We present a comprehensive computational study of some 900 possible "lambda-lac" mutants of the lysogeny maintenance switch in phage lambda, of which up to date 19 have been studied experimentally (Atsumi & Little, PNAS 103: 4558-4563, (2006)). We clarify that these mutants realise regulatory schemes quite different from wild-type lambda, and can therefore be expected to behave differently, within the conventional mechanistic setting in which this problem has often been framed. We verify that indeed, within this framework, across this wide selection of mutants the lambda-lac mutants for the most part either have no stable lytic states, or should only be inducible with difficulty. In particular, the computational results contradicts the experimental finding that four lambda-lac mutants both show stable lysogeny and are inducible. This work hence suggests either that the four out of 900 mutants are special, or that lambda lysogeny and inducibility are holistic effects involving other molecular players or other mechanisms, or both. The approach illustrates the power and versatility of computational systems biology to systematically and quickly test a wide variety of examples and alternative hypotheses for future closer experimental studies.
We present a comprehensive computational study of some 900 possible "λ-lac" mutants of the lysogeny maintenance switch in phage λ, of which up to date 19 have been studied experimentally (Atsumi & Little, PNAS 103: 4558-4563, (2006)). We clarify that these mutants realise regulatory schemes quite different from wild-type λ, and can therefore be expected to behave differently, within the conventional mechanistic setting in which this problem has often been framed. We verify that indeed, within this framework, across this wide selection of mutants the λ-lac mutants for the most part either have no stable lytic states, or should only be inducible with difficulty. In particular, the computational results contradicts the experimental finding that four λ-lac mutants both show stable lysogeny and are inducible. This work hence suggests either that the four out of 900 mutants are special, or that λ lysogeny and inducibility are holistic effects involving other molecular players or other mechanisms, or both. The approach illustrates the power and versatility of computational systems biology to systematically and quickly test a wide variety of examples and alternative hypotheses for future closer experimental studies.
The study of bacteriophage λ has played a large role in the development of molecular biology [1,2], and particularly in the understanding of gene regulation [3,4]. It is a temperate phage which can grow lytically, or remain in a lysogenic state in the host for many generations. While lysogeny as a phenomenon was known since the 1920’ies, and early quantitative studies centered on other systems, coliphage λ became the central model system of lysogeny since its discovery in the early 1950’ies [5,6]. Consequently, λ lysogeny has also been the system of choice for mechanistic explanations of gene regulation, ranging from systematic explanations of the data to detailed mathematical models of the kind first presented over twenty years ago [7]. This line of work has been taken up several other groups [8,9,10,11], with the aims to reproduce, in a model, known phenomena, and to shed light on particular aspects of such systems. Together with the lac system this approach has been the prototype for theoretical understanding of gene regulation in prokaryotes, generally taken to be one of the corner-stones of quantitative systems biology [12,13,14].
In a recent series of experimental studies by Atsumi & Little [15,16] the lytic repressor, Cro, was replaced by the Lac repressor, LacR. The stated goal was to continue along the lines of [17] in testing the modularity of the lambda circuit, i.e., in this case, to determine if stable and inducible lysogeny is affected by a change of the lytic repressor protein. Therefore, the authors of [15,16] constructed mutants in which the cro operon was replaced by the lac repressor operon, lacI, including the Shine-Dalgarno (SD) sequence for lacI. To enable repression of PR and PL, a lac operator site, lacO, was put downstream of the PR and PL transcription initiation sites. Moreover, in these new λ-lac mutants, some carried an intact OR3 site, only binding CI and hence without any lacI regulation of PRM. Others had the OR3 site replaced with a lacO site, hence disrupting the cI negative control of PRM, but at the same time allowing a negative feed-back from PR. Figure 1 illustrates three different circuits; the wild-type λ (WT), circuit A, with intact λ OR, and circuit B, where OR3 has been changed into a variant of lacO.
The great advantage of the new λ-lac mutants from the systems biology point of view is that there are potentially so many of them. While experimental studies have only so far been carried out on a fraction of all defined variants, it should be possible to extend the studies in [16] to many more. Computationally, as we will show, one can survey all variants in one screen, and find clear patterns.
The overall conclusion of our computational study presented here is that the new λ-lac mutants are not explainable in standard mathematical models of gene regulation. We believe this is of significant interest. First, if λ lysogeny cannot be explained, the whole program of computational systems biology may be in trouble. We address this issue in the Discussion. Second, at least for λ, this program is but the formalization, in terms of defined models and equations, of what is known or accepted in the experimental literature, often for quite some time. Therefore, the implication would be that the functioning of the λ lysogeny switch is quite different to what is generally believed.
The problem can be explained by concentrating on one example, the mutant labelled AWCF, displayed in Figure 1 in [16]. This mutant carries a version of lacI instead of cro, a normal λ OR region, a strong lacO binding site at PL, an intermediately strong lacO binding site downstream of PR, and a (relatively) poor Shine-Dalgarno sequence. It therefore is an example of control circuit A in Fig.
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