Computer Aided Simulation Of Cycle Regulation Of MPF In Mouse 1-Cell Fertilized Eggs

IntroductionEukaryotic cell cycle division is mainly regulated by a complex network which includes: 1. cyclin - dependent kinase ( CDKs ) and their associated cyc-lins; 2. kinases and phosphatases that regulate CDK activity, and 3. inhibitors that sequester cyclin - CDK dimers. After CDK combines with specific cyclins, CDK can trigger the events in the cell cycle through phosphorylatases or dephos-phorylatase the target protein in the chromosome and /or other places. MPF is the major regulator in the control of cell cycle, which is consist of Cdkl ( Cdc2) and cyclin B, and its activity changes periodically during the cycle. The activity of MPF is regulated by combination of Cdkl and cyclin B and phosphorylation of Cdk1. In a normal cell cycle, the activity of MPF behaves spontaneous oscillation : high in the mitotic phase during cell division and low in the interphase. So that MPF plays master role in the cell division. The concentration of catalytic subunit Cdkl does not vary considerably and the Cyclin B accumulates from interphase to M phase and destructed at anaphase; in the interphase, Cdc2 combines with cyclin B, which induces Tyrl5 and Thrl4 of Cdc2 to be phosphoryla-ted, and be inactive complex called preMPF. Cdc25 is dephosphorylated by active MPF and its activity rises in the mitosis, and in the interphase its activity lowered again.Because the cell cycle plays a central role in all process of biological growth, reproduction and development, cell biologists have invested much effort in identifying the molecular components and protein interaction of its control. In the process of the cell cycle of the early embryos of many species, continuous division is its important characteristics, and MPF is the marker of mitosis.When cell enters its anaphase of mitosis, anaphase — promoting complex (APC) is activated and degrades anaphase inhabitators such as cyclin B for ubiquitination. The destruction of mitotic Cdks at anaphase allows cells to divide and enter Gl phase of the next cell cycle and the sister chromosomes are separated and the transition anaphase is completed.So, MPF is in the central position of cell cycle regulation, in which many proteins are its regulators and/or its substrates, which form a complicated signal transduction system. There are many protein kinases in the system whose regulation mechanisms are different and many important kinases are not discovered yet, and the detailed mechanism of the known kinases is still not very clear.In the vertebrates the mouse fertilized egg is a simple and natural cell cycle model very closed to human species and its early development is controlled by MPF. Although the regulatory mechanisms of cell cycle of a variety of organisms have been studied in great details and several mathematic models have been constructed , the mathematic model of the mouse 1 — cell fertilized eggs is still a virgin soil.Materials and MethodsWe transform the functions among the proteins into a series of quantitative equations which describe evolution of the system in terms of the time and space. For the cell cycle control system, it is appropriate to apply the ordinary differential equations because molecular diffusion, transcription and membrane transportation are fast compared with cycle duration..For the different reaction involved in the system we applied different rate laws to obtain our ordinary differential equations. For example:1. The change rate of cyclin B concentration can be expressed as: _ ^ [ cyclinB ] [ APC ] - k3[ cyclinB] [ Cdc2]atin which the time rate of change of cyclin B is composed of the formation minus consummation of cyclin B, and kis(i = 1-3) are rate constants of eachreaction.2. For change rate of Cdc25 concentration, which is a enzyme -regulated reaction, we use Michaelis - Menten equation as:d[ Cdc25P] = ka[ MPF] (1 - Cdc25P]) kb[PPase] [Cdc25P] dt " Ka +1 - [ Cdc25) ] ~ Kb + [ Cdc25P]in which Ka and Kb represents the Km of the two Michaelis - Menten reactions, respectively.Software implementation;We construct the model with software GEPASI ( version 3.0) by inputting all necessary reactions to the software.ResultsEukaryotic cell cycle is controlled by negative feedback between MPF and APC. MPF inactivate APC and APC degrades the cyclin subunit of MPF. MPF must inhibit APC. If the activity of MPF is high, that of APC must be low to make MPF stable. On the other hand, if the activity of MPF is low the activity of APC will be high so that the activity of MPF will be low because of the degradation of cyclins.Recent study made it clear that the inactivity of MPF occurs after the first mitosis and it is due not only to the degradation of cyclin Bl but also to the control of dephosphorylation of cdc2 ( Cdkl).The activity of MPF and APC change periodically: when that of MPF rises, APC is activated indirectly and its activity rises, and high level activity of APC degrades cyclin and inhibit MPF. Low active MPF decreases the activity of APC. APC can be activated again only in the mitosis of next round of cycle when MPF is activated once more again.In G2/M, Cdc2 and cyclin B forms MPF, Weel and Mytl phosphates Cdc2 in Thrl4 and Tyrl5 to MPF as exists in the form of PreMPF. When cell enters division, a part of MPF is activated and the activated MPF activates Cdc25 by phosphorylation and the activated Cdc25 then dephosphorylates Thrl4and Tyrl5 of Cdc2 so that more MPF is activated and the cell enters mitosis.The activity of PKA in the mouse 1 - cell fertilized eggs is oscillated: high in M phase and low in interphase. PKA induces Cdc25 inactivated and down -regulates MPF. PKA appears negative regulation of MPF.DiscussionBecause of the complexity of the control system of cell cycle, it is difficult to be described in ordinary biochemical language. Computer can build a bridge between the cell biology and physiology. The computational model about mouse 1 - cell fertilized eggs has not been established yet although some papers have been published about eukaryotic organism such as xenopus and yeast.Recent study made it clear that we need the computer to understand the complexity of the molecular information. The molecular mechanism is strikingly conservative, controlled by CDKs and APC, although there are some different cell cycle in a series of organism. So we tried to design a simple model to explain the mechanism of fertilized eggs.In the mouse 1 - cell fertilized eggs the mechanism of MPF regulation is similar to that of normal eukaryotic cells. After 12 rapid, continuous division, the size of the fertilized eggs does not enlarge very much, different to that of yeast and somatic cells. So we dismiss restriction of the checkpoint such as size control and DNA integrity check which are essential to yeast cells. That is to say, the early development of fertilized eggs is fully controlled by the parameters of biochemical reactions in the cells. Only after 12 division, the checkpoint returns to play its important role again.Modeler faces many problems in trying to find the solution of different rate - order reactions, stable solutions of the system and most of all: the rate constants of biochemical reactions. In fact, we use the relative values to our model instead of absolute ones.