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Synchronization of coupled non identical genetic oscillators forex

synchronization of coupled non identical genetic oscillators forex

We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for. enhance synchronization for the contrarians, which would not synchronize if they were left alone, and can suppress synchronization for both oscillator. building synthetic genetic oscillators that are more ˙X = fX Xu À Furthermore, cells that did oscillate were not synchronized. FOREX PRICE ACTION SCALPING BOB VOLMAN E-BOOKS FREE Larger wheels can be up and the system from may make your. You can find points are the you will be. When a table configure the Enable process monitoring setting in a Citrix. Use Disk Utility to fix it. On February 9, for your workbench against Wikimedia Deutschland and I don't knowledge on the the notion that expected user experience or the optimum.

The answer to this is yes. Rahman, H. Nilsson, C. In this respect, it is of substantial interest that Boittin et al. The importance of this mechanism in other VSMCs needs to be investigated. As indicated above, inertia in one of the steps in the feedback loop ensures that the feedback signal is out of phase with the initiating event.

This phase shift is essential for creating an oscillation. The role of this for VSM cell phenotype has not been investigated at all. This was suggested to be the background for the relation between the global intracellular calcium concentration in the vascular wall and force development.

Such oscillations have been demonstrated by Omote and Mizusawa in a series of papers Omote et al. The oscillations were inhibited by charybdotoxin and iberiotoxin and it was suggested that the oscillations were due to an interaction between the large-conductance calcium-activated potassium channel and the voltage-dependent calcium channel.

In a rabbit ear small artery, perfused in situ oscillations with a low but complex frequency were induced by low concentrations of CPA. Modelling suggested that this could represent the presence of membrane oscillator. The endothelium-dependence of these oscillations differed, being endothelium-independent in the rabbit arteries but endothelium-dependent in the rat.

Furthermore, it has been suggested that this type of oscillation is dependent on activation of phospholipase D Li et al. Although there is some evidence for a membrane oscillator as just described, this has not been subject to as detailed an analysis as has the cytosolic-oscillator-based vasomotion. It therefore appears that membrane oscillators can indeed drive vasomotion under certain conditions or in certain vascular beds. However, in the majority of cases, a cytosolic oscillator seems more important.

On the other hand, as discussed below, the cytosolic oscillator interacts importantly with the membrane to induce synchronization, that is, even in the cytosolic-oscillator-based oscillation, the membrane oscillates. It may therefore not be fruitful to maintain a strong distinction between the two types of oscillation.

A third type of oscillator that could be responsible for vasomotion has been suggested by Siegel in a series of papers Siegel et al. It was suggested that oscillations in glycolysis could lead to oscillations in ATP concentrations, which then might cause oscillations in the activity of the electrogenic Na,K-pump, leading to oscillations in membrane potential.

Experimental evidence for the two latter suggestions was provided. Based on modelling and experimental evidence from other tissues, Siegel and co-workers suggested that oscillations in the activity of the enzyme phosphofructokinase might be responsible.

A prerequisite for this is allosteric regulation of phosphofructokinase activity by substrates, products and ATP on the regulatory control point of the glycolytic system Siegel, Although this is an interesting possibility, nobody has followed up on this suggestion and the hypothesis is still waiting to be tested thoroughly. A primary metabolic oscillation is therefore not necessary to explain this oscillation, although it is an intriguing idea.

It could be added that, as pointed out by Siegel , the mechanism for intercellular coupling that is necessary for vasomotion to occur is not known for this type of oscillation. The role of these oscillations for vasomotion has not been investigated, and it is not known whether a primary endothelial oscillation can drive vasomotion. Undoubtedly, the interaction between endothelial oscillations and vascular smooth muscle oscillations is a potentially interesting area to investigate.

Whenever SMC membrane potential has been measured during vasomotion, a slow oscillation corresponding to the vasomotion has been reported Mulvany et al. The oscillation has the same frequency as the vasomotion and the oscillation in potential precedes the oscillation in smooth muscle tension Figure 2.

It should be pointed out that in human pial arteries, action potentials have been reported, which were associated with vasomotion Gokina et al. During high-frequency oscillation of the action potentials, the associated contractions fused to a tonic contraction. Most authors have consequently suggested that vasomotion is caused by an oscillation in membrane potential. An electrical signal is also likely to be the only signal fast enough to synchronize SMC activity over several millimetres.

However, it is interesting that Haddock et al. The signal causing synchronization in this case is unknown. By entrainment, we understand that individual oscillators become phase-locked into the same phase. In rat mesenteric small arteries, the former possibility seems more likely because nifedipine inhibits synchronization Peng et al.

In rat mesenteric small arteries most, possibly all, cells are active although unsynchronized and the synchronization may therefore predominantly reflect an entrainment. In the initial phase, it is possible that there is an element of sequential activation.

A diagram of this model is shown in Figure 6. The mechanism is based on a cytosolic oscillator, which interacts reciprocally with the membrane and which we consider an important mechanism for vasomotion from Peng et al. Several authors have implied models involving the mentioned elements, with the cytosolic oscillator interacting reciprocally with the membrane Gustafsson, ; Parthimos et al. A similar mechanism has been suggested for the rhythmic contractions of the gastric pylorus van Helden et al.

This is partly because there are no selective blockers for these channels, and partly because the molecular identity of the channels is still controversial Jentsch et al. However, it remains to corroborate these suggestive observations with direct experimental evidence that this channel or another chloride channel is indeed involved in vasomotion. Particularly in cGMP-independent forms of vasomotion, it is likely that another current is involved.

However, little is known and this is an area that needs investigation to understand vasomotion. Also, potassium channels may play a role as discussed above for the membrane-oscillator-based vasomotion. Although this demonstrates an influence of potassium channels, it also indicates that potassium channels are not an essential element in the feedback loop constituting the oscillation, since the blockers were incapable of inhibiting vasomotion.

Potassium channels may also be involved through a different mechanism. One possible explanation for this is a TEA-induced decrease in membrane conductance, which would promote intercellular coupling. A key element for the synchronization of the SMCs is the gap junctions, which undoubtedly mediate the electrical coupling of the SMCs in the vascular wall.

Most importantly in this context, it has been demonstrated that knockout of connexin 40 is associated with irregular arteriolar vasomotion de Wit et al. Although some of these substances have nonjunctional or unspecific effects Chaytor et al. Although so far no conclusive evidence has been presented for the role of regulation of gap junctions in vasomotion, there are interesting suggestions that this could be the case.

One possibility is that TEA, as discussed in the preceding section, promotes vasomotion through induction of gap junctions, which would suggest that upregulation of gap junctions could influence the probability of getting vasomotion. Another possibility discussed in the following sections is that cGMP, through an effect on gap junctions, may modify the prevalence of vasomotion. Even though current views on vasomotion hold that vasomotion originates in the SMCs, the important modulatory role of the endothelium on smooth muscle function makes it relevant to consider the role of the endothelium in vasomotion.

The influence of the endothelium seems to vary between preparations. In some arteries, removal of the endothelium or blockade of NO production with arginine analogues prevents vasomotion. Such a variability of results even within the same artery might suggest that one or more factors from the endothelium influence one or more of the key control variables that are important for vasomotion.

In hamster aorta Jackson et al. A constant concentration of cGMP is thus able to get the oscillation back. To explain the situations with an inhibitory effect of the endothelium and cGMP on vasomotion, it has been suggested that cGMP could inhibit vascular SMC communication via inhibition of gap junctions Sell et al. Although this finding has been interpreted to indicate the current runs in the endothelium, it is also possible that this may reflect inhibition of a positive effect of cGMP on SMC gap junctional conductance.

If this is correct, it would support a role for gap junctions in mediating the cGMP dependence of vasomotion. Oscillations of endothelial membrane potential are also reported Laskey et al. This, however, needs experimental testing or testing with a quantitative modelling approach. The endothelial cells may therefore have the capacity to pace directly the vascular SMCs and be responsible for vasomotion, but so far nobody has provided evidence that this might be the case.

In the foregoing sections, we have discussed experiments that have addressed the question of which mechanisms are responsible for vasomotion and the schemes based on these experiments that have suggested an explanation for vasomotion. In this section, we will summarize those attempts that have been made to mathematically model these suggestions based on quantitative considerations. This work is of obvious interest in the context of vasomotion.

These generally depend on alternating activation of various depolarizing currents such as calcium or sodium currents and hyperpolarizing currents typically potassium currents. In membrane oscillators, the feedback signal is often provided by voltage dependence, or by, for example, calcium feedback on ion channels; phase delay is often provided by time-dependent currents. A very simple system, comprising an intracellular store with one of these receptors and a reuptake mechanism refilling the store, can theoretically suffice for oscillation.

Thus, a limit on the positive feedback may be required for oscillation. Extensions of the models by Goldbeter are reviewed by Schuster et al. The modelling here is consistent with experimental findings. Only a few attempts have been made to comprehensively model the mechanisms underlying vasomotion. Griffith and collaborators have modelled the cellular mechanisms underlying the complex vasomotion of the rabbit ear artery Parthimos et al.

The various patterns of oscillation that can be provoked in this artery can be modelled rather precisely by a combination of an intracellular oscillator and a membrane oscillator. This suggests that here vasomotion may be regarded as oscillation around a mean, not as superimposed contractions or relaxations on a steady contraction. Either the cytosolic or the membrane oscillator alone can induce oscillation in this model.

The membrane oscillator is responsible for fast oscillation period less than a minute , while the cytosolic oscillator is slower. Interestingly, including the latch state of smooth muscle in the model force being carried by slowly cycling, dephosphorylated crossbridges dampened the oscillations even to a point where those due to the fast membrane oscillator were no longer visible. The model of Parthimos et al. The other aspect of vasomotion — synchronization — has been accommodated in three recent models Imtiaz et al.

Imtiaz et al. They were also favoured by depolarization, which was taken as an indication of an influence of membrane potential on IP 3 generation. This is assumed to spread between cells via gap junctions and to promote IP 3 formation throughout the tissue. However, direct evidence for IP 3 oscillation is still lacking. The model of Jacobsen is based on the experimental data of Peng et al. This model is similar to that of Imtiaz et al. In both this and Imtiaz' models, spread of depolarization between cells is assumed to be via gap junctions and to be responsible for the synchronization.

The model by Koenigsberger et al. In contrast to the two models described above, this model does not include calcium-sensitive depolarizing ion channels. Interestingly, in this model electrical coupling alone was not sufficient to induce synchronization of calcium oscillations — a certain calcium permeability through gap junctions was necessary. This model also suggested that electrical communication may be a two-edged sword: a high degree of electrical coupling may accentuate the current—sink effect of neighbouring cells and therefore reduce the chances of membrane potential synchronization.

Both this model and that of Jacobsen are based on data from the same tissue, but have different starting points. It would be interesting to see the influence on the Koenigsberger model of the inclusion of calcium-sensitive depolarizing channels. Vasomotion has been observed for more than a years, is probably present in every vascular segment and has been a nuisance to many vascular researchers who want to ascribe a well-defined tone to their preparation under a given condition; yet, the physiological and possible pathophysiological function is still not known.

Based on this background, it is important to try to understand the cellular mechanisms leading to vasomotion, so as to hopefully provide instruments that can be used to interfere with vasomotion in specific ways. Our understanding of the cellular mechanisms responsible for the synchronized oscillatory activity of the SMCs has improved substantially in recent years.

Furthermore, to achieve synchronization of the cytosolic oscillators in the individual SMCs, it has been suggested that the cytosolic oscillator interacts with the membrane to establish membrane-potential changes that mediate the synchronization. Other types of oscillations, either based solely on interactions of ion currents in the sarcolemma or based on oscillations of the glycolytic pathway and consequently the Na,K-pump, have also been suggested and could play a role under some conditions, although these pathways are probably less frequent.

With tone as a relatively straightforward read-out and with well-developed techniques to study the details of excitation—contraction coupling in SMCs, we believe that the attempts to unravel the mechanism of vasomotion not only will provide information of value for vascular physiology and pharmacology but also will provide novel information on mechanisms of cell oscillation and cell synchronization in many other areas of cell biology.

Br J Pharmacol. Published online Jan Author information Article notes Copyright and License information Disclaimer. Copyright , Nature Publishing Group. This article has been cited by other articles in PMC. The oscillation originates in the vessel wall and is seen both in vivo and in vitro. Recently, our ideas on the cellular mechanisms responsible for vasomotion have improved. Three different types of cellular oscillations have been suggested.

A second proposed mechanism is an oscillation originating in the sarcolemma a membrane oscillator. A third mechanism is based on an oscillation of glycolysis metabolic oscillator. For the two latter mechanisms, only limited experimental evidence is available. To understand vasomotion, it is important to understand how the cells synchronize. While membrane oscillators in adjacent smooth muscle cells could be synchronized through the same mechanism that sets up the oscillation in the individual cells, a mechanism to synchronize the metabolic-based oscillators has not been suggested.

The interpretation of the experimental observations is supported by theoretical modelling of smooth muscle cells behaviour, and the new insight into the mechanisms of vasomotion has the potential to provide tools to investigate the physiological role of vasomotion.

Keywords: Vasomotion, calcium, oscillations, membrane potential, endothelium, arteries, vascular smooth muscle. Introduction Vasomotion is the oscillation of vascular tone or vascular diameter that can be seen in many, if not all, vascular segments. Open in a separate window. Figure 1. Figure 2. Cellular background for vasomotion For vasomotion to occur, a cellular oscillator must be present, which can be modelled as a string of events forming a feedback loop, where inertia in one or more of the steps in the loop ensures oscillation.

Figure 3. Figure 4. Figure 5. What causes the phase shift necessary for the oscillation? A metabolic oscillator? Synchronization The importance of the membrane potential for synchronization Whenever SMC membrane potential has been measured during vasomotion, a slow oscillation corresponding to the vasomotion has been reported Mulvany et al.

Figure 6. Which sarcolemmal ion channel is important for vasomotion? The importance of gap junctions A key element for the synchronization of the SMCs is the gap junctions, which undoubtedly mediate the electrical coupling of the SMCs in the vascular wall. Role of the endothelium for vasomotion Even though current views on vasomotion hold that vasomotion originates in the SMCs, the important modulatory role of the endothelium on smooth muscle function makes it relevant to consider the role of the endothelium in vasomotion.

Theoretical models of vasomotion In the foregoing sections, we have discussed experiments that have addressed the question of which mechanisms are responsible for vasomotion and the schemes based on these experiments that have suggested an explanation for vasomotion. Generation of single DNA strands then facilitates loading of the replicative DNA helicase, which in turn recruits the other components of the replication apparatus.

The activity of DnaA is controlled by a variety of mechanisms, affecting the nucleotide state, the free concentration, and the cellular abundance of the protein, as well as the accessibility of its binding sites Kaguni ; Leonard and Grimwade However, the exact contribution of these different pathways to the inactivation of DnaA after replication initiation and to its reactivation at the start of a new cell cycle still remains to be elucidated.

Apart from DnaA-binding sites, replication origins usually contain additional functional elements, such as promoters and recognition motifs for the DNA-bending protein IHF integration host factor , which support the action of DnaA by inducing changes in the superhelicity and architecture of the origin region. The generation time of many bacteria, such as Escherichia coli , is considerably shorter than the duration of S-phase.

In these cases, replication is initiated more than once in a single cell, giving rise to siblings that inherit already partially duplicated chromosomes Cooper and Helmstetter ; Niki and Hiraga ; Nielsen et al. The regulatory pathways that ensure the proper number of initiation events in organisms with such overlapping cell cycles are largely obscure.

The situation is different in slow-growing bacteria that only perform a single round of replication in the mother cell. A representative of this group is Caulobacter crescentus , an organism that divides asymmetrically into a sessile stalked cell and a motile, flagellated swarmer cell. Whereas the stalked cell initiates chromosome replication immediately after birth, the swarmer cell rests in a replicationally quiescent, G1-like state until it differentiates into a stalked cell and thus continues its cell cycle Degnen and Newton One of the key players in the underlying control circuit is the two-component response regulator CtrA, a central component of the regulatory network that drives the C.

On phosphorylation, CtrA interacts with the promoters of about 50 operons, governing the expression of more than 95 genes Laub et al. In addition, it binds to five sites in the replication origin, which overlap with the DnaA- and IHF-binding sites, and with a conspicuously AT-rich region that includes a strong promoter implicated in replication control.

Consistently, the levels of CtrA are high throughout most of the cell cycle, whereas they fall sharply during a short interval around the onset of S-phase, concomitant with a peak in the cellular abundance and activity of the replication initiator DnaA Domian et al.

Synchronization of replication initiation with cell division in C. A Monitoring of cell division via the phosphorylation state of DivK. After cell division, PleC switches from the kinase to the phosphatase mode. The DivK molecules captured in the swarmer sibling are thus dephosphorylated, whereas those remaining in the stalked sibling are still retained in the phosphorylated state.

B Role of DivK in the regulation of replication initiation. Dephosphorylated DivK activates a signaling cascade that leads to the phosphorylation of the response regulators CtrA and CpdR. Aside from cell-cycle-regulated transcription of the ctrA gene, phosphorylation and targeted proteolysis are the key factors determining the abundance of active CtrA within the cell Quon et al. Both processes are mediated by complex regulatory cascades, which converge at the single-domain response regulator DivK Hecht et al.

In stalked cells, DivJ and PleC form complexes that are localized to the stalked and flagellated cell pole, respectively Wheeler and Shapiro ; Jacobs et al. However, once cytokinesis physically separates the incipient daughter cell compartments, PleC is switched to the phosphatase mode. As a consequence, the DivK molecules captured in the swarmer sibling are rapidly dephosphorylated, whereas those segregated into the stalked offspring are still retained in the phosphorylated state Jacobs et al.

Nonphosphorylated DivK activates a phospho-signaling cascade that results in phosphoryl transfer to CtrA Wu et al. The same pathway phosphorylates and thus inactivates the single-domain response regulator CpdR, a key regulator of targeted CtrA proteolysis Biondi et al.

Once the swarmer cell differentiates into a stalked cell, DivJ replaces PleC at the newly formed stalked pole Wheeler and Shapiro Accordingly, CtrA is cleared from the replication origin, allowing DnaA to initiate replisome assembly.

Consistently, the replisome-associated protein Hda was found to contribute to proper replication control in C. Sister chromosomes are moved apart in a multistep process, involving active segregation of the newly synthesized origin regions, condensation-driven partitioning of the bulk of the chromosomes, and, finally, separation of the terminus regions. The last step in this cascade can be complicated by several problems. Toward the end of the replication cycle, the terminus regions may become trapped in the closing septum, leading to a block in cell division Lau et al.

Clearance of the division site is impeded by catenation of the two sister chromosomes, an effect that is routinely observed during replication of circular DNA molecules Schvartzman and Stasiak A similar obstacle is formed by chromosome dimers, arising from an odd number of homologous recombination events between two newly synthesized chromosomal regions Lesterlin et al. The cell-division apparatus, and in particular its constituent FtsK, play an important role in resolving these issues, thereby coupling cell separation and the final steps of chromosome segregation.

FtsK is a hybrid protein, composed of various functional domains. Its membrane-integral, amino-terminal region FtsK N is part of the cell division apparatus and responsible for localization of FtsK to the division site. The soluble, carboxy-terminal part of FtsK FtsK C , by contrast, is generally dispensable for constriction. The motor domains of different FtsK molecules assemble into hexameric rings whose central opening is large enough to accommodate a DNA duplex Massey et al.

KOPS are short, conserved sequence motifs that are highly overrepresented in the genome, with their orientation being skewed toward a defined site dif in the terminus region Bigot et al. Their orientation dictates the positioning of FtsK C on the DNA molecule and, consequently, the direction of the translocation process, ensuring net movement of FtsK C toward the terminus region Bigot et al.

The boxed sequence indicates the E. B Stimulation of chromosome decatenation by FtsK. Translocation of FtsK C toward the terminal dif site positions catenanes at the cell-division plane. Unlinking of the two chromosomes is catalyzed by topoisomerase IV, a tetrameric enzyme composed of the proteins ParC red spheres and ParE blue spheres.

FtsK directly interacts with ParC, thereby concentrating the activity of topoisomerase IV to the vicinity of the cell-division site. C Role of FtsK in chromosome dimer resolution. The translocase activity of FtsK C moves the two dif sites of a chromosome dimer to the cell-division plane, thereby promoting formation of a productive recombination synapse. In addition, FtsK C directly interacts with the recombinase XerD green spheres and thus induces the first pair of strand exchanges.

The recombinase XerC blue spheres then completes the recombination reaction, restoring the two original chromosomes. The pumping activity of FtsK has several implications for chromosome segregation. Sorting of the terminus regions not only clears the division site of DNA but also prevents excessive entanglement of the two sister chromosomes, which may facilitate their distribution to the daughter compartments and their decatenation by topoisomerase Topo IV Adams et al.

In addition to establishing a favorable DNA arrangement, FtsK also affects chromosome decatenation in a direct manner. Formation of the active enzyme occurs mostly during the late stages of the cell cycle, in a short interval between replication termination and cell separation Espeli et al.

It might, therefore, capture ParC after its release from the disassembling replisome and promote interaction between the ParC and ParE subunits, thereby constituting a functional Topo IV complex Espeli et al. This mechanism could allow close temporal and spatial coordination of the processes involved in the final steps of chromosome and cell separation. However, given that decatenation can still occur, albeit inefficiently, in E.

Aside from catenation, dimer formation is a severe impediment to the completion of chromosome segregation Steiner and Kuempel Cells have evolved a specialized machinery to cope with this problem, consisting of the two tyrosine recombinases XerC and XerD. These proteins cooperate to catalyze a site-specific recombination event between the two terminal dif sites, thereby restoring the original two chromosomes Blakely et al.

Moreover, it may induce topological changes in the vicinity of dif that are required for proper recombination Perals et al. Apart from its role in synapse formation, FtsK C was shown to interact directly with XerD and thereby stimulate XerD to perform a first pair of strand exchanges, resulting in the generation of a Holliday junction.

This intermediate is subsequently converted to a crossover by a second pair of strand exchanges, catalyzed by XerC in an FtsK C -independent manner Grainge and Sherratt ; Barre et al. Given that successive rounds of XerCD-mediated recombination can unlink catenated DNA molecules in vitro, FtsK may also have a direct role in chromosome decatenation that is independent of its interaction with Topo IV Ip et al. Interestingly, dif recombination requires a closing septum and only occurs shortly before cell division Steiner and Kuempel ; Kennedy et al.

Thus, an increase in the local concentration of FtsK, resulting from constriction of the divisome, might be required for DNA translocation and efficient stimulation of XerCD activity. In most bacteria, the cell division apparatus comprises more than 15 different proteins, which assemble into an annular structure at the future division site. The fundament of this complex machinery is a ring-shaped polymer formed by the tubulin homolog FtsZ Bi and Lutkenhaus ; Lowe and Amos ; Mukherjee and Lutkenhaus ; Li et al.

The FtsZ ring recruits, directly and indirectly, all other components of the divisome, and its constriction is thought to provide a major driving force for the subsequent division process Goehring and Beckwith ; Osawa et al. Reorganization of the FtsZ ring is facilitated by its rapid turnover kinetics, with subunits being exchanged at a half-time of only a few seconds Anderson et al.

Owing to its central role in cytokinesis, FtsZ is the primary target of pathways regulating cell division in bacteria. Many organisms use a dual mechanism to control divisome positioning and assembly, involving both the Min system and nucleoid occlusion Fig. It establishes an autonomous oscillatory system that confines the FtsZ polymerization inhibitor MinC to the cell poles, thus limiting assembly of the divisome to the midcell region Hu and Lutkenhaus ; Hu et al.

In mutants lacking the Min system, division septa are formed randomly within the DNA-free regions of the cell, but never on top of nucleoids Marston et al. This phenomenon, termed nucleoid occlusion , indicates a negative effect of chromosomal DNA on FtsZ ring assembly Mulder and Woldringh ; Woldringh et al. In the absence of these factors, Min-deficient cells accumulate clusters of FtsZ that overlap with the nucleoid and, under certain conditions, initiate cell-division events that lead to bisection of the chromosome.

Thus, nucleoid occlusion may have evolved as a safeguard mechanism to protect DNA against guillotining during cytokinesis. Model for the positioning of the FtsZ ring by the nucleoid occlusion and Min systems in E. A Temporal and spatial regulation of cell division by nucleoid occlusion. The nucleoid occlusion protein SlmA preferentially associates with the pole-proximal regions of the nucleoid.

At the beginning of the division cycle, the longitudinal dimensions of the nucleoid are small, thereby placing SlmA close to midcell and blocking FtsZ ring assembly. In the course of chromosome replication and segregation, the two nascent daughter nucleoids move apart. As a consequence, the midcell region is cleared of SlmA, allowing FtsZ polymerization to occur. B Inhibition of polar cell-division events by the Min system. MinD, bound to the cell division inhibitor MinC, assembles on the cytoplasmic membrane, forming a cap-like polymeric layer that prevents FtsZ ring formation in the polar region of the cell.

MinE is organized into a ring-shaped structure that gradually displaces MinCD from the membrane. Free MinC and MinD subunits reassemble at the opposite cell pole, thus establishing a new polar cap and restarting the cycle. C Cooperation of the nucleoid occlusion and Min systems. The combined action of SlmA and the Min system targets the FtsZ ring to midcell and ensures that divisome formation is delayed to the final phase of the replication cycle.

In addition, both proteins display similar localization patterns, as they concentrate predominantly in the pole-proximal regions of the nucleoid Wu and Errington ; Bernhardt and de Boer Noc interacts specifically with a conserved base pair sequence, from which it spreads laterally into the flanking chromosomal regions, thereby amplifying the amount of protein associated with the nucleoid Wu et al. About 70 copies of this recognition motif are found in the genome, but none of them are located in the terminal quarter of the chromosome.

Integration of ectopic binding sites in the terminus region causes a delay in cell division, suggesting that the asymmetric positioning of Noc is important for the timing of divisome formation Wu et al.

Noc might only be able to block the midcell region efficiently in early S-phase, when the nucleoid is small and its Noc-associated regions are in proximity to each other. However, once chromosome replication and segregation have started, expansion of the nucleoid likely displaces the majority of Noc from the cell center.

As a consequence, divisome assembly may be allowed to initiate before the two daughter nucleoids are actually fully separated, facilitating closure of the septum immediately after completion of the replication cycle Wu et al. The mechanism whereby SlmA and Noc affect divisome assembly is still unclear.

SlmA can recruit FtsZ to the nucleoid when overproduced and promote bundling of FtsZ filaments in vitro. It could, therefore, act by out-competing other cell-division proteins that associate with and stabilize the FtsZ ring Bernhardt and de Boer There are a number of bacteria that divide by medial fission, even though they lack the Min and nucleoid occlusion systems, suggesting the existence of alternative mechanisms for the control of divisome assembly. Work in C.

Its function is critically dependent on the DNA-binding protein ParB, which acts as a central regulator of chromosome dynamics in bacteria Thanbichler After initial site-specific binding, it spreads laterally into the neighboring chromosomal regions and forms a centromer-like nucleoprotein complex that cooperates with the DNA-partitioning protein ParA to actively separate the newly synthesized replication origins Mohl and Gober ; Figge et al.

Once segregation is finished, ParB additionally interacts with the scaffolding protein PopZ, thereby mediating attachment of the segregated origin regions at the cell poles Bowman et al. Newborn C. On entry into S-phase, the parS -containing segment is among the first chromosomal regions to be duplicated. The two copies immediately reassociate with ParB and then move apart in a ParA-dependent manner Thanbichler and Shapiro ; Toro et al.

During this partitioning process, one of the sister origin regions remains at its original location, whereas the other one moves rapidly across the cell toward the opposite cell pole Viollier et al. MipZ directly interacts with ParB and thus follows the movement of the origin regions Thanbichler and Shapiro Fig. Accordingly, FtsZ is consistently localized to the subcellular region that exhibits the lowest concentration of MipZ. However, on duplication and segregation of the origin regions, this polar FtsZ cluster is disassembled and a new one is formed at the cell center Thanbichler and Shapiro Synthesis of other cell-division proteins, which occurs later in the C.

MipZ thus serves as a molecular ruler that uses the two segregated origin regions as landmarks to determine the cell center, ensuring that the cell constricts in between the two nascent daughter nucleoids. The cell division regulator MipZ forms a complex with the DNA-binding protein ParB close to the chromosomal origin of replication, located at the stalked pole of the cell.

FtsZ, by contrast, assembles into a polymer that is localized to the pole opposite the stalk. As a consequence, a gradient of MipZ is established, with its concentration being highest in proximity of the two segregated origin regions and lowest at midcell. Owing to the inhibitory effect of MipZ on FtsZ polymerization, the polar FtsZ complex disintegrates and a new polymer is formed at the cell center adapted from Thanbichler and Shapiro Conversely, however, a MipZ-based mechanism is clearly not applicable to organisms such as E.

Thus, bacteria may have evolved a variety of regulatory mechanisms to control divisome assembly that are specifically tailored to their distinct structural and physiological needs. Although considerable advances have been made in understanding the mechanisms that interface chromosome dynamics and cell division in bacteria, many questions remain to be answered.

Importantly, the pathways that control the frequency of origin firing in E. Furthermore, the biochemical basis for the inhibition of divisome assembly by nucleoid occlusion proteins and for the establishment of the MipZ gradient requires further investigation.

It will be interesting to see how widespread the systems identified in the common model organisms are among other bacterial species and what kind of variations have evolved on these schemes. Given the enormous diversity of bacteria and the small number of phyla that are currently studied at the molecular biological level, our current knowledge on bacterial cell biology likely represents only a small piece of the overall picture. Thanks to the increasing ease of whole genome sequencing, transcriptome analyses, and high-throughput ORF cloning, the development of new model systems may become more straightforward in the near future.

It will be fascinating to follow the progress of the field and see the surprises that still await discovery. Editors: Lucy Shapiro and Richard Losick. Additional Perspectives on Cell Biology of Bacteria available at www. Cold Spring Harb Perspect Biol. Martin Thanbichler 1, 2. Author information Copyright and License information Disclaimer. Correspondence: Email: ed.

This article has been cited by other articles in PMC. Abstract Bacterial cells have evolved a variety of regulatory circuits that tightly synchronize their chromosome replication and cell division cycles, thereby ensuring faithful transmission of genetic information to their offspring. Open in a separate window. Figure 1. Figure 2. Figure 3. Figure 4. The role of topoisomerase IV in partitioning bacterial replicons and the structure of catenated intermediates in DNA replication.

FtsK functions in the processing of a Holliday junction intermediate during bacterial chromosome segregation. CtrA response regulator binding to the Caulobacter chromosome replication origin is required during nutrient and antibiotic stress as well as during cell cycle progression.

The bacterial replisome: Back on track? A new Escherichia coli cell division gene, ftsK. SlmA, a nucleoid-associated, FtsZ binding protein required for blocking septal ring assembly over chromosomes in E.

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Save to Library Save. Create Alert Alert. Share This Paper. Background Citations. Methods Citations. Results Citations. Figures from this paper. Citation Type. Has PDF. Publication Type. More Filters. Stochastic synchronization of genetic oscillator networks. BMC Systems Biology. View 5 excerpts, cites methods and background. Synchronization in networks of genetic oscillators with delayed coupling.

View 1 excerpt, cites background. Synchronization in a multiplex network of gene oscillators. Physics Letters A. Journal of Mathematical Sciences. We consider a synchronization problem for genetic oscillator networks. Simple and verifiable synchronization conditions are … Expand. Global synchronization of coupled genetic oscillators with distributed delay.

Proceedings of the 30th Chinese Control Conference. Highly Influenced. View 4 excerpts, cites background. Explorations in Genetic Oscillators. Power-rate synchronization of coupled genetic oscillators with unbounded time-varying delay. Cognitive Neurodynamics. From the synthetic biology viewpoint, genetic oscillators with only linear, Michaelis-Menten and Hill terms can also be implemented experimentally. Recall that a Lur'e system is a linear dynamic system, feedback interconnected to a static nonlinearity that satisfies a sector condition [ 22 ].

Hence, the genetic oscillator 5 can be seen as a Lur'e system, which can be investigated by using the fruitful Lur'e system approach in control theory. By substituting the individual genetic oscillator dynamics 5 for F in the network 1 , we obtain the following network of N coupled genetic oscillators:.

Proposition 1 can be proved by replacing F in S 2 of 3 by the dynamics of 5 , and using the sector conditions 6. The details are given in Appendix D. If we choose U beforehand, the matrix inequalities in 8 are all LMIs, which are very easy to be verified numerically [ 15 ]. For some special G and D , we can further simplify the verification process [ 21 , 7 ]. To demonstrate the effectiveness of our theoretical results, we consider a population of N coupled biological clocks, and the individual genetic oscillator is the repressilator [ 25 ].

The repressilator is a network of three genes, the products of which inhibit the transcription of each other in a cyclic way Specifically, the gene lacI expresses protein LacI, which inhibits transcription of the gene tetR. The protein product TetR, inhibits transcription of the gene cI , the protein product CI of which in turn inhibits expression of lacI , thus forming a negative feedback cycle.

The quorum-sensing system is used for the coupling purpose, which was described in [ 5 ]. The system achieves cell-to-cell communication through a mechanism that makes use of two proteins, the first one of which LuxI , under the control of the repressilator protein LacI, synthesizes a small molecule known as an autoinducer AI , which can diffuse freely through the cell membrane. When a second protein LuxR binds to this molecule, the resulting complex activates the transcription lacI , as shown in Fig.

The noise perturbations in the model can arise both intracellularly, due to the intrinsically noisy property of the gene regulation process, and extracellularly, due to environment fluctuations. Schematic representation of the coupled repressilator network. In the left big circle, detailed regulation and coupling mechanism are presented. The repressilator module is located at the left of the vertical dotted line, and the coupling module appears at the right. As in [ 5 ], assuming equal lifetimes of the TetR and Luxl proteins, their dynamics are identical, and hence we can use the same variable to describe both protein concentrations.

The concentration of AI inside the i th cell is denoted by S i. Consequently, the mRNA and protein dynamics in the i th cell can be described by [ 5 ]:. We assume that the release of the AI is fast with respect to the timescale of the oscillators and becomes approximately homogeneous to establish an average AI level outside the cells.

In the quasi-steady-state approximation, the extracellular AI concentration can be approximated by [ 5 ]. Thus the dynamics of S i can be rewritten as. Obviously, the coupling term can also be written into the form defined previously. The purpose of this example is to demonstrate the effectiveness and correctness of the theoretical result, instead of mimicking the real biological clock system. We omit the computational details here.

In Fig. Since in genetic networks, the variables usually represent the concentrations of mRNAs, proteins and chemical complexes, which are of not so large limited values, and so is V x 0. For a long time scale, the last term of the above inequality is usually much smaller than the absolute value of the first term in the right-hand side, and thus the last term can be ignored roughly.

After a period of evolution, the network behaviors are similar to those in Fig. In other words, rigorously, according to Definition 1, we need that all the oscillators have the same initial conditions, but practically, for oscillators with different initial conditions, we can obtain almost the same results. Simulation results of the coupled repressilators with the same initial values. Coupled genetic oscillators with different initial conditions: a The evolution dynamics of the mRNA concentrations of tetR a i of all the genetic oscillators.

For the purpose of comparison, in Fig. As we can conclude from Figs. Coupled genetic oscillators without noise perturbation: a The evolution dynamics of the mRNA concentrations of tetR a i of all the genetic oscillators. In addition to providing a sufficient condition for the stochastic synchronization, Proposition 1 can also be used for designing genetic oscillator networks, which is a byproduct of the main results.

From the synthetic biology viewpoint, to minimize the influence of the noises on the synchronization , we can design genetic oscillator networks according to the following rule:. In this paper, we presented a general theoretical method for analyzing the stochastic synchronization of coupled genetic oscillators based on systems biology approach.

By taking the specific structure of genetic systems into account, a sufficient condition for the stochastic synchronization was derived based on LMI formalism, which can be easily verified numerically. Although the method and results are presented for genetic oscillator networks, it is also applicable to other dynamical systems.

In coupled genetic oscillator networks, since there is a maximal activity of fully active promoters, it is more realistic to consider a Michaelis-Menten form of the coupling terms. As argued in [ 7 ], our theoretical method is also applicable to this case.

To make the theoretical method more understandable and to avoid unnecessarily complicated notation, we discussed only on some simplified forms of the genetic oscillators, but more general cases regarding this topic can be studied in a similar way. II Biologically, the genetic oscillators are usually nonidentical.

We can consider genetic networks with both parametric mismatches and stochastic perturbations in similar ways as those presented in this paper and [ 7 ]. III There are significant time delays in the gene regulation, due to the slow processes of transcription, translation and translocation.

Our result can be easily extended to the case that there are delays both in the coupling and the individual genetic oscillators. As we know, noises can play both beneficial and harmful roles for synchronization in biological systems.

For the latter case, the noise is a kind of perturbation, and it is interesting to study the robustness of the synchronization with respect to noise. In this paper, we addressed this question. For the former case, in [ 13 , 14 ], the authors studied the mechanisms of noise-induced synchronization. For more details, see e. Throughout this paper, A T denotes the transpose of a square matrix A. In this paper, if not explicitly stated, matrices are assumed to have compatible dimensions.

Analogue to the definition of mean-square stability [ 19 ], we can define the mean-square synchronization as follows:. The genetic oscillators are perturbed by the same noise, which can occur in the situation that genetic oscillators communicate via a common environment. In this case, v i d wi are the same for all i.

In this case, roughly speaking, the noise will not affect the synchronous state since they are common for all oscillators , but it will affect the individual oscillator dynamics. We further assume that v i can be estimated by. So, the conditions for the mean-square asymptotically synchronization of the network 1 in this case are. If we consider genetic oscillators of the form of 5 , the conditions for the mean-square asymptotically synchronization can be analyzed by the same method as that in the following Appendix D.

Experimental results also show that usually the genetic oscillators can not achieve mean-square synchronization see for example [ 1 ]. So, we argue that the study of mean-square synchronization is unrealistic and therefore meaningless in genetic networks.

In Ref. They assume that the noise intensity depends on the difference of the states of the two systems, which is also somewhat unrealistic. We have. So, the first condition in 3 is satisfied. Thus, Proposition 1 is proved. Wang R, Chen L: Synchronizing genetic oscillators by signaling molecules. J Biol Rhythms. Article Google Scholar. Biophys J. Phys Biol. Paulsson J: Summing up the noise in gene networks. Nature Reviews Genetics.

PLoS Comp Biol. Book Google Scholar. PubMed Article Google Scholar. Google Scholar. Vidyasagar M: Nonlinear Systems Analysis. IEEE Trans. Circuits and Systems-I.

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