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Taking into account the difference between the relaxation times of the constituents of the model, given by the inverses of d * (see Table 1), we can interpret it as composed of two temporally separated systems: a rapid one, formed by HetR and NtcA, showing fast dynamics that relaxes to its steady state almost instantaneously and a slow one, composed of PatS and cN, whose evolution is dictated by the values of HetR and NctA in their instantaneous equilibrium. This corresponds to an adiabatic elimination technique [ 49] that helps in reducing the complexity of the dynamical system by splitting it into two simpler interdependent subsystems. Bintu L, Buchler N, Garcia H, Gerland U, Hwa T, Kondev J, et al. (2005) Transcriptional regulation by the numbers: models. Curr Opin Genet Dev 15: 116–124. pmid:15797194 To validate the PatS6-binding mode, we determined the binding affinities of PatS6 towards the wild-type HetR or mutants. PatS6 showed a K d of 12 nM towards the wild-type HetR, similar to the previous report of Feldmann et al. 19. Mutation of E253A totally abolished the PatS6-binding affinity, suggesting its indispensable role. Single mutation of E254A, D256A, D270A or D278A led to a dramatically lower binding affinity ( Supplementary Fig. 3), with a K d of 91, 427, 2252 or 1626 nM, respectively, whereas the double mutant D270A/D278A showed no detectable binding affinity. In fact, in vivo experiments of strains with a hetR allele coding for conservative substitutions at residues Glu253–Asp256 showed an altered percentage of heterocysts; moreover the E253D mutant strain had a drastically reduced sensitivity to PatS5 18.

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Distinct from the previously reported HTH motif 25, the DNA-binding motif of HetR is composed of three helices: the two canonical helices α4 and α5, in addition to an auxiliary helix α10 from the symmetric subunit. Moreover, both the flap and the hood domains adopt novel folds; thus HetR represents a novel transcription factor. The DNA-binding pattern of Anabaena HetR

Buikema WJ, Haselkorn R (2001) Expression of the Anabaena hetR gene from a copper-regulated promoter leads to heterocyst differentiation under repressing conditions. P Natl Acad Sci USA 98: 2729–2734. Wolk, C. P. Physiological basis of the pattern of vegetative growth of a blue-green alga. Proc. Natl. Acad. Sci. USA 57, 1246–51 (1967).By reducing the flow of cN from the exterior of the cell ( l n = 0) we find that a stable fixed point appears in the upper branch, a heterocyst state, while the vegetative state gets closer to the bifurcation region, thus becoming more susceptible to perturbations that can make the system reach the upper branch. In the absence of cN, the cyanobacterium would evolve from state A to state B in the lower branch until a perturbation pushes it to the upper branch, eventually becoming an heterocyst due to the field acting on that branch ( Fig. 5B and C). To get a closed system of equations, we shall investigate the relation between cN and 2-OG. Both are related by means of the GS/GOGAT cycle ( Fig. 2). Assuming the cycle is in equilibrium and reactions are grounded on the law of mass action, the following two conditions must be satisfied: Rectangular boxes represent genes ( ntcA, hetR and patS) while rounded boxes and circles represent transcription factors (NtcA, HetR and PatS) and smaller molecules (2-OG and cN) respectively. Normal-tipped and flat-tipped arrows stand for up-regulating and down-regulating processes respectively. Dashed lines stand for indirect or imperfectly understood interactions. The accumulation of 2-OG enhances the DNA-binding activity of NtcA, which in turn up-regulates the transcription of ntcA and hetR. HetR activates ntcA and hetR (composing the central NtcA-HetR autoregulatory loop), the inhibitor patS and other genes that lead to nitrogen fixation and the morphological changes involved in heterocyst differentiation. 2-OG and cN levels are linked through the GS/GOGAT cycle (see Fig. 2).

In the bistable region the system behaves as a switch that can be either OFF in a vegetative state (lower branch, with a small production of HetR and NtcA) or ON in a heterocyst state (upper branch, with a high production of HetR and NtcA). A sufficient large perturbation may result in the system crossing the manifold of the saddle and falling into the other stable branch of solutions. The distance between the saddle and the nodes determines the size of the perturbation needed to activate or inactivate the system.which constitutes the model for a cyanobacteria filament. To account for environment variability we add white noise, G i, *( t), of the same amplitude, ⟨ G i, *( t) G i, *( t ′)⟩ = ξδ( t − t ′), for all the components of the system. Based on these equations, we investigate the conditions that lead to a heterocyst pattern. It is easy to notice that they correspond to an activator-inhibitor system of cells coupled in a reaction-diffusion scheme [ 50]. This kind of system produces regular pattern formation [ 51– 53]. Turing (linear stability) analysis of equations (16) (see S2 text) provides insight on the periodicity of patterns. It is interesting to show that the minimum periodicity observed in such analysis is larger than 1, which means that a single bacteria is unable to differentiate.

Yoon Hs, Golden JW (2001) PatS and Products of Nitrogen Fixation Control Heterocyst Pattern PatS and Products of Nitrogen Fixation Control Heterocyst Pattern. J Bacteriol 183: 2605–2613. pmid:11274121Anabaena (also Nostoc) sp. strain PCC7120, hereafter Anabaena, is a cyanobacterium that fixes atmospheric N 2 in specialized cells called heterocysts. Heterocyst differentiation is regulated by a homodimeric transcription factor, HetR. HetR is expressed at a basal level in all cells but its expression increases in differentiating cells early after nitrogen deprivation. HetR is required for heterocyst development, and therefore nitrogen fixation and diazotrophic growth. Overexpression of HetR leads to multiple contiguous heterocysts (Mch phenotype). HetR binds in vitro to DNA fragments upstream of several genes upregulated in heterocysts, including hetZ, hetP, hepA, patS, pknE, and hetR itself. HetR binds an inverted repeat sequence upstream of a few of these genes; however, HetR binds to promoters that do not contain this sequence, such as the promoter regions for patS and pknE. Results Liang J, Scappino L, Haselkorn R: The patA gene product, which contains a region similar to CheY of Escherichia coli, controls heterocyst pattern formation in the cyanobacterium Anabaena 7120. Proc Natl Acad Sci U S A. 1992, 89 (12): 5655-5659. 10.1073/pnas.89.12.5655.