关于血红蛋白(或变构酶)的一组动力学方程的定性分析
Qualitative Investigation of Dynamical Equation System of Hemoglobin(or Allosteric Enzymes)
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摘要: 本文对文献[1]提出的血红蛋血的基本动力学方程组(三维自治系统)做以下定性分析:1.指出有意义的解应在一空间闭四面体内,证明四面体的四个面是无切面,积分曲线进入此体即永不复出.2.找到全部奇点,并证明其中两个奇点分别在四面体的一对不相邻的棱上(相应的棱是积分曲线),其余奇点一般都在四面体外无实际意义.3.证明在方程的7个物理参数中,仅参数b的符号决定奇点的性质.4.澄清该模型与MWC模型的关系.分析表明,该方程组较好地反映了变构酶的动力学性质.Abstract: For the dynamical equation system(a three-dimensional autonomous system) of hemoglobin, given in [1],we make the following qualitative investigation:(1)pointing out that, all meaningful solutions should be in a tetrahedroid. and -that,its..four surfaces are without contact;(2)finding all singular points, and proving that only two, of them are respectively situayed on a pair of seperate edges,and that other singular points are outside the tetrahedroid and meaningless;(3)proving that, among seven physical parameters of this system, only the sign of parameter b determines the properties of these two singular points;(4)clearing up the relation between this system and MWC model[3]. The investigation shows that this system reflects the dynamical properties of hemoglobin satisfacto rily.
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[1] 王宝翰、倪向善,血红蛋白(或变构酶)的统计动力学,分子科学学报,1(1982),113-121. [2] 王宝翰.寡聚蛋白结合配位体的研究——统计力学模型I.I,生物化学与生物物理学报.9(1977),177-304. [3] Monod.J Wyman and J,-P.Changeug,On the nature of allosteric transitions:A plausible model,J Mol,Biol.,12(1965),88-118. [4] 秦元勋、王联、王慕秋,《运动稳定性的理论及其应用》,科学出版社专著丛书(1981). [5] Л.Д.朗道,E,M栗弗席兹,《统计物理学》,人民教育出版社.(1964),189-190.
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