驱动蛋白马达动力学机制研究
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摘要
驱动蛋白马达是一类以微管为轨道向其正向运动的线性分子马达。它们广泛存在于真核细胞中,并在细胞内的输运过程、细胞形成、有丝分裂及细胞功能等方面扮演着重要角色。对于驱动蛋白马达运动定向性、行进性和较高能量转化效率的研究,不仅有助于人们理解驱动蛋白马达两个头部之间的协同作用、步行机制以及各种相干因素对定向运动的影响,而且对于生物体内诸多生物蛋白马达行为的理解以及人工合成纳米机械都具有重要意义。
本文采用基于布朗运动理论的布朗棘轮模型研究了驱动蛋白马达两个地位对等的头部交替与轨道蛋白结合,并沿微管做定向运动的物理学机制。研究内容主要包括以下两个大的方面：
驱动蛋白马达的开环棘轮模型。驱动蛋白的两个头部弹性连接,马达与轨道的相互作用用不对称势描述,不对称势随机或周期性变化于马达的几个状态之间,但是不对称势的变化与系统的状态无关。主要提出了三个模型,包括(1)闪烁势中弹性耦合的双头分子马达模型。势能在两态间随机跃迁,马达定向流的大小和方向依赖于噪声强度、颈部尺度以及跃迁速率三者的耦合；另外,后两者大小的变化会引起流的反转,这很好地解释了拥有不同颈部尺度的分子马达沿细胞骨架不同方向运动的情况。(2)弹性耦合双头分子马达的inchworm模型。马达两个头部在一维不对称周期势下,周期性闪烁对应于一个ATP水解循环,运动轨迹呈现inchworm模式。随弹性系数k的增加,几率流趋于定值,且存在最优的颈部原长a使几率流达到最大值。马达效率随噪声强度变化存在有极大值,且随势打开时间ton的增加,马达效率呈现非线性递减。(3)二维弹性耦合双头分子马达的hand-over-hand模型。二维相互作用势下,双头分子马达的闪烁棘轮模型模拟了驱动蛋白马达的hand-over-hand运动。虽然粒子在y方向上的几率不为零,但是依然表现为x正方向上的定向运动。当存在外部负载情况下,流可以发生反转。马达做功的效率与温度和负载力有关,且随二者的变化都存在有极大值。
反馈控制作用下的布朗棘轮模型。分别研究了马达系统根据马达的位置,或者环境温度的变化,通过系统的态来控制势的开关的信息模型。(1)在前一个模型中,无负载存在时,流随颈部尺度原长的变化在一定温度范围内呈现出周期性变化,当原长近似为势周期的整数倍时,耦合粒子的流为最小；施加外部负载力时,存在最优的颈部原长,流随负载力的变化会发生反转,马达的效率随温度及负载力的变化都存在有极大值。(2)布朗马达在温度控制的反馈作用下可以产生定向运动。反馈控制下的平均速度与能量比参数α、温度比参数β以及势的不对称参数α有关。当温度梯度发生反转时,粒子的平均速度也发生了反转。当α=0或者是β=1时,没有定向运动。当α和β与1的绝对值的差值越大,即参数的不对称性越大时,粒子的平均速度就越大。
Kinesins are a class of linear molecular motors, which move along microtuble towards its plus end. In all eukaryotic cells, kinesin plays an important role in intracellular transport, mitosis, cellular morphogenesis and cellar functions. Study on directionality, processivity and higher efficency of kinesin, can not only help people to understand the two-headed cooperation, walking manner and influence of related factors, but also can help people to understan other biological molecular motors' motility and can shed light on synthesizing nano-machines.
In this paper, we focus on the physical mechanics of kinesin by using Brownin ratchet method, which identical heads attach to the microtuble alternatively and step unidirectionally along linear track. The research mainly includes the following two aspects:
First, open-loop ratchet models of kinesin are presented. In which, the two heads coupled through an elastic spring, asymmetrical periodical potential flash between two states stochastically or perodically which is applied independently of the state of the systems to be controlled. There are three models, including:(1) A model of elastically coupled two-headed molecular motors in flashing potential. In the model, the potential swtiches on or off between two states stochastically. The current is sensitive to the transition rates, neck length and other parameters. The coupling of transition rates and neck length leads to variations both in the values and directions of current, which is very likely the case of different molecular motors with different neck length can move along cytoskeleton in different direction.(2) A model for inchworm motion of elastically-coupled molecular motors. Corresponding to ATP hydrolyzed circle, the motor has four states which each head submitted to a one-dimension flashing ratchet potential. It is concluded that the trajectory is inchworm manner, and the probability current changes with the neck's initial length a and the elastic coefficient k.With the increase of k, the probability current reaches to some a certain value, and there is optimal values for initial length to achieve the maximal current. Efficiency decrease nonlinearly with the increase of the open time of potential ton, and a maximum value can be obtained for some certain noise strength.(3) Two-dimensional model of elastically coupled molecular motors. A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins. The directed motion is obtained along the x direction, although the probability finding the particle along the y direction is non zero. When the external load is present, the current reversion is observed. The efficiency varies with both the temperature and the load, and there is a maximum value for a certain temperature and a certain load, which accords with experimental obserbations.
Secondly, feedback controls of Brownian ratchet models are studied.(1)In the former model, the positions of the two Brownian motors are monitored and the flashing ratchet potential can be switched on or off depending on the positions of the two particles. Without external load, the currents of Brownian motors show a periodic change in a certain temperatur range, and when the initial length of the spring reaches a value that approximately equals an integer times of the period of the potential, the average velocity reaches a minimum. Under external load, there is an optimal value of spring constant. And the dependence of the current on the opposing force is reversed. There are optimal values of temperature and the opposing force to obtain the better efficiency.(2)In the latter model, a feedback-controlled Brownian ratchet is operated by a temerature switch. The velocity induced by the feedback ratchet is a function of several parameters, including the ratio of the potential height and the noise strenghth α, the ratio of the two switching temperatures β and the asymmetry parameter of the potential field. The motor shows a current inversion when the gradient of β inverse, and there is no current when α=0or β=1. When the absolute values of difference between a and1, or β and1is big (ie. The intension of asymmetry actions is stronger), the mean velocity is big as well.
本文采用基于布朗运动理论的布朗棘轮模型研究了驱动蛋白马达两个地位对等的头部交替与轨道蛋白结合,并沿微管做定向运动的物理学机制。研究内容主要包括以下两个大的方面：
驱动蛋白马达的开环棘轮模型。驱动蛋白的两个头部弹性连接,马达与轨道的相互作用用不对称势描述,不对称势随机或周期性变化于马达的几个状态之间,但是不对称势的变化与系统的状态无关。主要提出了三个模型,包括(1)闪烁势中弹性耦合的双头分子马达模型。势能在两态间随机跃迁,马达定向流的大小和方向依赖于噪声强度、颈部尺度以及跃迁速率三者的耦合；另外,后两者大小的变化会引起流的反转,这很好地解释了拥有不同颈部尺度的分子马达沿细胞骨架不同方向运动的情况。(2)弹性耦合双头分子马达的inchworm模型。马达两个头部在一维不对称周期势下,周期性闪烁对应于一个ATP水解循环,运动轨迹呈现inchworm模式。随弹性系数k的增加,几率流趋于定值,且存在最优的颈部原长a使几率流达到最大值。马达效率随噪声强度变化存在有极大值,且随势打开时间ton的增加,马达效率呈现非线性递减。(3)二维弹性耦合双头分子马达的hand-over-hand模型。二维相互作用势下,双头分子马达的闪烁棘轮模型模拟了驱动蛋白马达的hand-over-hand运动。虽然粒子在y方向上的几率不为零,但是依然表现为x正方向上的定向运动。当存在外部负载情况下,流可以发生反转。马达做功的效率与温度和负载力有关,且随二者的变化都存在有极大值。
反馈控制作用下的布朗棘轮模型。分别研究了马达系统根据马达的位置,或者环境温度的变化,通过系统的态来控制势的开关的信息模型。(1)在前一个模型中,无负载存在时,流随颈部尺度原长的变化在一定温度范围内呈现出周期性变化,当原长近似为势周期的整数倍时,耦合粒子的流为最小；施加外部负载力时,存在最优的颈部原长,流随负载力的变化会发生反转,马达的效率随温度及负载力的变化都存在有极大值。(2)布朗马达在温度控制的反馈作用下可以产生定向运动。反馈控制下的平均速度与能量比参数α、温度比参数β以及势的不对称参数α有关。当温度梯度发生反转时,粒子的平均速度也发生了反转。当α=0或者是β=1时,没有定向运动。当α和β与1的绝对值的差值越大,即参数的不对称性越大时,粒子的平均速度就越大。
Kinesins are a class of linear molecular motors, which move along microtuble towards its plus end. In all eukaryotic cells, kinesin plays an important role in intracellular transport, mitosis, cellular morphogenesis and cellar functions. Study on directionality, processivity and higher efficency of kinesin, can not only help people to understand the two-headed cooperation, walking manner and influence of related factors, but also can help people to understan other biological molecular motors' motility and can shed light on synthesizing nano-machines.
In this paper, we focus on the physical mechanics of kinesin by using Brownin ratchet method, which identical heads attach to the microtuble alternatively and step unidirectionally along linear track. The research mainly includes the following two aspects:
First, open-loop ratchet models of kinesin are presented. In which, the two heads coupled through an elastic spring, asymmetrical periodical potential flash between two states stochastically or perodically which is applied independently of the state of the systems to be controlled. There are three models, including:(1) A model of elastically coupled two-headed molecular motors in flashing potential. In the model, the potential swtiches on or off between two states stochastically. The current is sensitive to the transition rates, neck length and other parameters. The coupling of transition rates and neck length leads to variations both in the values and directions of current, which is very likely the case of different molecular motors with different neck length can move along cytoskeleton in different direction.(2) A model for inchworm motion of elastically-coupled molecular motors. Corresponding to ATP hydrolyzed circle, the motor has four states which each head submitted to a one-dimension flashing ratchet potential. It is concluded that the trajectory is inchworm manner, and the probability current changes with the neck's initial length a and the elastic coefficient k.With the increase of k, the probability current reaches to some a certain value, and there is optimal values for initial length to achieve the maximal current. Efficiency decrease nonlinearly with the increase of the open time of potential ton, and a maximum value can be obtained for some certain noise strength.(3) Two-dimensional model of elastically coupled molecular motors. A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins. The directed motion is obtained along the x direction, although the probability finding the particle along the y direction is non zero. When the external load is present, the current reversion is observed. The efficiency varies with both the temperature and the load, and there is a maximum value for a certain temperature and a certain load, which accords with experimental obserbations.
Secondly, feedback controls of Brownian ratchet models are studied.(1)In the former model, the positions of the two Brownian motors are monitored and the flashing ratchet potential can be switched on or off depending on the positions of the two particles. Without external load, the currents of Brownian motors show a periodic change in a certain temperatur range, and when the initial length of the spring reaches a value that approximately equals an integer times of the period of the potential, the average velocity reaches a minimum. Under external load, there is an optimal value of spring constant. And the dependence of the current on the opposing force is reversed. There are optimal values of temperature and the opposing force to obtain the better efficiency.(2)In the latter model, a feedback-controlled Brownian ratchet is operated by a temerature switch. The velocity induced by the feedback ratchet is a function of several parameters, including the ratio of the potential height and the noise strenghth α, the ratio of the two switching temperatures β and the asymmetry parameter of the potential field. The motor shows a current inversion when the gradient of β inverse, and there is no current when α=0or β=1. When the absolute values of difference between a and1, or β and1is big (ie. The intension of asymmetry actions is stronger), the mean velocity is big as well.
引文
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