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.
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 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 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 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.
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