Tyson J J, Chen K C, Lederman M, Bates R C
Department of Biology, Virginia Polytechnic Institute and State University, Blacksburg 24061.
J Theor Biol. 1990 May 22;144(2):155-69. doi: 10.1016/s0022-5193(05)80316-9.
All linear DNA molecules face special problems in replicating their 5' ends, as DNA polymerases add nucleotides only to pre-existing strands with free 3'-OH groups. Parvoviruses, a group of small animal viruses with a linear single-stranded DNA genome, cope with this problem by having palindromic terminal sequences that can fold back on themselves to form hairpin structures essential in priming DNA replication. The 3' terminal sequence that initiates replication becomes reversed in orientation during the process, and if the palindrome is imperfect, two different, reverse-complementary terminal sequences are generated. The relative abundances of the terminal sequence orientations at each end of the DNA molecules can be measured and give information about the replication process. From such clues, we developed a "kinetic hairpin transfer model" based on differential rates of hairpin formation and inversion processes depending on the conformations of the 3' termini. Numerical studies showed that this simple idea can account for the diverse pattern of DNA distributions observed in the family Parvoviridae. In this paper, we simplify the model to a set of coupled linear first-order ordinary differential equations in order to delineate its essential properties by Perron-Frobenius theory. Secondly, we examine our assumption of linear kinetics by modeling enzyme catalysis of the component steps of the hairpin transfer process. We show that the rate-determining step of the process is the binding of initiation complex to the self-priming hairpin structures. Furthermore, we find that if the replication machinery is saturated by DNA substrate late in an infection, the differential equations become non-linear but the steady-state DNA distribution is still given by the solution of our original linear equations.
所有线性DNA分子在复制其5'末端时都面临特殊问题，因为DNA聚合酶仅将核苷酸添加到具有游离3'-OH基团的预先存在的链上。细小病毒是一类具有线性单链DNA基因组的小型动物病毒，它们通过具有回文末端序列来解决这个问题，这些序列可以自身折叠形成引发DNA复制所必需的发夹结构。在这个过程中，启动复制的3'末端序列的方向会发生反转，如果回文结构不完美，就会产生两种不同的、反向互补的末端序列。可以测量DNA分子两端每种末端序列方向的相对丰度，并获得有关复制过程的信息。基于这些线索，我们根据取决于3'末端构象的发夹形成和反转过程的不同速率，开发了一个“动力学发夹转移模型”。数值研究表明，这个简单的想法可以解释在细小病毒科中观察到的DNA分布的多样模式。在本文中，我们将该模型简化为一组耦合的线性一阶常微分方程，以便通过佩龙 - 弗罗贝尼乌斯理论来描述其基本性质。其次，我们通过对发夹转移过程的组成步骤的酶催化进行建模，来检验我们的线性动力学假设。我们表明，该过程的速率决定步骤是起始复合物与自引发发夹结构的结合。此外，我们发现，如果在感染后期复制机制被DNA底物饱和，微分方程将变为非线性，但稳态DNA分布仍然由我们原始线性方程的解给出。
