Adaptive response of a gene network to environmental changes by fitness-induced attractor selection
Switching between attractors has been studied in dynamical systems as noise-induced selection of attractors [33], [34]. In these previous studies, however, the direction of switching was not adaptive. In contrast, in the case presented here, due to the coupling of the attractor states with the cellular activity which influences the rate of the turnover of the deterministic state variables, an adaptive attractor with its higher cellular activity is inevitably selected in the presence of noise.
We propose here the concept of attractor selection based on experimental and theoretical studies on a simple network with mutually inhibitory operons in which the network autonomously chooses the appropriate gene expression pattern associated with the adaptive attractor in response to environmental changes that are not mediated by a cognate signal transduction machinery. This mechanism for environmental adaptation of gene expression crucially depends on the ratio of the metabolic rate (mRNA, protein turnover) controlled by the regulatory circuit and on the presence of noise in gene expression. The latter is relatively high compared to the deterministic regulation when cells are in unfavorable conditions so that the overall metabolic regulation is weak due to low cellular activity. Thus, the ratio of (deterministic) metabolic regulation relative to noise is reduced or increased around non-adaptive or adaptive attractors, respectively. As long as this correlation is satisfied, network structures other than the simple network investigated here will be able to respond to environmental changes through attractor selection if they possess multiple attractors [theoretically confirmed by Furusawa and Kaneko, unpublished]. Thus, noise-driven selection between two alternative attractor states differs from previously studied decision between functional states, such as glucose/lactose utilization in E. coli or lysogeny/lysis in lambda phages, in that there is no explicit, specific molecular link between proteins of the gene network and an external signal (metabolite as allosteric regulator of a key regulatory protein; UV light, etc.).
Our simple regulatory circuit utilizes common promoters and their repressors. However, the noise in gene expression from plasmids does not appear to differ markedly from that of the genomic genes [35], [36]. The existence of attractor selection in genome-encoded networks should be investigated in future studies, although the response of the whole genomic network in terms of attractor selection will be not as simple as that described here as it will involve combinations of many molecular mechanisms, including canonical signal transduction pathways.
Signal transduction is a basic mechanism for cellular responses to environmental changes, which is based on complex networks that connect the environment to genome. Each signal transduction network must have evolved through natural selection by responding to environmental changes that have occurred frequently in the past. Signaling pathways then have been conserved because they allow the host cells to adapt rapidly to specific environmental changes.
However, in addition to such frequently occurring environmental changes, unicellular organisms may encounter a large number of different starvation conditions each of which may appear only a few times during their lifespan. In addition, cells may not have evolved an attractor state to every environmental condition, yet some may confer better adaptation than others. It is then hard to imagine that the cells would have evolved and maintained specific signal transduction machineries for all possible rare environmental changes so as to map every environment to an optimal attractor, because of the high cost of maintaining all these signaling machineries. Even for frequently occurring environmental changes, attractor selection can be beneficial for cells since it requires no specific signal transduction apparatus, if speed of state transition is not an issue.
Due to its stochastic nature, attractor selection may not be as efficient as ordinary signal transduction, but it may prevent cells from dying in fluctuating environments. Molecular signal transduction may have evolved for efficient adaptation, but in view of our present results it is plausible that attractor selection may still be utilized as a primitive adaptation for sustainability in broadly changing environments. Attractor selection may facilitate the design of a network that can robustly respond in an adaptive manner to unknown environmental changes without requiring a large number of specific sensors and transducers. It may also be viewed as a sort of Darwinian preadaptation for the evolution of signal-specific transduction pathways when a particular new environmental condition becomes dominant and hence contributes to evolvability.
All plasmids were constructed using standard molecular cloning techniques [37]. Genes and promoters were obtained from the following sources: Ptrc from pTrc99A (Amersham Biosciences); PtetA from pASK-IBA3 (Sigma Genosys); lacI from pTrc99A; tetR from pcDNA6/TR (Invitrogen); egfp from pEGFP (BD Biosciences Clontech); dsRed.T4 (a gift from Dr. B. S. Glick, The University of Chicago) [21]; mdhfr from pQE16 (Qiagen); and gls-h from pKGN-H [19]. The plasmid contained the ColE1 origin of replication and ampicillin resistance gene. The t0 terminator from pPROTet.E333-lacZ (BD Biosciences Clontech) and rrnBT1T2 terminator [38] from pTrc99A were used to terminate transcription from Operon 1 and Operon 2, respectively.
E. coli strain OSU1, a derivative of DH1 [39], was constructed by replacing the glnA gene with the cat gene by homologous recombination [40]. For cells carrying pALL7, the following three media were employed. 90 mg/l ampicillin was added to Medium C to prepare Medium M [41]. Medium N consisted of Medium M plus 90 µM glutamine, which compensates for the lack of the glnA gene in the genome of OSU1. Medium T was Medium N plus 580 mg/l of trimethoprim lactate, which completely inhibits bacterial DHFR and requires a high level of expression of mDHFR for survival of E. coli cells. To match the effective strength of PtetA to that of Ptrc, anhydrotetracycline, which inhibits Tet repressor, was added to the three media at equal concentrations of 0.5 µg/l. All culture steps were conducted at 37°C with aeration after inoculation of 6×107 cells/l, unless otherwise noted. The number of cells was measured using a Particle Analyzer SD-2000 (SYSMEX). The cells from each population were stored at −80°C before flow cytometric analysis.
The samples stored at −80°C were thawed at 25°C in a water bath and kept on ice before analysis. The single-cell fluorescence measurements were carried out on a COULTER® EPICS® ELITE Flow Cytometer (Beckman Coulter) with a 488-nm Argon excitation laser and band-pass filters of 525±25 nm for green fluorescence and a 600 nm dichroic filter for red fluorescence. All flow event data were converted to text format using WinMDI Version 2.8 and analyzed with MATHEMATICA 5.0 (Wolfram Research) and DeltaGraph Version 5.0.1.
Total bacterial RNA was prepared with RNeasy kits (Qiagen). Northern blotting and hybridization were performed according to standard methods and visualized with the AlkPhos Direct™ Labeling and Detection System (Amersham Biosciences). Double-stranded lacI and dsred.T4 DNAs were used as probes for transcripts from Operon 1 and Operon 2, respectively. Hybridization signals for the mRNAs from Operon 1 and Operon 2 were quantified using ImageJ 1.29.
The numerical simulation of the Langevin equation (1) was conducted by the Runge-Kutta method using a program developed in Microsoft Visual C++, as well as by FORTRAN program using algorithms in Numerical Recipes [42]. The noise term was calculated as an independent Gaussian random number. We confirmed the accuracy by reducing the time grid for integration.