### Abstract

By using molecular dynamics simulation, the dynamic behaviors of particle permeation through a four-helix-bundle model channel are studied. The interior cavity of the four-helix-bundle provides the “routes” for particle permeation. The main structural properties of the model channel are similar to those that appear in natural four-helix-bundle proteins. It is found that the interior structure of the model channel may greatly influence the permeation process. At the narrow necks of the model channel, the particle would be trapped during the permeation. There is a threshold value for the driving force. When the driving force is larger than this threshold value, the mean first permeation time decreases sharply and tends to be saturated. Increasing the temperature of either the model channel or the particle reservoir can also facilitate the permeation. Enhancing the interaction strength between the particle and monomer on the four-helix-bundle model chain will hinder the permeation. Hence, the electrical current which is induced by the particle permeation is a function of the driving force and temperature. It is found that this current increases monotonically as the strength of the driving force or the temperature increases, but decreases as the interaction strength between the particle and monomer increases. It is also found that the larger the friction coefficient, the slower the permeation is. In addition, the multiparticle (or multi-ion) permeation process is also studied. The permeation of multiparticle is usually quicker than that of the single particle. The permeation of particle through a five-helix-bundle shows similar properties as that through a four-helix-bundle.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 90103031, 10474041, 90403120, and 10021001), and the Nonlinear Project 973 of NSM (Grant No. G2000077300).

I. INTRODUCTION

II. METHOD

A. Channel model

B. Potential energy

C. Langevin dynamics

D. Analyzed quantities

III. RESULTS AND DISCUSSION

A. Channel properties

B. Single particle permeation

C. Multiparticle permeation

D. Permeation through a five-helix-bundle

IV. SUMMARY

## Figures

The structural profile of the coarse-grained four-helix bundle model channel. (a) is the backbone picture of the four-helix bundle model channel; upside is the extracellular; underside is the intracellular; the particle above the bundle is the model of ion. Two loops at the upside form the open mouth. Both termini are in the intracellular. The full length of the model channel is around 35 Å. The equilibrium values of cross angles between subunits are , , , and , respectively. (b) The projection from upside to underside. Every circle with a number in it is a monomer forming the four-helix-bundle. The number is the index of that monomer. The central dashed circle depicts the inner pore of the model channel. The four dashed elliptic circles around the dashed circle are the inner sides of four subunits of the bundle. The outside dashed circle is the outer most boundary of the model channel. The bold line depicts the first subunit which is composed of monomers from the 1st to the 16th. (c) shows the statistical distance distribution of monomers away from axis. The filled squares on the left of the graph are for inner sides of four subunits. The open circles on the right of the figure are for the outer sides of four subunits.

The structural profile of the coarse-grained four-helix bundle model channel. (a) is the backbone picture of the four-helix bundle model channel; upside is the extracellular; underside is the intracellular; the particle above the bundle is the model of ion. Two loops at the upside form the open mouth. Both termini are in the intracellular. The full length of the model channel is around 35 Å. The equilibrium values of cross angles between subunits are , , , and , respectively. (b) The projection from upside to underside. Every circle with a number in it is a monomer forming the four-helix-bundle. The number is the index of that monomer. The central dashed circle depicts the inner pore of the model channel. The four dashed elliptic circles around the dashed circle are the inner sides of four subunits of the bundle. The outside dashed circle is the outer most boundary of the model channel. The bold line depicts the first subunit which is composed of monomers from the 1st to the 16th. (c) shows the statistical distance distribution of monomers away from axis. The filled squares on the left of the graph are for inner sides of four subunits. The open circles on the right of the figure are for the outer sides of four subunits.

Two typical permeation processes. The abscissa is on the base of logarithm. The driving force is ; the simulation temperature is . The friction coefficients are (a) and (b) , respectively.

Two typical permeation processes. The abscissa is on the base of logarithm. The driving force is ; the simulation temperature is . The friction coefficients are (a) and (b) , respectively.

The single-particle energy profile of the channel. The abscissa is the position at axis; the ordinate is the potential energy in reduced unit. “A,” “B,” “C,” and “D” indicate four potential wells. The wells correspond to the narrow necks and loops of the channel.

The single-particle energy profile of the channel. The abscissa is the position at axis; the ordinate is the potential energy in reduced unit. “A,” “B,” “C,” and “D” indicate four potential wells. The wells correspond to the narrow necks and loops of the channel.

The MFPT as a function of driving force. The simulation temperature is . From up to down, the friction coefficients are 10.0, 5.0, 1.0, and 0.05, accordingly. The driving force is cut off at . The inset is the deduced electrical current as a function of membrane voltage. The dashed line in the inset is extrapolated from the high voltage side.

The MFPT as a function of driving force. The simulation temperature is . From up to down, the friction coefficients are 10.0, 5.0, 1.0, and 0.05, accordingly. The driving force is cut off at . The inset is the deduced electrical current as a function of membrane voltage. The dashed line in the inset is extrapolated from the high voltage side.

The change of MFPT along with the interaction strength between monomer and particle. The temperature is and the driving force is . From up to down, the friction coefficients are 6.0, 5.5, 5.0, 1.0, and 0.05, respectively. The inset is the relation between electrical current and . The dashed line is extrapolated from the low limit of .

The change of MFPT along with the interaction strength between monomer and particle. The temperature is and the driving force is . From up to down, the friction coefficients are 6.0, 5.5, 5.0, 1.0, and 0.05, respectively. The inset is the relation between electrical current and . The dashed line is extrapolated from the low limit of .

The influence of temperature on the MFPT. The abscissa is the temperature in a log base and the ordinate is the MFPT. The driving force is . (a) Both the particle reservoir and monomers have the same temperature, and the uplimit of temperature is set at . The friction coefficients from left to right are , 3.5, 2.0, 1.0, and 0.05, respectively. (b) Only the temperature of particle reservoir is changeable. The temperature of monomers is set to be 0.1. From up to down, the friction coefficients are , 0.2, 0.1, and 0.05, accordingly. The insets are the currents as functions of channel temperature and the temperature of particle reservoir. The dashed line is extrapolated from the high limit of temperature.

The influence of temperature on the MFPT. The abscissa is the temperature in a log base and the ordinate is the MFPT. The driving force is . (a) Both the particle reservoir and monomers have the same temperature, and the uplimit of temperature is set at . The friction coefficients from left to right are , 3.5, 2.0, 1.0, and 0.05, respectively. (b) Only the temperature of particle reservoir is changeable. The temperature of monomers is set to be 0.1. From up to down, the friction coefficients are , 0.2, 0.1, and 0.05, accordingly. The insets are the currents as functions of channel temperature and the temperature of particle reservoir. The dashed line is extrapolated from the high limit of temperature.

The multiparticle energy profiles. The dashed line is the single-particle energy profile, which is the same as in Fig. 3. A, B, C, and D are relevant four energy wells. (a) The two-particle energy profile. The solid line is the energy profile for the second particle when the first particle is fixed at , in the channel. The dotted line is energy profile of the first particle when the second particle falls into the energy well at . (b) The three-particle energy profile. The solid line is the energy profile of moving the third particle along axis when the first two particles are set at , and . The dotted line is the energy profile of the first particle when the second and the third particles are placed at and , respectively.

The multiparticle energy profiles. The dashed line is the single-particle energy profile, which is the same as in Fig. 3. A, B, C, and D are relevant four energy wells. (a) The two-particle energy profile. The solid line is the energy profile for the second particle when the first particle is fixed at , in the channel. The dotted line is energy profile of the first particle when the second particle falls into the energy well at . (b) The three-particle energy profile. The solid line is the energy profile of moving the third particle along axis when the first two particles are set at , and . The dotted line is the energy profile of the first particle when the second and the third particles are placed at and , respectively.

The typical permeation process involving three particles. The simulation is performed under temperature of and driving force of . Two particles reside at and in advance, then the third particle enters the channel. The lowest line is the trajectory of the first particle, the middle line is for the second, and the up line is for the third particle.

The typical permeation process involving three particles. The simulation is performed under temperature of and driving force of . Two particles reside at and in advance, then the third particle enters the channel. The lowest line is the trajectory of the first particle, the middle line is for the second, and the up line is for the third particle.

The comparison of permeation time between five-helix-bundle and four-helix-bundle under different friction coefficients. The simulation is at temperature of and under driving force of . The filled square is for the four-helix-bundle; the blank circle is for five-helix-bundle. The abscissa is the friction coefficient in a log base, and the ordinate is the MFPT.

The comparison of permeation time between five-helix-bundle and four-helix-bundle under different friction coefficients. The simulation is at temperature of and under driving force of . The filled square is for the four-helix-bundle; the blank circle is for five-helix-bundle. The abscissa is the friction coefficient in a log base, and the ordinate is the MFPT.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content