DNA-Membrane Interactions Can Localize Bacterial Cell Center

AVINOAM RABINOVITCH1, ARIEH ZARITSKY2 AND MARIO FEINGOLD1

Departments of Physics1 and Life Sciences2

Ben-Gurion University of the Negev

POB 653, Be’er-Sheva 84105, Israel

Abstract: - The surprising precision in symmetry between daughters ensuing of bacterial cell division requires a mechanism that determines the exact cell length mid-point. No current model seems satisfactory to us, including the one relying on MinCDE oscillations. The so-called “Tug Of War” concept of Koch & Holtje [1] requires the bacterium to find its midpoint by discerning stress levels, but the mechanism they propose is far from complete. We validate this concept [2] using the interactions between the Cytoplasmic Membrane (CM) and the bacterial nucleoid. The nucleoid is diffuse in actively growing and dividing cells, occupying a large portion of the cytoplasm and is connected to the CM, while it is compacted in the center of resting cells. This transformation is explained by a change in the balance between two opposing forces that determine the dynamic nucleoid structure, i.e., compaction and expansion. Coupled transcription, translation and insertion (“transertion”) of nascent CM proteins are considered to expand the nucleoid [3]. We suggest that the counter-stress exerted on the CM by the DNA in actively growing cells, in addition to the turgor caused by osmotic pressure, is applied through the transertion process, and demonstrate that the strength of this interaction varies along cell length with a minimum at the mid-point. The rate of transition at mid-cell from a minimum to zero during nucleoid separation, being the maximal spatial rate, could actually serve as the signal to start the division process through FtsZ ring assembly, the first molecular sign of the division process. This mechanism provides a physical foundation to the “nucleoid occlusion” model [4]. In a reciprocal action, the strings’ pull on the nucleoid stabilizes it in the axial portion of the cell and imparts to it a cylindrical symmetry.

Key-Words: - Nucleoid Occlusion, Tug Of War, Mid-Cell Determination, Membrane Stress

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1. Introduction

Division of E. coli usually takes place at the midpoint of the long axis of the cell. The accuracy of finding the midpoint is extremely high with a measured deviation of between 1% [5] to 4% [6]. This precision is much better than other cell-cycle events such as cell size, age at birth, initiation and termination of chromosome replication, rate of elongation etc. (e.g. [7]) There are at the moment two basic models to explain the mechanism of this precision, one being the effect of the MinCDE proteins and the other is the so called nucleoid occlusion.

In the first model [8-10] the presence of the MinC protein at a certain location prohibits the attachment of the FtsZ tubulin-homologue to this site, and since the FtsZ is the substance responsible for the beginning of division by the creation of the “Z-ring”, no division will occur there. The actual interaction between the MinCDE complex and the membrane of the cell is quite complicated. Thus, according to Huang et al [10] for example, the MinD, which enhances MinC adsorption to the membrane can appear in two forms: MinD-ATP and MinD-ADP. The former attaches to the membrane. MinE from the cytoplasm attaches to a MinD complex on the membrane and causes ATP hydrolysis, transforming the MinD into the second form and thus releasing it from the membrane. This molecule is converted back to MinD-ATP in the cytoplasm and so on. By mathematical modelling of such processes, using differential diffusion rates of the species, it can be shown that MinC becomes periodically attached to the cell poles and therefore no Z-ring would be created there, and division would rather occur at the midpoint.

The nucleoid occlusion model [3, 4] refers to an apparent emission of an “inhibitory signal” by the nucleoid which prevents division in locations where it is present. Thus only after the replication termination, a possible division site between the two daughter nucleoids appears. Although very tempting, this nucleoid occlusion model lacks an exact definition of the inhibitory signal which precludes division.

A unified Min-nucleoid occlusion model (promoted e.g. in [2]) has appeared in [11], in which it is the combined effect of the two processes which actually directs division location. Thus the occlusion leaves only two locations as possible sites for division, the poles and the mid section while the MinC concentration at the poles terminates the division possibility there, allowing it to occur only at midpoint.

A somewhat different interesting mechanism for center location [1] is based on the so-called “Tug Of War” (TOW) concept. This process is analogous to two teams pulling at two sides of a rope leading to a stress maximum at the midpoint. The bacterium would find its midpoint if it could discern stress levels. During growth, the peptidoglycan pulls the cytoplasmic membrane (CM) causing an uneven stress level in the CM. The mechanism proposed by Koch & Holtje [1] relies on a delicate imbalance between the growth rates of the peptidoglycan and the CM. Since information about these rates is incomplete and other unverified assumptions are necessary for their model, it is yet to be tested.

We have recently shown [2] that the TOW concept can be validated by the use of membrane-chromosome interactions. Moreover, our model can provide a physical foundation to the nucleoid occlusion model by providing a possible candidate of the “inhibitory signal” there.

2. The Model

2.1 Cell membrane structure

The bacterium can be modeled as an open cylinder with two hemispherical caps at its ends and constant internal pressure Pl that is generated by osmosis. Such a structure is well known in engineering as a “pressure vessel”. In the thin wall of such a structure of radius R and thickness t, two stress forces operate (e.g., [12]), namely, hoop, sh = PR/t, and longitudinal, sl = PR/2t. These stresses are the same throughout the whole cylindrical part of cell wall, and identical in the two half spheres (s1 = s2 = PR/2t). Therefore, the internal pressure alone cannot be used to locate the center of the bacterial cell.

2.2 Nucleoid-membrane interaction

The nucleoid is assumed to be of a cylindrical shape inside the cell (Fig. 1). During the life cycle, between two successive divisions, the nucleoid is tethered to the CM with strings of DNA/mRNA/m-proteins. These strings result from the transcription/translation of genes coding for membrane (or excreted) proteins (m-proteins) and their coupled insertion to the CM by the so-called “transertion” process [3, 13, 14]. The strings are assumed to be distributed evenly only along the cylindrical parts of the membrane and the nucleoid (see Fig. 1), in line with pole inertness [15, 16]. The DNA exerts on the CM a constant force f per string. The longitudinal stress (in addition to sl) due to this interaction can easily be obtained as follows.

Fig. 1. The modifed TOW model of a bacillary bacterium. The membrane is composed of two layers, CM (inner) and peptidoglycan (outer). The straight lines connecting the nucleoid to the CM represent the DNA/mRNA/m-proteins strings. Strings in the first quadrant only are displayed; those not shown that are present in the other quadrants preserve the symmetry of the cell. (From [2].)

Denoting the areas of the membrane and the nucleoid as S and s, respectively, and the related string densities as N and n, we have

n/N = S/s = Rb/ra , (1)

where (2b+2R), 2R and 2a, 2r are the dimensions of the cell and the nucleoid, respectively (Fig. 1). The angle q(x) between the string and the membrane is

q (x) = arctg[(R - r) / (x - y)] , ( 2)

where x varies between 0 and b, and y between 0 and a, such that the largest value of q is arctg[(R-r)/ (b-a)]. In the plane AA’ (Fig. 1), the deviation Dsl from the constant longitudinal stress (sl = PR/2t) is obtained from the balance between the forces of the strings (right hand side of Eq. 3 below) and the internal reaction forces of the membrane (Dsl 2pRt). Assuming that the strings are homogeneously and continuously distributed along the cylindrical part of the CM,

, (3)

where t is the thickness of the CM. In Eq. (3),

cosq = a x / (p2 + a2 x2) . (4)

Here a = 1 – a/b, p = R – r and use is made of the relation y = (a/b) x. The integral in Eq. (3) is straightforward, leading to

Ds l = N f [(p2 + a2 b2)1/2

– (p2 + a2 x2)1/2] / (a t) 0 x b . (5)

Fig. 2 displays the change in longitudinal stress Ds l as a function of the distance from the center x. As can be seen, there is a minimum of stress at x = 0 stemming from the TOW cooperative influence of all the strings. It is thus conceivable that the proposed TOW model represents the mechanism for locating the midpoint of bacterial cells.

Fig.2. The change of longitudinal stress in the CM due to DNA strings according to Eq. (5) with the following parameters: R = 0.5 mm, r = 0.25 mm, a = 1 mm, b = 2 mm, t = 20 nm, N = 10, f = 1 pN. (From [2].)

3. DISCUSSION

During nucleoid separation, the strings’ directions change such that the “midpoint” passes from a minimum to a zero of tensional stress (Fig. 3). Meanwhile, two new minima are developed which serve as “midpoints” for the daughter cells. The rate of transition at midcell from a minimum to zero, being the maximal spatial rate, could actually serve as the signal to start the division process through FtsZ ring assembly.

Fig. 3. A schematic transition from a minimum tensile stress to zero at the midpoint of a cell during nucleoid separation. (A) Before separation, the midpoint is under minimum stress. (B) In the initial stage of nucleoid separation, stress at midpoint is around zero. (C) After separation, midpoint stress vanishes. (From [2].)

In wide cells (dilated in their midst) (Fig. 4, left): the nucleoid is “attached” randomly to one side of the membrane by short strings and “detaches” itself from the other, thus loosing its cylindrical symmetry. Under such circumstances, the ability of an E. coli to place FtsZ ring with a subsequent constriction in mid-cell and perpendicular to its length axis is limited, often resulting in tilted planes of division and branched cells [18-20]. Under a brief mecillinam treatment, such multi-nucleoid cells are transformed into spheroids (Fig. 4, right); their nucleoids are localized adjacent to the membrane, and seem to exclude the assembling FtsZ rings (Fig. 5).

Our model could of course be further refined and quantified; the qualitative result should however remain valid, namely, that the TOW brought about by the DNA-to-CM transertion interaction causes unevenness in stress. The gradients thus formed, particularly the rate of transition between minimum and zero predicted at cell’s midpoint during nucleoid separation, may be translated to a biochemical signal that activates FtsZ ring formation, subsequently nucleating the division process [21]. The translation may utilize proteins that appear (at least in E. coli) to detect decreased cell turgor or membrane tension directly by a mechanism similar to that regulating expression of porin in response to extracellular osmolarity [22].

Fig. 4. Fluorescence microscopy of DAPI-stained nucleoids in thymine-limited cells (left) and after brief treatment with mecillinam (right) (From [18]).

Fig. 5. DAPI-stained nucleoids (false red colored) superimposed on GFP-tagged FtsZ (false green colored). (From [20].)

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