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\section*{Appendix 1}

The coarse-grained (CG) simulation model used in this work has been previously used to study single-spanning membrane proteins \cite{Zhang2012f}. Here, the key features of the model are summarized, and the minor modifications introduced in the current work are emphasized.

\paragraph{Coordinate system}
The CG model projects all system coordinates onto a 2D plane passing through the lateral gate (LG) of the translocon channel. The coordinate system is defined with the x-axis passing through the channel perpendicular to the bilayer and the y-axis running parallel to the bilayer as shown in Figure 1-figure supplement 2. The origin is set at the center of the channel such that negative x-values correspond to cytoplasmic locations. The LG is positioned in the positive y-direction and facilitates membrane entry. 

\paragraph{Interactions}

Interactions in the CG model are defined in terms of the reduced units $\epsilon$ and $\sigma$, where $\epsilon = 0.833$ $kT$ sets the energy scale and $\sigma = 0.8$ nm sets the length scale. $\sigma$ is equivalent to the diameter of a CG bead. $T$ is equal to 300 K in all simulations and $k$ is the Boltzmann constant. 

The nascent protein is treated as a freely jointed chain with connectivity enforced by a finite extension nonlinear elastic (FENE) potential between consecutive beads,

\begin{equation}
U_{bond}(r) = -1/2 KR_0^2 \ln(1-r^2/R_0^2),
\end{equation}

\noindent where $r$ is the distance between beads, $K = 7\epsilon/\sigma^2$ is the spring constant and $R_0 = 2\sigma$.

Short-ranged nonbonding interactions are modeled using a cutoff Lennard-Jones (LJ) potential,

\begin{equation}
U_{LJ}(r) = 
\begin{cases}
4\epsilon_{ij} \left [ \left ( \frac{\sigma}{r}\right )^{12} - \left ( \frac{\sigma}{r} \right )^6 \right ] + \epsilon_{cr} & r_{cl}<r \leq r_{cr} \\
0 & r<r_{cl}, r>r_{cr}
\end{cases}
\end{equation}

\noindent where $\epsilon_{ij}$ defines the strength of the interaction between bead $i$ and $j$, $r_{cl}$ is a cutoff at low values of $r$, and $r_{cr}$ is a cutoff at large values of $r$. $\epsilon_{cr}$ is a constant to shift the potential to 0 at $r_{cr}$. The LJ interactions among beads of the nascent protein and between beads of the nascent protein and the ribosome are chosen to be purely repulsive by setting $r_{cr} = 2^{1/6} \sigma$ and $\epsilon_{ij} = \epsilon$. Weak attractive interactions are included between of the nascent protein and beads in the translocon by setting $r_{cr} = 2.5 \sigma$ and $\epsilon_{ij} = 1.5 \epsilon$. $r_{cl}$ is set to 0 for all interactions between CG beads with the exception of interactions between the nascent protein and the LG in the open state, in which case $r_{cl} = \sigma$ to allow beads to exit the channel and enter the membrane. 

Electrostatic interactions between charged beads are modeled using the Debye-H\"{u}ckel potential,

\begin{equation}
U_{DH}(r) = 
\begin{cases}
\sigma q_i q_j (\beta r)^{-1} \exp(-r / \kappa) & r \geq \sigma \\
 q_i q_j \beta ^{-1}\exp(-\sigma/ \kappa) & r < \sigma 
\end{cases}
\end{equation} 

\noindent where $\kappa = 1.4 \sigma$ approximates the Debye screening length in typical biological media, $\beta = 1/kT$, and $q$ is the charge of a CG bead. The electrostatic potential is capped from below to prevent singularities as beads exit the channel and interact with charges on the open LG.

The effect of the implicit bilayer is modeled by calculating the solvation energy of CG beads, 

\begin{equation}
U_{solv} = g_iS(x; \phi_x, \psi_x) \left [ 1 - S(y; \phi_y, \psi_y)\right ],
\end{equation}

\noindent where $g_i$ is the transfer free energy of bead $i$ and $S(x, \phi, \psi)$ is a switching function that defines the membrane region,

\begin{equation}
S(x; \phi, \psi) = \frac{1}{4} \left [ 1+\tanh \left ( \frac{x-\phi}{0.25 \sigma} \right )\right ]  \left [ 1-\tanh \left ( \frac{x-\psi}{0.25 \sigma} \right )\right ]
\end{equation}

This form of the solvation energy and switching function defines the implicit bilayer as the region where $\phi_x < x < \psi_x$ and $y < \psi_y$ or $y > \phi_y$, where $\phi_x = -2.0\sigma$, $\psi_x = 2.0\sigma$, $\phi_y=-1.5\sigma$, and $\psi_y = 1.5\sigma$. The transfer free energy, $g$, for each bead type is approximated from the Wimley-White hydrophobicity scale which measures water-octanol transfer free energies \cite{Wimley1996}. Values of $g$ for the different bead types are summarized in Appendix table 1. Bead types for all EmrE variants studied in this work are listed in Appendix table 2.

\begin{table*}[h]
	\centering
	\caption{\label{tbl:beadparam}
		CG bead charges ($q$) and water/membrane transfer free energies ($g$).
	}
	\begin{tabular*}{0.6\textwidth}{@{\extracolsep{\fill}}ccccc}
		\hline
		&Q &L &V &K \\ 
		\hline
		$q$%\tablenote{charge} 
		&0.0 &0.0 &0.0 &2.0 \\
		$g/\epsilon$%\tablenote{transfer free energy from water to membrane (unit in $\epsilon$)} 
		&2.0 &-4.0 &-2.0 &6.0\\
		\hline
	\end{tabular*}
\end{table*}

\paragraph{System dynamics}

The time-evolution of the nascent protein is modeled with Brownian dynamics with the equation of motion,

\begin{equation}\label{brownian_dynamics}
x_i(t+\Delta t) = x_i(t) - \beta D \frac{\partial V(\mathbf{x}(t))}{\partial x_i} \Delta t + \sqrt{2D\Delta t}\eta_i,
\end{equation}

\noindent where $x(t)_i$ is the position (in two dimensions) of bead $i$ at time $t$, $V(\mathbf{x}(t))$ is the potential energy of the system, $D$ is the isotropic bead diffusion coefficient, $\Delta t$ is the time step, and $\eta_i$ is random noise drawn from a Gaussian distribution with zero mean and a variance of one. Only beads in the nascent protein are subject to Brownian dynamics. $D$ is set to a value of 758.7 nm$^2$/s and the $\Delta t$ is set to 100 ns. 

LG dynamics are modeled by attempting to stochastically open or close the LG at every simulation timestep with a probability $p_{open} = k_{open} \Delta t$ or $p_{close} = k_{close} \Delta t$, where

\begin{align}
k_{open} &= \frac{1}{\tau_{LG}} \frac{\exp(-\beta \Delta G_{tot})}{1+\exp(-\beta \Delta G_{tot})} \\
k_{close} &= \frac{1}{\tau_{LG}} \frac{1}{1+\exp(-\beta \Delta G_{tot})}
\end{align}

\noindent $\tau_{LG} = 500$ ns is the timescale for attempting lateral gate opening/closing and $\Delta G_{tot}$ is the change in the free energy for opening the LG. $\Delta G_{tot}$ depends on the presence of the nascent protein beads in the channel and is defined as

\begin{equation}
\Delta G_{tot} = \sum_{i=1}^M g_i + \Delta E + \Delta G_{empty} \chi_{empty},
\end{equation}

\noindent where $M$ is the number of beads occupying the translocon, $\Delta E$ is the difference between the total LG/protein LJ interactions in the closed state and total LG/protein LJ interactions in the open state, $\Delta G_{empty} = 16 \epsilon$ is the free energy cost for opening the LG when there is no nascent protein in the channel, and $\chi_{empty}$ is the fraction of the channel that is empty for a given timestep. The first term promotes LG opening when hydrophobic beads enter the channel, the second term prevents the LG from closing when occluded by a nascent protein, and the third term promotes LG closing once the nascent protein exits the channel. Additional details on the development and numerical testing of the CG model are provided in Ref. \cite{Zhang2012f}.

\paragraph{Wall potential}

A modification that appears in the current implementation of the CG model is a wall potential that prevents the nascent protein from returning to the translocon once it completes translation and diffuses a given distance away from the channel. The potential has the form

\begin{equation}
U_{wall}(y) = 
\begin{cases} 
1/2 K_{wall} (y - 10\sigma)^2  &  y < 10\sigma \\
0 & y \geq 10\sigma
\end{cases}
\end{equation}

\noindent where the spring constant, $K_{wall}$, is set to 10 $\epsilon/\sigma^2$. The potential is only added to the system when all beads of the nascent protein have y-positions greater than $12\sigma$. Inclusion of the wall potential was found to avoid artifacts associated with the nascent protein interacting with the translocon long after exiting the channel. These artifacts were expected to be accentuated in the CG model due to its reduced dimensionality; nonetheless, the results are qualitatively unchanged if the wall potential is not included. 

\begin{table*}[h]
	\centering
	\caption{\label{tbl:beadparam}
		CG bead sequences for each of the 16 EmrE mutants and the cotranslationally-biased mutant. Moderately hydrophobic (V), very hydrophobic (L), neutral-hydrophilic (Q) and charged (K) beads are colored as light gray, gray, black, and red respectively. Loops and TMDs are labeled.
	}
	\begin{tabular*}{1.0\textwidth}{@{\extracolsep{\fill}}lccccccccc}
		\hline
		Protein &L1 &TMD1 &L2 &TMD2 &L3 &TMD3 &L4 &TMD4 &L5 \\ 
		\hline
		EmrE & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{\color{red}K\color{black}Q\color{red}K\color{black}QQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQQ} \\
		
		EmrE(N$_{\mathrm{cyto}}$) & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{\color{red}K\color{black}QQQQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{black}QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQ\color{red}K} \\
		
		EmrE(N$_{\mathrm{peri}}$) & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{\color{red}KKK\color{black}QQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}KK\color{black}QQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{black}QQQQQ} \\
				
		K3 & \textbf{\color{red}K\color{black}QQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{\color{red}K\color{black}Q\color{red}K\color{black}QQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQQ} \\
		
		T28R & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{\color{red}KKK\color{black}QQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQQ} \\

		A52K & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{\color{red}K\color{black}Q\color{red}K\color{black}QQ} & \textbf{\color{gray}LLLL} &\textbf{QQ\color{red}K\color{black}QQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQQ} \\

		L85R & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{\color{red}K\color{black}Q\color{red}K\color{black}QQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}KK\color{black}QQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQQ} \\
		
		R111 & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{\color{red}K\color{black}Q\color{red}K\color{black}QQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQ\color{red}K} \\
		
		\hline
		
		nEmrE & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{QQQQQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} \\
		
		nK3 & \textbf{\color{red}K\color{black}QQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{QQQQQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} \\		
		
		nT28R$^{\mathrm{1}}$ & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{\color{red}K\color{black}QQQQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} \\
		
		nT28R$^{\mathrm{2}}$ & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{\color{red}K\color{black}Q\color{red}K\color{black}QQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} \\
		
		nT28R & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{\color{red}KKK\color{black}QQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} \\
		
		nA52K & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{QQQQQ} & \textbf{\color{gray}LLLL} &\textbf{QQ\color{red}K\color{black}QQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} \\
		
		nL85R & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{QQQQQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}KK\color{black}QQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} \\
		
		nR111 & \textbf{QQQQQ} & \textbf{\color{lightgray}VVVV} &\textbf{QQQQQ} & \textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{QQQQQ} &\textbf{\color{gray}LLLL} &\textbf{\color{red}K\color{black}QQQQ} \\
		\hline
	\end{tabular*}
	
	
	\begin{tabular*}{1.0\textwidth}{@{\extracolsep{\fill}}lccccc}
		CB mutant & L1 & TMD1 & L2 & TMD2 & L3 \\
				  & \textbf{\color{red}K\color{black}QQQ\color{red}K}
				  & \textbf{\color{gray}LLLL}
				  & \textbf{\color{black}QQQQQQQQQQ}
				  & \textbf{\color{gray}LLLL}
				  &\textbf{\color{red}K\color{black}QQQQQQQQ\color{red}K\color{black}}
	\end{tabular*}
	\begin{tabular*}{1.0\textwidth}{@{\extracolsep{\fill}}lcccccc}
	 &	&  TMD3 & L4 & TMD4 & L5 & \\
	 &	& \textbf{\color{gray}LLLL}
		& \textbf{\color{black}QQQQQQQQQQ}
		& \textbf{\color{gray}LLLL}
		& \textbf{\color{red}K\color{black}QQQQQQQQ\color{red}K\color{black}
		}
	\end{tabular*}
\end{table*}

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