Fig 1.
The modified six-state mechanism of cotransport.
An alternating access model of E. coli lactose—H+ cotransport by Jardetzky modified with the transition between cotransporter states 2 and 5. A simple schematic of the “six-state” mechanism of cotransporter LacY protein of E. coli during cotransport is shown in the figure above. Numbers 1 to 6 indicate state 1 to state 6, which are the six effective conformations of LacY protein. The blue double-head arrows refer to the six states of cotransporter in relation to each other, and the yellow dashed arrow refers to the way to modify the present model—allowing the transition between cotransporter states 2 and 5.
Fig 2.
Equilibrium properties of lactose permease symport in E. coli as ξ and η changes.
The cases are shown as ξ and η takes the twenty partition points of interval [0, 1](0.05 × i, i = 0, 1, ⋯, 20) with the following initial conditions: . And also, we set Vc = Vp = 106/C0, C0 is a constant with the unit of nm−3. The meaning of C0 is the same as which in [14], similarly hereinafter. (a) The value of
/
at equilibrium. (b) The value of
/
at equilibrium. (c) Time used to reach equilbrium state for H+ and lactose with the unit of Δt.
Fig 3.
Equilibrium properties of lactose permease symport in E. coli when ξ = η.
Only the ξ ≠ 0 cases are shown with the initial conditions the same as Fig 2. The vertical coordinate represents the number of particles in (a) and (b). (a) The equilibium solution of H+ in periplasm and cytoplasm. (b) The equilibium solution of lactose in periplasm and cytoplasm. (c) Time used to reach equilbrium state for H+ and lactose with the unit of Δt.
Fig 4.
The equilibium solutions for ξ = 0 when Vc or Vp is fixed and the other one varies.
(a) The equilibium solutions of H+ and lactose when Vc is fixed to 106/C0 and Vp/Vc > 1, with initial conditions ,
,
. (b) The equilibium solutions of H+ and lactose when Vc is fixed to 106/C0 and Vp/Vc < 1, with the same initial conditions before.
Fig 5.
Time to reach equilibrium for ξ = 0 when Vc or Vp is fixed and the other one varies.
Time used to reach equilbrium state with the unit of Δt when the initial concentrations of H+ and lactose are fixed in periplasm and cytoplasm, which has the initial conditions , ξ = 0. (a) Vc fixed to 106/C0. (b) Vp fixed to 106/C0.
Fig 6.
Time to reach equilibrium for ξ = 1 when Vc or Vp is fixed and the other one varies.
Different time for H+ and lactose to reach equilbrium state with the unit of Δt when the initial concentrations of H+ and lactose are fixed in periplasm and cytoplasm, which has the initial conditions , ξ = 1. (a) Vc fixed to 106/C0. (b) Vp fixed to 106/C0.
Fig 7.
Time to reach equilibrium with the variation of periplasm fraction , ξ = 0.
The sum of volumes of periplasm and cytoplasm is fixed, Vc+ Vp = 2 × 106/C0. (a) Initial particle concentration fixed, and the initial conditions are like . (b) Initial particle population fixed, and the initial conditions are like
.
Fig 8.
Time to reach equilibrium with the variation of periplasm fraction , ξ = 1.
Different time for H+ and lactose to reach equilbrium state with the unit of Δt. The sum of volumes of periplasm and cytoplasm is fixed, Vc+ Vp = 2 × 106/C0. (a) Initial particle concentration fixed, and the initial conditions are like . (b) Initial particle population fixed, and the initial conditions are like
.
Fig 9.
Lactose translocated into cytoplasm by E. coli T184 wild-type lactose permease.
The horizontal axis of the graph indicates the time E. coli T184 cells were incubated under specific conditions, and the vertical axis shows the increase in lactose concentration in cytoplasm compared to the initial condition. The red dots are the experimental data extracted from the article of Ujwal et al[19]. The solid and dashed lines are the results of our simulations when ξ = 1, η = 0 and ξ = 1, η = 1, respectively.