lac</i> Promoter Region and Two Variant CRRs

<p>The input functions describe the promoter activity as a function of the concentrations of the two inducers IPTG (in μM) and cAMP (in mM), measured in midexponential growth in an automated fluorimeter by means of a GFP-promoter fusion on a low-copy plasmid. (A) Surface plot of log wild-type input function. (B) Contour plot of wild-type input function. (C) Schematic drawing showing the activation thresholds and the four plateaus of the input function. (D–F) Same for strain U340, with an OR-like input function. (G–I) Same for strain U339 with an AND-like input function. The plateaus of the input functions are marked by roman numerals in (C, F, and I). Plateau I occurs at zero concentration of inducers, plateau II at saturating cAMP and zero IPTG, plateau III at saturating IPTG and zero cAMP, and plateau IV occurs when both inducers are saturating.</p

Input Functions of <i>lac</i> CRR Variants

<p>The input functions are ordered from top left to bottom right to range from those that most resemble OR gates to those that most resemble AND gates. (A) The most OR-like input function. (B) Input function resembles a single-input switch that responds only to IPTG and not to cAMP (note the elevated plateau III compared to the wild-type). (C) Wild-type input function. (D) The most AND-like input function, whose main difference from wild type is a lower plateau III.</p