A Symbolic Topological View of Chromosome Replication

It is generally agreed that following initiation at a particular origin of replication, DNA synthesis occurs bidirectionally at two "growing forks" which diverge from each other on the contour of DNA(1). The leading strand synthesis is continuous and is performed by d DNA polymerase, and the lagging stand is replicated discontinously in a process involving an RNA primase, at least one additional DNA polymerase (a ) and perhaps more, RNase H which degrades the RNA primers, and a DNA ligase which knits the short (2000 bp) sections of discontinuously synthesized DNA together. The polymerase complexes are assisted in propagating along the DNA duplex with the assistance of a helicase which unwinds the DNA duplex, and by "sliding clamps" which enhances the processivity of each DNA polymerization process (2). As the original DNA duplex is fed into the "growing fork" where the DNA is unwound, each single strand is replicated by the polymerase complex. In this manuscript, each such polymerase complex including helicase, sliding clamps and the captured DNA is referred to as a replication fork, and such forks are the basis of our topological thoughts about DNA replication.

A second firmly established fact is the existence of multiple replication origins within the eukaryotic chromosome (1). At each origin, two replication forks (oppositely oriented, as shown in Fig. 1A) are generated at a definite site of replication initiation which is believed to be defined by the binding of an "origin binding complex", ORC. During replication, the two forks propagate away from each other on the DNA contour, creating two nascent DNA duplexes.

In this work, we make no assumptions relating to the detailed structure or linkage of protein components which define the replication forks; nor is any particular structure implied or required for our discussion beyond the assumption of the topological integrity of the template strands of DNA comprising the initial DNA duplex prior to replication. There has been very valuable consideration to the issues of DNA topology relating to replication by others. (3) Often the issues which have been addressed have related to the degree of superhelicity or torsional tension created by the replication process, both in the parental template duplex between converging replication forks which initiated on adjacent origins of replication, and in the daughter duplex regions, which are also dependent upon the details of the local model involked. We are concerned here with the issue of nascent duplex entanglement which might be created either by the active rotation of the fork every 10 basepairs, associated with the active rotation of both diverging replication forks during propagation (3), or with the relative rotation of diverging pairs of replication forks, simply from diffusion. Fig. 1 provides a graphic example of how the relative independent rotation of diverging replication forks will result in entanglement of nascent duplex DNA. Note that the issue of entanglement is distinct from the issue of DNA superhelicity or torsional tension, either in the parental template duplex or in the nascent (newly synthesized) daughter duplexes.

In order to avoid the potential entanglement of the nascent duplexes between diverging replication forks, we hypothesize that the forks are physically connected and therefore unable to rotate with respect to each other. If replication is due to independent dimer forks, there would be inevitable entanglement of the two nascent DNA duplexes during replication, and segregation would require a special mechanism independent of the replication process itself to eliminate the entanglements. The most elementary possible entanglement is cartooned in Fig. 1.

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Fig.1. The simplest case of strand entanglement. (A) Adjacent replication forks with no entanglement. (B) The diverging replication forks diffuse rotationally by one full turn with respect to each other, causing a simple entanglement . (C) In mitosis, the entangled nacsent daughter DNA duplexes cannot separate without a pass-through.

The figure is a cartoon in which the blue oval structure denotes that portion of the replication fork proteins interacting with the leading strand. In contrast, the red circular structure is intended to represent that portion of the replication fork proteins interacting with the lagging strand of the fork. The physical attachment between these two groups of fork proteins may be entirely through DNA or may involve protein-protein interactions between the two classes of proteins in the replication fork. The issue of "fork rotation" and therefore `nascent duplex entanglement' is independent of the local fork structure, but depends entirely on the assumption of the retention of the topological integrity of the parental template strands during replication. A class I topoisomerase acting either on the parental duplex of on the nascent daughter duplexes does not alter the topological integrity to which we speak. On the other hand, there could be a local structure recognition (4) associated with a class II topoisomerase activity which could alleviate entanglement associated with the active rotation of the replication forks during fork propagation. We present our example in the interest of simplicity and as an example. A more complex mechanism could be envisioned and has been suggested in which a disentanglement mechanism would violate the assumption of the topological integrity of the parental strands.

The idea of physical attachment of diverging growing forks is not original to these authors. In a classic paper, Sundin and Varshavski (5) make the following statement; "If, during replication, the two growing forks were to rotate with respect to each other, entanglement of daughter chromatin strands could occur. To avoid this difficulty, we suggest that both replication forks are tied together and uniquely orientated within a binary complex". In addition, Wessel, Schweizer, and Stahl (6) have reported experimental evidence for such an attachement in SV40 bidirectional replication. This work cannot prove the correctness of such an hypothesis. What we do here is address the mechanistic consequences of making such an hypothesis. There are well established enzymatic activities in all living cells which under appropriate conditions can pass one DNA duplex through another (Class II topoisomerase activities) (7). But in a complex knot which is not localized to a small volume is space such that the acting enzyme has a basis for structure recognition, the random passage of one strand through another is just as likely to increase the knotting as to decrease it (8) . Disentanglement requires a global knowledge of the topology of the knot, but enzyme systems must sense and act within a very local volume, limited by the short range of intermolecular forces. A solution to this Gordian disentanglement problem has been suggested (4), in which the enzyme, attaching to two separate binding sites on the duplex DNA might track (migrate along the contour), collecting catenations into local recognizable structure. Such a mechanism is most easily applied to circular DNA's. It might be applied between diverging growing forks, but again, most transparently if they are physically attached to each other, at least at the end of the fork migration. Again, we emphasize that our work is not intended to establish which of several alternatives might be correct. It is intending to demonstrate the topological consequences of the connected growing fork hypothesis.

The connected growing fork model lends itself to representation in a kind of molecular symbolism to which one can apply a mathematical operator calculus, the so-called "lambda" calculus (9). We give the name symbiologic to this new way of thinking. The basic concepts of the lambda calculus are already embodied in advanced computer languages, and this has inspired a concrete algorithm that generates a detailed symbolic scenario for the tetrameric replication of any given symbolic chromosome. At present, we use the symbolic scenario as data for a simple movie of chromosome reproduction. The movie show a possible side effect of the connected replication fork model; namely, chromosome linear condensation during replication. In the future, it would be possible to include detailed DNA properties (composition, elasticity, histone and other attachments, and topology) in such symbiologic calculations and their visual representations.

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Fig. 2. Bidirectional connected groving fork replication. (A) A duplex of DNA with an incomplete replication complex. (B) The completion of the complex including a arrival of an initiation signal generates two internal back-to-back forks, incapable of rotation with respect to each other. (C) A later stage of replication, with two nascent loops of duplex DNA extruding from opposite sides of the replication fork complex.

The site of origin or the position of ORC binding is the first part of the DNA to be replicated and extruded. It has been proposed that newly synthesized origin regions are prevented from another initiation of replication at the same site a second time in the cell cycle because another signal for initiation does not occur. Nascent loops from the same replication fork complex or from neighboring fork complexes might become long enough to twine perhaps even after chromatin reassmbly, but an entanglement cannot occur as long as the pair forks experience no relative internal rotation. This permits immaculate segregation.

The eukaryotic genome contains linear chromosomes with origins of replication spaced by approximately 100 kilobase pairs (1), each 100 kilobase pair region being referred to as a replicon. During S-phase these various linearly associated origins of replication initiate at programmed non-simultaneous times and in programmed orders by virtue of specific signals.

Fig. 3 is a representation of the replication of a very small chromosome. It begins in an extended state with origin dimers in place (Fig. 3A). In Fig. 3B, the replication fork complexes form and the DNA fork pairs are created, inevitably back-to-back. As replication proceeds in Fig. 3C and Fig. 3D, the nascent loops grow and the parental duplex sections between the converging replication fork complexes shrink until finally all that is left is an extended row of replication fork complexes (Fig. 3E), each with two long but unknotted loops of nascent DNA attached to their sides. The length contraction seen in this figure is realistic, and might contribute to chromosome condensation prior to mitosis. It is known that other factor are important for chromosome condensation both from experiment and from the fact that metaphase chromosome chromatids are much smaller in diameter then the linear lengths of the newly replicated DNA loops, indicating that other mechanisms of condensation must be essential in the final formation of the metaphase chromosome.

In the final frame, the replication complexes split up again in an exact reverse of their formation step, with half the protein content assigned to each double strand. At this point mitosis can begin, inherently free of any entanglement.

A detail of the fully collided configuration in Fig. 3E needs discussion. A small length of DNA in direct contact with the collided fork complexes has not completed replication when collision first occurs, and it must be completed by a special replication mechanism inherent to these collided structures. This "end game" in DNA replication has been studied in some detail using SV40 as a model, and if left unperturbed it is efficient at avoiding entanglement (5). This process is reported to require a Class II topoisomerase activity.

(click here to see the full size figure)

Fig. 3. Connecting growing fork replication of a chromosome, with immaculate mitosis. (A) complex assembling, (B) forking, (C,D) replication, (E) collision, (F) mitosis.

Mitosis must be followed by extension of the chromosome so that its information may be accessed during G1-phase. It is possible that the replication fork complexes dissociate from the DNA, allowing it to expand into the volume it occupies in the cell nucleus by diffusion. The new complexes would then be targeted for reassmbly by the origin recognition complexes, ORC (10). As an alternative, in the movie we show chromosome extension to be associated with the return of some component of the now disconnected replication proteins still on the DNA and migrating by being driven along the contour of the DNA in a process which reverses their paths during replication, until they find origins of replication or ORC's that define them. Questions about the extension phase suggest need for more experimental work identifying DNA polymerase subunit pairing rules and the actual locations of origin sites, but none of these involve any Gordian problems-in-principle.

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This page was last modified on 11/20/2007.

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