It can be of evolutionary advantage for a cell to grow (and reproduce) as rapidly as possible in favourable conditions. Such growth involves RNA polymerases transcribing genes to make mRNA, and ribosomes translating mRNA to make proteins. There is a finite minimum distance between two RNA polymerases transcribing a gene [57] (and between two ribosomes translating mRNA [58]). This means that in the absence of the DNA replication part of the cell cycle, the density of RNA polymerases per unit DNA eventually reaches a maximum (i.e., when the polymerases cannot get any closer). From then on, growth can no longer be exponential. A selective pressure therefore exists in favour of cells that replicate their DNA before it becomes limiting. The solution would be transcriptional sensing which has been proposed for bacteria [59] but which is equally applicable to eukaryotes. The signal leading to DNA replication—indeed, the actual trigger itself—could take one or more diverse forms including multivalent ions, enzymes and metabolites (see Figure 1). The creation (and perhaps the nature of the signal(s) itself) might involve coupled transcription-translation (transertion) of a proteolipid hyperstructure [59], coupled transcription-translation-assembly (transembly) of a ribosomal hyperstructure with a particular topology [27,60], a giant elastic or electromagnetic oscillation [61], changes in water structure and ion condensation [28], and changes related to supercoiling [27]. A related solution—but which would not involve DNA directly—would be via metabolic sensing in which the dynamics of cytoskeletal hyperstructures (and hence cell cycle progress) would depend on the activity of metabolic enzymes such that, for example, an enzyme that is catalyzing its reaction has a greater affinity for the replication and/or cytoskeletal hyperstructures and helps to stabilize/destabilize them [62]. A good example of metabolic sensing occurs in the control over cell size in Bacillus subtilis where assembly of the tubulin-like FtsZ into an effective division structure is inhibited by interaction between FtsZ and the glucosyltransferase UgtP; this interaction is greater when UDP-glucose levels are high, as during growth in rich medium, leading to bigger cells [63]. In studying the relationship between metabolism and signaling in silico, we have found that a judicious choice of different sets of rate constants, equilibrium constants and initial conditions produces a variety of kinetics of metabolite concentrations and enzyme associations that could serve as signals [64].

Even in conditions that are generally favorable for growth, there will be times when the non-equilibrium hyperstructures can either only grow linearly or just maintain themselves or shrink, whilst the equilibrium hyperstructures continue to accumulate. As the cell grows in the run-up to the key cell cycle event, new material (macromolecules, molecules and inorganic ions) comes from the non-equilibrium hyperstructures feeding both themselves and the equilibrium hyperstructures. An example of this material may be certain ribosomal subunits which can participate both in the non-equilibrium ribosomal hyperstructure and, conceivably, in equilibrium hyperstructures that also contain DNA [24,65]; note that inactive ribosomes can exist as clusters [66,67]. Another example may be EF-Tu [22,23] which can be active in translation but perhaps—evidence is needed—inactive as a cytoskeletal filament. In one version of the Dualism hypothesis, this progressive addition of material is accompanied by other changes such as a redistribution of water structures and changes in the topologies and sizes of both the equilibrium and non-equilibrium hyperstructures (note that resonant frequencies of oscillations are another possibility). This redistribution of material and water structures eventually results in the charge parameters of the equilibrium and non-equilibrium hyperstructures reaching a threshold that leads to ion decondensation and condensation, respectively [28,68]. This threshold is dependent on the topology and composition of the hyperstructures, such as the alignment of positive or negative charges, rather than, say, the average level of charge. The changes that occur at this threshold time the cell cycle.

DnaA, a protein found in many bacteria, is commonly believed to be responsible for the initiation of chromosome replication in bacteria [49,69,70,71]. In the Beginning, however, DnaA was not present and a more fundamental mechanism operated. DnaA would therefore have evolved as a veneer on this mechanism. If so, it may prove possible to interpret DnaA action in the framework of Dualism. This we now attempt.

DnaA binds with different affinities to sites in the origin of replication, oriC, and elsewhere on the chromosome [72,73]. The synergistic binding to oriC sites results in the unwinding of an AT-rich region and the opening of the double helix that constitutes the first step in initiation [74]. DnaA binds ATP and ADP, can form oligomers, and interacts with lipids. But what controls DnaA? One regulatory mechanism affects the availability of DnaA: substantial proportion of DnaA binds to the datA locus [53].

Another regulatory mechanism for controlling DnaA depends on the direct activation of DnaA [75] which results from it binding and hydrolysing ATP (only the ATP-DnaA form is active in initiation [76]). Sufficient activation for initiation requires the reactivation of existing ADP-DnaA since de novo synthesis of DnaA is not enough [77]. This activation can result from the binding of DnaA to either the membrane [78] or DnaA-reactivating sequences, DARS1 and DARS2, on the chromosome [52].

Another factor to take into account in the control over DnaA is that fluorescent DnaA-GFP hybrids bind not only to oriC and datA to give foci or clusters but also elsewhere in the chromosome to give a helix [79,80,81]. It should be noted here and elsewhere that fusions with fluorescent probes such as GFP can lead to artifactual localization of the protein under study [82,83]. It might be argued that such fusions may sometimes increase slightly the degree of a self-association that occurs naturally. It has been shown recently that MreB, rather than forming a helix on its own, forms a proteolipid domain with fluid phospholipids [154] and these patches move independently along a helical path [84,85]. It may turn out that the distribution of DnaA and MreB are both controlled by helical lipid domains created by transertion [86].

How can these characteristics of DnaA be accommodated by the Dualism hypothesis in the context of intensity sensing and quantity sensing (see Table 1 for a summary)?

The membrane is strongly implicated in the behaviour of DnaA. Acidic phospholipids in a fluid phase dissociate ADP or ATP from DnaA so as to convert, in the presence of ATP, inactive ADP-DnaA to the active ATP-DnaA and allow DNA replication in vitro [51,94,95]; in this, cardiolipin is particularly effective whilst phosphatidylethanolamine and other lipids are either ineffective or inhibitory [96,97,98]. Membrane domains have long been proposed to regulate the bacterial cell cycle [99,100,101] and there is now considerable evidence for domains enriched in cardiolipin at the poles and between segregating chromosomes [2,90,102,103]. There is also complementary evidence for the existence of domains of high microviscosity, resulting from transertion, around the chromosomes [104,105] and even for an increase during the cell cycle in the level of cardiolipin and other lipids [104,105,106,107]. In the context of Dualism, cardiolipin-rich, fluid domains might correspond to equilibrium structures such that their accumulation would correspond to quantity sensing. More specifically, during the build-up to initiation, transertion hyperstructures around the chromosome become increasingly active (i.e., with more transcription, more translation and more insertion of nascent proteins into membrane) generating and releasing cardiolipin to accumulate elsewhere until a threshold for reactivation of DnaA is attained. This threshold quantity would be the one at which there is sufficient membrane to allow successful completion of a new round of the cell cycle. Note too that this threshold might also depend on domains of cardiolipin acting as a proton trap to sense the energy status of the cell [108].

The binding of DnaA to its sites plays a central role in its activity. There are around 350 DnaA proteins per origin (but up to a total of 2500 DnaA in a fast growing cell where there are also many origins) [109] and these proteins can bind with differing affinities to around 300 DnaA boxes in the chromosome [110]. These boxes are found in regions that include oriC and datA, which are able to bind 45 and 370 DnaA proteins with apparent dissociation constants of 8.6 × 10⁻⁹ M and 1.7 × 10⁻⁸ M respectively [111]. DnaA binding to datA is consistent with a titration role in initiation because such binding appears to delay initiation or prevent hyper-initiation [81,112,113].

In this titration role, datA does not fit readily into the class of equilibrium structures that are subject to quantity sensing (if it were to perform quantity sensing, we might expect, for example, the number of copies of datA to accumulate—which they do not—and, in accumulating, progressively bind only ADP-DnaA to give an increased ratio of free ATP-DnaA:ADP-DnaA); unless, of course, datA is physically part of an equilibrium origin hyperstructure—certainly, it does seem close to oriC [71,81]. In this case, the equilibrium material that accumulates (and that is sensed by the origin hyperstructure in its equilibrium state) might include some of the Nucleoid-Associated Proteins or NAPs, which are central to the organization, replication, segregation, repair and expression of bacterial chromosomes, and which are essential if a new cell cycle is to be completed successfully. The NAPs include HU, H-NS, Fis, Integration Host Factor (IHF), StpA and Dps, each of which binds to several hundred specific sites throughout the chromosomes and which together bind non-specifically to the chromosome at an average of one NAP per hundred base pairs [114,115,116,117,118]. Several NAPs, including IHF, HU and Dps, associate with DnaA [91,92]. IHF, for example, binds to many sites on the chromosome [16], and, in bending DNA, often acts together with other NAPs and transcription factors; for example, IHF interacts with DnaA and Fis to initiate replication via IHF binding to a site in oriC to stimulate unwinding [119,120]. This makes IHF a good candidate for playing a role in quantity sensing. It is therefore significant that IHF binds to datA and that this binding increases the number of DnaA proteins that bind datA [93]. It will be apparent to the reader at this stage that the DNA-binding protein best-placed for the lead role in a quantity sensing hyperstructure—perhaps as the first amongst equals—is DnaA itself.

Instead of datA belonging to the class of quantity sensing, equilibrium hyperstructures, could it belong to the class of intensity sensing, non-equilibrium hyperstructures? Here, one is looking for evidence, for example, that the superhelicity of the datA region increases during the build-up to initiation and that this releases DnaA. We know of no direct evidence for this (although DnaA binding to DNA is affected by superhelicity, see below). It is, of course, conceivable that a datA-IHF-DnaA hyperstructure is involved in intensity sensing. Such a role could be related to the proximity to oriC of the genes encoding subunits of ATP synthase which themselves are likely to create an ATP synthase transertion hyperstructure with a size and topology that should change with continued growth (and also to the distribution of gyrase sites as discussed in [27]); in the case in which spiral lipid domains result from transertion, it is significant that disruption of the domains of MreB plus fluid phospholipids affects the activity of LacY and the F₁F₀ ATP synthase [154].

DARS1 and DARS2 [52], in the chromosome are directly responsible for part of the conversion of ADP-DnaA into ATP-DnaA needed for initiation. DARS1 (located between bioD and uvrB) and DARS2 (located between ygpD and mutH) contain three similarly organised DnaA-binding sites and, in the case of assembly of DnaA proteins into homomultimers on DARS1, the resultant interactions between them reduce the affinity of DnaA for ADP. Since the reactivation of DnaA could be observed in vitro with a fragment DARS1, supercoiling is not needed. This excludes one way in which DARSs could form part of an intensity sensing, non-equilibrium hyperstructure. There may, however, be something else related to a quantity sensing, equilibrium hyperstructure. To follow the reasoning, a reminder about ion condensation may be useful here.

The condensation of positive ions such as potassium, magnesium, calcium and polyamines onto negatively charged linear polymers (such as DNA, RNA and certain protein filaments) and onto anionic membrane domains leads to these counterions being delocalised and diffusing in the near region in intimate contact with the polymers and membranes [121,122,123]. Ion condensation onto linear polymers occurs when the dimensionless charge parameter, ξ, reaches a critical value where ξ = βe/(4πε₀εkT), β is the linear charge density (defined as β = z_pe/b with z_p the valence of the charges on the polymer, b the distance in nm between these fixed charges and e the elementary charge), ε₀ is the permittivity of vacuum, ε is the relative dielectric constant of the medium, k the Boltzmann constant and T the absolute temperature. In water at 25 °C, ξ = 0.71/b for monovalent fixed charges on the polymer. When ξ exceeds a critical value of 1/z, counterions of valence z condense onto the polymer. As counterions condense onto such polymers they lower the linear charge density. Counterions condense onto the polymer in the order of their valence, for example, first all the tetravalent ions condense (providing the charge parameter remains high enough), then the trivalent, then the divalent and finally the monovalent ions condense. The dielectric constant of water, on which the charge parameter depends, must vary with water structure, which remains an important area of uncertainty.

Ion condensation onto charged polymers, such as DNA or protein filaments, is related to temperature so that it might occur at 30 °C but not at 0 °C [7,8]. It may therefore be significant that a PCR-generated fragment containing DARS1 promoted dissociation in vitro of ADP-DnaA at 30 °C but not at 0 °C [52]; the binding of DnaA itself to DARS1 and DARS2 is not affected by these temperatures [52]. As mentioned above, such condensation is related to both the charge of the counterion and the density of charge along the polymer: at the critical charge parameter of the polymer, for example, all the quadrivalent ions such as ATP⁴⁻ would condense onto the polymer before the trivalent ones such as ADP³⁻; moreover, the linear structure of the polymer is important. It may therefore also be significant that ATP can recharge DARS-bound DnaA and that, for this to happen, several copies of DnaA must bind to the DARS [52]; this might be explained by the condensation of ATP⁴⁻ onto a DARS-bound DnaA structure. In the Dualism approach, it is speculated that quantity sensing may take the form of positively charged counterions condensing onto equilibrium hyperstructures until the threshold is attained at which counterions decondense from the origin region and the consequent repulsion of the phosphates leads to strand separation and initiation of replication [28,124,125]. If there is some substance to this speculation, it would not be surprising to see the same phenomenon recapitulated with the DARS in which they have evolved to become representative of ion condensation on quantity sensing, equilibrium structures. One might take it further and speculate that when the DARS cease to be equilibrium structures they cease to be able to reactivate DnaA. The speculation goes like this: DARS1 and DARS2 are located right next to genes that are expressed in response to DNA damage; if this were to result in a change in the conformation of the DARS (e.g., their becoming single-stranded), the critical charge parameter would be lowered, the condensation of ATP⁴⁻ might cease, ATP-DnaA levels drop and initiation be averted until the damaged DNA had been repaired.

To return to intensity sensing, consider again the distribution of DnaA. The protein, is distributed at the membrane either as foci that colocalise with the origin of replication, oriC [81], or as a helical spiral [80] or as both (but for B. subtilis see [79]). Such hyperstructures may well contain acidic phospholipids such as cardiolipin [126]. In the following, we reason in terms of a linear polymer of DnaA rather than a cluster (or even a higher order spiral of clusters) because the role we propose for ion condensation is easier to explore for a linear polymer than for a two dimensional domain. The helical form of DnaA may—or may not—interact with both the numerous sites of DnaA on the chromosome and the membrane [80]. (Note here that the spiral is seen in the nucleoid regions and, even if it can be seen in inter-nucleoid regions, these regions may still contain DNA). If we suppose that the DnaA in this spiral is binding to both its sites on the chromosome and to membrane, there is an interesting possibility that this DnaA hyperstructure is involved in intensity sensing. This is because this spiral hyperstructure might well be responsive to the changes in superhelicity that can accompany growth [27] such that at a threshold superhelicity the spiral would be destabilized (e.g., partly unwound) and DnaA released from these sites ready to recharged and to participate in initiation; there is indeed evidence that DnaA in some circumstances can be detached from DNA by increased superhelicity [87]. The DnaA spiral would therefore constitute an intensity sensor. In fact, it might be even better than this: the DnaA spiral hyperstructure might act as a quantity sensor by responding to an increase in cardiolipin. This is because acidic phospholipids (such as cardiolipin) in a fluid phase can detach DnaA from DNA [87] and hence an increase in cardiolipin might also be sensed by the DnaA spiral hyperstructure and transduced into the signal for the initiation of replication.

In the hyperstructure dynamics approach to the cell, the interactions between hyperstructures determine the phenotype. If, then, the spiral DnaA hyperstructure is indeed acting as a sensor, there should be interactions with other hyperstructures in addition to the origin hyperstructure. These might be expected to include the recently described H-NS hyperstructure, which regulates 5% of all E. coli genes and brings together its regulated operons into two or so clusters per chromosome [16]. Deletions of H-NS halved the time to replicate the chromosome and delayed initiation (insofar as there was a 50% increase in the mass at which initiation occurred) [127]. This would be consistent with the H-NS hyperstructure normally contributing to destabilizing the spiral DnaA hyperstructure. It should be noted that IHF, which does not form the same type of hyperstructure [16], has similar effects on the initiation mass and replication times [128].

In the quantity sensing vein, a sensible cell would ensure that it had enough nucleotides before embarking on a new cell cycle. Deoxyribonucleotides can be generated from the ribonucleotides that constitute RNA (and from the ATP and GTP that make up the energy currency of the cell) by the enzyme ribonucleotide reductase which is located in the replication hyperstructure [129,130,131].

The central carbon metabolism is the set of biochemical pathways responsible for the transport and oxidation of main carbon sources and, in E. coli, comprises the phosphotransferase system, glycolysis, gluconeogenesis, the pentose-monophosphate bypass with the Entner-Dudoroff pathway, Krebs cycle with the glyoxylate bypass and the respiratory chain. A relationship between the enzymes involved in CCM and the elongation step in DNA replication was first observed in B. subtilis [132]. This has now been extended to E. coli where it has been found that the temperature sensitivity of a strain containing the dnaB(ts) mutation could be suppressed by dysfunction of pgi or pta; dnaE486(ts) by dysfunction of tktB; dnaG(ts) by dysfunction of gpmA, pta or ackA; dnaN159(ts) by dysfunction of pta or ackA [133]. In particular, a full suppression of the thermosensitivity of dnaA46(ts) was observed in pta (encoding phosphate acetyltransferase) or ackA (encoding acetate kinase) double mutants. The acetyl phosphate level, which may be reduced in the Pta- and raised in the AckA⁻ contexts, is thought to act as a global signal in two-component systems linking metabolism with other systems [134]. Could this relationship between DnaA and Pta/AckA reflect intensity sensing? Suppose that free Pta/AckA were to bind DnaA. Then, if the formation of a FDS containing Pta and AckA (and perhaps other CCM enzymes too) were to depend on the intensity of functioning of these enzymes, the availability of ATP-DnaA might increase as the proportion of free Pta/AckA decreased. There is, however, no evidence for direct interaction between DnaA and CCM enzymes and other explanations are possible, as discussed by the authors [132,133].

Interactions between DnaA and ribosomal protein L2 (or truncated L2) have been shown to inhibit initiation in vitro and it has been proposed that DnaA may act as a sensor coordinating initiation with cell growth [92]. However, interpreting this result in the context of Dualism is not straightforward. It is not in line with a ribosomal hyperstructure acting as an intensity sensor because, the prediction is that if DNA is becoming limiting, redundant ribosomes may start to accumulate, become inactive and perhaps release L2 (we are trying here to see past layers of sophisticated feedback controls) which should stimulate initiation. The opposite occurs. It is not in line with quantity sensing either because, again, the prediction is that if ribosomes accumulate as equilibrium structures, release of L2 should again stimulate initiation. Although no hypothesis should be required to explain all the data, Dualism might offer an explanation: the signal that results from the combination of intensity and quantity sensing and that initiates replication also then prevents further initiation (along the lines of the Regulatory Inactivation of DnaA in which, after initiation, the Hda protein plus DNA promote the hydrolysis of active ATP-DnaA to inactive ADP-DnaA [71]). So the prediction from Dualism would then be that in the conversion of equilibrium to non-equilibrium structures—and the consequent redeployment of ribosomes—L2 is released to contribute the inhibition of further initiations. Finally, given that L2 also interacts with a heat shock protein, HtpG, it is conceivable that its inhibition of DnaA is simply a response to stress rather than part of regulation in an unperturbed cycle [135].

Many levels of classical regulatory systems have been glossed over in this and other sections. One of the most important is growth rate control. In the rest of this subsection, we suggest how growth rate control might fit into our scenario. Growth rate control is about the major changes that occur in Enterobacteriaceae as they adapt to environments that differ in their nutritional richness. The mechanisms involved in growth rate control might therefore be expected to be involved in the changes that we propose occur during the cell cycle. As a result of growth rate control, Enterobacteriaceae change as the rate of balanced growth increases: they become larger, have more replication forks per chromosome and have an increased RNA:mass ratio (primarily because more ribosomes are formed per unit mass) [34,56,136,137,138]. This increase in ribosomes affects the size and topology of the ribosomal hyperstructure [26,56]. One of the major players in control rate control is (p)ppGpp [139]. pppGpp and ppGpp are phosphorylated derivatives of GTP and GDP, respectively, obtained when a ribosome engaged in translation encounters an uncharged tRNA [139]. (p)ppGpp is an important link in coupling nutrient availability with many aspects of bacterial physiology including growth rate control, adaptation, secondary metabolism, survival, persistence, motility, biofilm formation, development, competence, virulence and initiation of DNA replication and cell division.

In section 5.4, the phenomenon of ion condensation was described in terms of positive counterions condensing onto negative linear polymers: it can be applied equally well to negative counterions condensing onto positive linear polymers. In E. coli, high levels of (p)ppGpp inhibit growth and change gene expression to reduce unnecessary activities in non-growing cells whilst excessively low levels result in cells responding inadequately to nutritional stress [139]. In the context of a role for ion condensation in life on the scales of equilibria, we might expect (p)ppGpp to decrease the average NE/E ratio. This might occur, for example, by (p)ppGpp condensing onto arrangements of positively charged residues within equilibrium hyperstructures so as to stabilise them and/or (p)ppGpp condensing onto similar arrangements of positive charges with non-equilibrium hyperstructures so as to increase the maximum density of usage that can be attained. RelA is the enzyme in E. coli that catalyses the reaction generating (p)ppGpp. It has been proposed that RelA can form oligomers in which it is inactive whilst starvation for amino acids results in the RelA oligomers dissociating to generate active enzymes [140]. It has also been proposed that RelA associated with the ribosome is inactive and that RelA dissociates from the ribosome to become active [141]. Both propositions are consistent with RelA activity depending on it being part of either a non-equilibrium or an equilibrium hyperstructure (that could respond to the condensation of ions including (p)ppGpp itself). Finally, (p)ppGpp inhibits replication by interacting with the DNA primase, DnaG, which is a key constituent of the replication hyperstructure [142] as well as being a product of the intriguing Macromolecular Synthesis operon which also contains rpoD and rpsU (encoding key proteins in transcription and translation) and which might therefore form a transcription-translation hyperstructure onto which (p)ppGpp condenses.

The existence of two types of extended structures with different time scales might be tested by pulse-labelling bacteria with nutrients enriched with isotopes such as ¹³C, ¹⁴C and ¹⁵N and imaging using Secondary Ion Mass Spectrometry [145,146].

If the phenomenon of condensation underlies the recharging of DnaA with ATP by the DARS, this might be demonstrated by combining an in vitro system of differentially, isotope-labeled ATP and ADP (or ATP-DnaA and ADP-DnaA) and fragments containing DARS, with the technique of Combing Imaging by Secondary Ion Mass Spectrometry, CIS [147]. This would require testing for the effects of varying temperature, ion concentrations and even water structures.

Runaway production of equilibrium hyperstructures should lead to initiation. Constructs might be used to induce the production of lipids and NAPs and the effects tested on the numbers of origins (e.g., using isotope-labeling and density gradient centrifugation or runout experiments, or indeed CIS). Such induction is also predicted to have effects on the distribution of DnaA (be it in spirals, patches, or spirals of patches).

Induction of formation of transertion or transembly hyperstructures [28], via expression systems based on IPTG, arabinose, T7, etc. should lead to initiation and could be tested as in 7.3. above. Alterations in the DnaA hyperstructure should result from changes in superhelicity and, as in quantity sensing, from changes in the composition of the membrane.

It would be interesting to investigate quantity sensing in this context by, for example, exploring the relationships between constitutive stable replication and the accumulation and distribution of phospholipids such as cardiolipin and of NAPs, where one might expect the genes neighboring the oriKs to be related to lipids and DNA-binding proteins. It has been reported that minichromosomes cannot be replicated in conditions of constitutive stable replication [143,148], which opens up the possibility that they might be replicated if they were to contain the genes and DNA-binding sites needed for intensity and quantity sensing hyperstructures.

In principle, hybrid automata such as HSIM [30] could simulate cells containing two sorts of molecule, black and red, that would assemble into non-equilibrium and equilibrium hyperstructures respectively. A third, blue, molecule or ion with an affinity for both types would then be responsible for the dialogue between the two types of hyperstructure; the numbers of this ion are proportional to the volume of the cell; the ion has an affinity for both hyperstructures. Movement of blue ions from the black non-equilibrium hyperstructures to the red equilibrium hyperstructures might then be achieved if the blue ions were to sense (via changes in affinities) the intensity of activity of the black hyperstructures and the quantity of the red hyperstructures. A fundamental question that might then be addressed is whether, in this competitive system, there are relationships between the parameters—and values of the parameters—that can generate a clear, precise signal.