# General Principles of Secondary Active Transporter Function

Oliver Beckstein<EMAIL_ADDRESS>Fiona Naughton  Department of
Physics, Arizona State University, Tempe AZ 85287, USA

(August 28, 2024)

###### Abstract

Transport of ions and small molecules across the cell membrane against
electrochemical gradients is catalyzed by integral membrane proteins that use
a source of free energy to drive the energetically uphill flux of the
transported substrate. Secondary active transporters couple the spontaneous
influx of a “driving” ion such as Na+ or H+ to the flux of the substrate. The
thermodynamics of such cyclical non-equilibrium systems are well understood
and recent work has focused on the molecular mechanism of secondary active
transport. The fact that these transporters change their conformation between
an inward-facing and outward-facing conformation in a cyclical fashion, called
the alternating access model, is broadly recognized as the molecular framework
in which to describe transporter function. However, only with the advent of
high resolution crystal structures and detailed computer simulations has it
become possible to recognize common molecular-level principles between
disparate transporter families. Inverted repeat symmetry in secondary active
transporters has shed light on how protein structures can encode a bi-stable
two-state system. More detailed analysis (based on experimental structural
data and detailed molecular dynamics simulations) indicates that transporters
can be understood as gated pores with at least two coupled gates. These gates
are not just a convenient cartoon element to illustrate a putative mechanism
but map to distinct parts of the transporter protein. Enumerating all distinct
gate states naturally includes occluded states in the alternating access
picture and also suggests what kind of protein conformations might be
observable. By connecting the possible conformational states and ion/substrate
bound states in a kinetic model, a unified picture emerges in which symporter,
antiporter, and uniporter function are extremes in a continuum of
functionality.

††preprint: arXiv: 1912.06275 [q-bio.BM]

Keywords: membrane protein, transporter, symmetry, molecular mechanisms.

##  I Introduction

Active transporters are integral membrane proteins that move substrate through
the membrane against an electrochemical gradient by using a source of free
energy. They are broadly classified as primary and secondary active
transporters, depending on the free energy source (Mitchell, 1967). _Primary
active transporters_ harness chemical reactions (e.g., phosphorylation by ATP)
or light. Some examples are the sodium-potassium pump (Na/K ATPase) (Morth
_et al._ , 2007), the rotary F0F1-ATPase and the light-driven proton pump
bacteriorhodopsin (Buch-Pedersen  _et al._ , 2009), complex I in the
respiratory chain (Sazanov, 2015), or ATP-driven ABC transporters such as
p-glycoprotein (Lespine  _et al._ , 2009).

_Secondary transport_ is driven by an electrochemical gradient in a _driving
ion_ , namely sodium or protons. Examples are neurotransmitter transporters
SERT (serotonin) and DAT (dopamine) (Gouaux, 2009), sodium-proton exchangers
(NHE) (Fuster and Alexander, 2014), the calcium exchanger (Ottolia  _et al._ ,
2007), and AE1, the anion exchanger in red blood cells also known as Band 3
(Västermark  _et al._ , 2014)). Secondary active transporters can be divided
into two classes based on their physiological behavior (Mitchell, 1967).
_Symporters_ move their substrate in parallel with the driving ion (Figure
1A). Both driving ion and substrate are bound at the same time and move in the
same direction. One part of the transport cycle consists of the movement of
the substrate- and ion-free (apo) transporter. In the _antiporter_ transport
cycle (Figure 1B), the driving ion is bound during one leg of the cycle while
the substrate is bound in the other leg and is transported in the opposite
direction.

Figure 1: Schematic transport cycle of A a symporter (transport of substrate
and driving ion in the same direction) and B an antiporter (transport in
opposite directions). The central cartoon summarizes the physiological
function. The V-shaped triangle symbolizes a membrane-embedded transporter
protein in the outward facing conformation in which its binding sites are
accessible from the outside. The hat-shaped triangle indicates the inward
facing conformation. The driving ion is drawn as a circle while the
transported substrate is shown as a square. The predominant direction of
reactions is shown by arrows, with horizontal arrows indicating
binding/unbinding and vertical arrows conformational transitions. The order of
binding and unbinding events and the stoichiometry of substrate to driving
ions may differ from this cartoon.

Variations of the above scheme are common, though. For instance, many
symporters transport another ion back instead of the apo leg of the transport
cycle. Sometimes, the driving ion is effectively part of the substrate as in
the AdiC transporter (Fang  _et al._ , 2009), which exchanges L-arginine with
its decarboxylated product agmatine to effectively export protons.

A third class of related transporters consists of non-coupled transporters.
These _uniporters_ facilitate diffusion through the membrane. Although we
specifically focus on active transporters, the discussion on transport cycles
(Section VI) will make clear that the uniporters are closely related to active
transporters and it is plausible that small changes in the protein may convert
between the two.

In this review we focus on overarching principles that are common across
almost all secondary active transporters. We begin with the _alternating
access model_ which provides the “standard model” for explaining transporter
function in a structural context (Section II). Although evolution always finds
ways to add a few exceptions to common rules (for instance, there are a few
transporters that do not appear to follow the classical alternating access
model), the physical principles under which transporters operate are not
negotiable. Transporters function out of equilibrium as “physical enzymes”
that catalyze transport by free energy transduction through cyclic processes
(Section III). Ten years ago, a remarkable insight was found into the
evolutionary mechanism that can generate protein structures that can switch
between the two states of the alternating access model: transporters contain
so-called inverted repeat sequences that fold into structures with an internal
pseudo two-fold symmetry. This symmetry is broken to generate two different
conformations, as discussed in Section IV. A complimentary view of
transporters is that of a pore with multiple coupled gates; originally
motivated by the description of ion channels as pores with a single gate, this
cartoon model has proven valuable because transporters actually contain
physical components that perform the functions of gates, as will be shown with
selected examples in Section V. When the alternating access/gated pore model
is considered together with the cycle view of transport, a simple unified
picture emerges that describes symporters, antiporters, and uniporters as
ideals in a spectrum of functionality (Section VI).

##  II The alternating access model

The _alternating access model_ in its basic form was described by Jardetzky
(1966) as a polymer molecule that contains binding sites for substrate and is
able to assume two different conformations that alternatingly expose the
binding sites to the interior and the exterior. The idea of a cyclical process
facilitated by a molecule that changes accessibility was expressed by Mitchell
(1967) in his “circulating carrier” model. Together these models describe in
abstract terms a basic framework or model to understand driven transport
across the cell membrane. The key insight was that coupling of two fluxes
(substrate and driving ion) could be accomplished by binding to different
conformations of the same molecule as discussed in more detail in the next
Section III. In particular, it is physically not possible to move substrate
against a gradient through a continuous pore, i.e., one that is simultaneously
accessible from both sides, regardless of any energy consuming mechanism to
open or close the pore (Tanford, 1983). The consequence of this insight is
that transporters cannot function if continuous pores are formed through the
membrane. The alternating access model with its two distinct states provides a
conceptual framework that avoids pore formation. However, it requires that a
membrane protein is able to change between different conformations on the sub-
millisecond time scale111Turnover numbers of transporters range from one
transport event per millisecond (for sodium/proton exchangers) to one per
second (some amino acid/cation transporters from thermophiles operating at
room temperature) with a typical number on the order of one hundred events per
second (e.g., lactose permease); see “transporter turnover rate” in the
BioNumbers database https://bionumbers.hms.harvard.edu/ (Milo  _et al._ ,
2010). This means that any step in the transport cycle, including the
conformational transition, must be faster than 1 millisecond for the fastest
transporters, and 10 milliseconds or 1 second for the slower ones., a speed
that is easily achievable for macromolecular conformational changes (Henzler-
Wildman and Kern, 2007; Schwartz and Schramm, 2009). The alternating access
model also does not give any insights into the actual molecular structure of a
transporter except the general requirement that substrate and ion binding
sites must switch accessibility in different conformations. In order to obtain
deeper mechanistic insights actual atomic-scale structures of transporters in
multiple conformations are needed.

Figure 2: Conformations of the nucleobase/sodium-coupled symporter Mhp1 from
X-ray crystallography. A Outward-facing open conformation (PDB ID 2JLN)
(Weyand  _et al._ , 2008). B Outward-facing occluded conformation with bound
substrate benzylhydantoin (PDB ID 4D1B (Simmons  _et al._ , 2014); this
structure superseded the original 2JLO structure (Weyand  _et al._ , 2008) but
the structural differences are small). C Inward-facing open conformation (PDB
ID 2X79; (Shimamura  _et al._ , 2010)). The approximate position in the
membrane is indicated by the gray rectangle in the background. The two
cartoons under A and C indicate the two states of the classical alternating
access model as used in Figure 1. Molecular images were produced with VMD
(Humphrey, Dalke, and Schulten, 1996).

The first secondary active transporter for which the major states in the
transport cycle were resolved at atomic resolution was the sodium-coupled
symporter Mhp1, a member of the nucleobase-cation-symporter 1 (NCS1) family
(Weyand  _et al._ , 2011; Jackson  _et al._ , 2013). The structures of wild-
type Mhp1 revealed a sodium binding and a substrate binding site deep at the
center of the transporter, roughly at the membrane midplane (Weyand  _et al._
, 2008). In one structure, these binding sites were accessible from the
extracellular side, making this the outward facing (OF) conformation as shown
in Figure 2. Shimamura  _et al._ (2010) managed to crystallize wild-type Mhp1
in an inward facing (IF) conformation in which the binding sites were exposed
to the intracellular side. Together they represent the two key conformations
required by the alternating access model. A third conformation was also found:
in this occluded conformation the binding sites were not accessible from any
compartment (Weyand  _et al._ , 2008; Simmons  _et al._ , 2014). The
alternating access model does not require such a conformation. As will be
argued in Section V, such occluded states are a necessary consequence of a
molecular architecture in which the alternating access conformations are
formed by gate domains.

The hallmark of the alternating access mechanism are relatively large
conformational changes in the protein conformation and these appear to exist
in many secondary transporters for which the alternating access mechanism
remains the standard structural framework in which to understand transporter
function (Boudker and Verdon, 2010; Law, Maloney, and Wang, 2008; Forrest and
Rudnick, 2009; Gouaux, 2009; Krishnamurthy, Piscitelli, and Gouaux, 2009;
Abramson and Wright, 2009; Boudker and Verdon, 2010; Kaback  _et al._ , 2011;
Forrest, Krämer, and Ziegler, 2011; Schweikhard and Ziegler, 2012; Henzler-
Wildman, 2012; Yan, 2013; Shi, 2013; Slotboom, 2014; Diallinas, 2014; Li  _et
al._ , 2015; Drew and Boudker, 2016; Bai, Moraes, and Reithmeier, 2017;
Kazmier, Claxton, and Mchaourab, 2017; Henderson, Fendler, and Poolman, 2019).

Although the alternating access model is the canonical model for active
transporters, some transporters appear not to be described well within this
framework. For example, chloride/proton antiporters are currently understood
to function by small changes in a central glutamate residue that alternatingly
binds chloride and protons (Miller, 2006; Accardi, 2015) and do not require
the large conformational change—the “alternating access transition”—that is
generally taken to be a key step in the classical alternating access model.
However, it could be argued that the fundamental principle of alternating
access and the need to maintain a pathway that can not directly conduct ions
and substrate always has to be maintained in order to support the cyclical
reactions that are required for energy transduction (see the next Section III)
even though different models are also sometimes discussed (Klingenberg, 2007;
Naftalin, 2010).

##  III Thermodynamics and cycles

Transport is driven by spontaneous influx of a driving ion. The free energy
dissipation from flowing down its electrochemical gradient is coupled to the
vectorial transport of a substrate molecule or ion. Hill (1989) clearly
explained the principle of free energy transduction in transporters (and
enzymes) through a cyclic process that tightly couples driving ion flux and
substrate flux. Following his treatment, we will first qualitatively explain
how a cyclical process that operates out of equilibrium transduces energy. We
will then briefly revisit the thermodynamic driving forces of the process in
order to motivate the idea that transporters are enzymes that catalyze
transport.

###  III.1 Transport is a non-equilibrium process

Figure 3: Transport by an antiporter is a cyclical out-of-equilibrium process.
A Equilibrium—all concentrations are at equilibrium values and all reactions
obey detailed balance. B Out-of-equilibrium—the outside ion concentration is
raised over its equilibrium value, which leads to moving all states out of
equilibrium. The states are numbered so that one can refer to, say, the
outward facing apo state (neither ion nor substrate bound) of the transporter
as $T_{1}$ or the inward facing, substrate-bound state as $T_{5}:S$ where the
presence of the substrate is included for clarity even though the label “5”
includes the presence of the substrate (as opposed to state 4, which does not
include it).

Consider, for instance, a hypothetical antiporter that uses one driving ion
(red circle in Figure 3A) to move one substrate molecule (blue square). We
initially imagine the system to exist in equilibrium, i.e., the net fluxes
between all states are zero, also known as the detailed balance condition. The
inside and outside populations $i$ of particles are in Nernst equilibrium,
i.e., when considering the concentrations on either side of the membrane and
the membrane potential, no net flux of particles would occur if a pore
selective for species $i$ were opened in the membrane.222It is also necessary
that the transporter state populations are in equilibrium with each other and
the ion and substrate concentrations. However, any imbalance in the
transporter populations would soon move towards the equilibrium values,
provided that the ion and substrate concentrations are at equilibrium. A
transport cycle cannot be driven by the transporter; only the
binding/dissociation of external ions and substrates can continuously draw on
a source of free energy. For example, the binding of a driving ion $I$ to the
empty transporter in the outward facing conformation $T_{1}$ is the
equilibrium reaction

$\displaystyle T_{1}+I\rightleftharpoons T_{2}:I.$ (1)

The isomerization between outward facing and inward facing conformation (the
alternating access transition) is

$\displaystyle T_{2}:I\rightleftharpoons T_{3}:I.$ (2)

Because all individual fluxes are zero, no net transport takes place. On
average, for every substrate molecule that is moved from inside to outside in
a given unit of time, the same number of molecules are moved from the outside
to the inside.

We now perturb the system away from equilibrium by increasing the outside
concentration of the driving ion, as indicated by the larger number of driving
ions in Figure 3B. Following Le Chatelier’s principle, the equilibrium of the
binding reaction Eq. 1 is moved as to increase the concentration of products
(Dill and Bromberg, 2003), i.e., the number of ion-loaded transporters
$T_{2}:I$ increases above its equilibrium value. Because the reactants
(inputs) of the isomerization reaction Eq. 2 are provided by the products
(output) of the binding reaction Eq. 1, which have increased, Le Chatelier’s
principle equally applies to the isomerization and pushes this equilibrium
towards the ion-loaded inward facing conformation, $T_{3}:I$. The same
reasoning is applied to each subsequent reaction and in this way, net flux of
substrate from the inside to the outside is induced in steps 5$\rightarrow$6\.
Crucially, the reactions form a _cycle_ so that after the steps
1$\rightarrow$2$\rightarrow$3$\rightarrow$4$\rightarrow$5$\rightarrow$6$\rightarrow$1
the transporter is in exactly the same state as it was before. However, the
environment has changed as one ion was transported from the outside to the
inside and one substrate was transported from the inside to the outside with
1:1 stoichiometry, as expressed by the transport reaction of the antiporter

$\displaystyle I_{\text{out}}+S_{\text{in}}\rightarrow
I_{\text{in}}+S_{\text{out}}$ (3)

where $I$ stands for the driving ion and $S$ for the substrate and subscripts
indicate their location relative to the membrane. The corresponding reaction
of the symporter is

$\displaystyle I_{\text{out}}+S_{\text{out}}\rightarrow
I_{\text{in}}+S_{\text{in}}.$ (4)

Different stoichiometries require different stoichiometric coefficients. For
instance, a 2:1 antiporter would be described with
$2I_{\text{out}}+S_{\text{in}}\rightarrow 2I_{\text{in}}+S_{\text{out}}$.

The interested reader is referred to Hill (1989) who makes the above reasoning
quantitative by considering how the net fluxes between states, which are zero
in equilibrium, become biased in one direction when a component is perturbed.
Based on reaction kinetics he develops a theory of cycle fluxes that can be
applied to arbitrarily complex cycles to compute steady state populations and
fluxes. In particular, more realistic transporter schemes contain additional
transitions such as the one between the two apo states $1\rightleftharpoons
4$, often referred to as leaks or slippage. Such a transition would allow
three cycles to become possible: The transport cycle that was just described
and two leak cycles: cycle $1\rightleftharpoons 2\rightleftharpoons
3\rightleftharpoons 4\rightleftharpoons 1$ would dissipate the ionic gradient.
Cells spend a substantial amount of their chemical energy to establish the
driving ion gradient. In mammals an estimated 19%–28% of ATP are used to power
the Na+-K+-ATPase that establishes the transmembrane sodium gradient (Rolfe
and Brown, 1997). Therefore, dissipation of the sodium gradient is costly and
reduces the organism’s fitness. The other leak cycle $1\rightleftharpoons
6\rightleftharpoons 5\rightleftharpoons 4\rightleftharpoons 1$ would run in
the opposite direction and let substrate molecules enter the cell, counter to
the physiological necessity of the transporter to remove them from the cell.
Under physiological conditions, leak cycles must be suppressed by decreasing
the rate for slippage transitions such as $1\rightleftharpoons 4$.

The qualitative discussion makes clear that energy transduction, i.e., the use
of the free energy stored in the driving ion gradient, requires a _complete
cycle_ that contains both ion and substrate translocation steps. If any part
of the cycle is broken, no energy transduction can take place. Thus, energy
transduction is a property of complete cycles and not of individual states
(Hill, 1989). Therefore, there is no specific step in the cycle that could be
described as an “energized” state or a state where energy is “gained by a
binding reaction” (Hill and Eisenberg, 1981).

In general, a protein that functions according to the alternating access
mechanism cannot function if it presents a continuous, leaky pathway (Tanford,
1983) as this prevents energy coupling. Similarly, non-productive leak cycles
also reduce the efficiency of a transporter. Although here we generally
discuss ideal, fully efficient cycles to elucidate the basic principles, real
transporters leak and therefore their transport stoichiometry is generally not
the ideal one (Hill, 1989; Henderson, Fendler, and Poolman, 2019). For
example, instead of an ideal 1:1 stoichiometry one might measure only 1:0.75,
i.e., on average 1.33 driving ions are needed to move one substrate because
only 75% of the total flux comes from productive cycles (1:1 stoichiometry)
and 25% comes from leak cycles (1:0). However, not all leak cycles need to be
deleterious for an organism. Recent work by Zuckerman and collaborators
(further discussed in Section VI) indicates that leak cycles enable kinetic
control over selectivity (Bisignano  _et al._ , 2020). The rates for these
slippage transitions could serve as an additional set of molecular parameters
that may be varied by evolution to increase organismal fitness.

The ion and substrate binding or dissociation steps are necessary components
of the cycle because without them the cycle cannot be driven in a specific
direction: these steps provide the only external “handle” to control the
process (Zuckerman, 2019). Therefore, no cyclical process with a net flux in
one direction exists in which only a protein changes through a repeated
sequence of conformational states; coupling to an external source of free
energy is always necessary.

Finally, it is worth emphasizing that because the transporter protein moves
cyclically through different conformations, it is not altered in any permanent
way. In the energetic description of the process (see Section III.2 below),
the transporter does not appear. Thus, transporters act as enzymes for moving
substrate, similar to how biochemical enzymes catalyze the formation and
breaking of chemical bonds. In this sense, transporters are “physical enzymes”
or “molecular machines” in that they catalyze a physical process instead of a
chemical one. Other proteins of this kind are molecular motors, which turn
chemical energy into movement of the protein itself, or rotary pumps such as
the V-type and P-type ATPases, which turn chemical energy into rotary motion
and movement of protons or ions across the cell membrane; the latter can run
in reverse to turn rotary motion by ion flow into chemical bonds. Similarly,
transporters run backwards if the concentrations are changed appropriately,
which becomes obvious when analyzing the thermodynamic driving forces.

###  III.2 Driving forces

Quantitatively, the only thermodynamic driving forces $X_{i}$ are the ones
originating in electrochemical potential ($\mu^{\prime}=\mu_{0}+kT\ln
c/c_{0}+q\Psi$) differences of ions and substrates across the cell membrane
(Dill and Bromberg, 2003); free energy differences due to the different states
of the protein cancel in the whole cycle and play no role (Hill, 1989). The
driving force for species $i\in\\{I,S\\}$ is

$\displaystyle
X_{i}=\mu^{\prime}_{i,\text{in}}-\mu^{\prime}_{i,\text{out}}=kT\ln\frac{c_{i,\text{in}}}{c_{i,\text{out}}}+q_{i}\Delta\Psi$
(5)

where $c_{i}$ is the concentration (or activity) on the indicated side of the
membrane, $q_{i}$ the charge, $\Delta\Psi=\Psi_{\text{in}}-\Psi_{\text{out}}$
is the transmembrane potential, $T$ is the temperature and $k$ is Boltzmann’s
constant. The membrane potential is typically negative, $\Delta\Psi<0$. Thus,
for typical driving cations (Na+, H+ with $q=+1e$) and
$\Delta\Phi\approx-100\,\text{mV}$ the membrane potential contributes at
$T=298$ K about $q_{I}\Delta\Psi\approx-3.9\,kT$. Typical sodium
concentrations are on the order of $100$ mM on the outside and $10$ mM inside
a cell and hence $kT\ln\frac{c_{I,\text{in}}}{c_{I,\text{out}}}=-2.3\,kT$. If
the substrate is neutral (the electrostatic component is zero for $q_{S}=0$)
then a positive net charge is moved into the cell down an electrostatic
potential and a sizable fraction of the available free energy will be provided
from the membrane potential component. In general, any electrogenic transport
(movement of a net charge) is affected by the membrane potential.

Denote by $J_{i}$ the flux at which particle $i$ is transported across the
membrane (in particles per unit time), with the direction out$\rightarrow$in
counting as $J_{i}<0$ and the reverse as $J_{i}>0$. Note that in a simple
cycle such as the one in Figure 1, exactly one ion is moved for each substrate
molecule and hence the absolute values of these fluxes must be the same,
$|J_{I}|=|J_{S}|$ but the signs will differ, depending on symport or antiport
processes.

When the driving force is negative, e.g., $X_{I}<0$, then spontaneous movement
occurs, such as influx of the driving ion and hence $J_{I}<0$. The antiporter
is supposed to move substrate against a gradient from the inside to the
outside, i.e., against the opposing driving force $X_{S}<0$ under which $S$
particles would spontaneously move into the cell. The rate of free energy
dissipation is

$\displaystyle\Phi=J_{I}X_{I}+J_{S}X_{S}\geq 0.$ (6)

$\Phi=0$ holds in equilibrium but then no transport occurs (see Section
III.1). The second law of thermodynamics requires $\Phi>0$ in non-equilibrium
steady state, i.e., when concentrations remain fixed at their non-equilibrium
values and do not change (Hill, 1989). In steady-state, the transporter moves
ions and substrates at a constant flux. Under which conditions will the
antiporter move $S$ from inside to outside, i.e., given $J_{S}>0$ (even though
$X_{S}<0$), what is required of $I$? Rearranging Eq. 6

$\displaystyle J_{I}X_{I}>-J_{S}X_{S}$ (7)

and noting that the right hand side is positive, it follows that $J_{I}X_{I}$
also has to be positive, i.e., the driving ion must flow down its
electrochemical gradient from the outside to the inside ($J_{I}<0$,
$X_{I}<0$). In other words, spontaneous fluxes always dissipate free energy,
which can be coupled to the substrate flux. This free energy dissipation rate
must be larger than the rate of free energy required to move $S$ against its
driving force. For a simple antiporter cycle without leakage, $J_{S}=-J_{I}$
(for each $I$ transported to the inside, one $S$ is transported to the
outside, in the same amount of time) and hence $-J_{S}X_{I}>-J_{S}X_{S}$ and
with $J_{S}>0$,

$\displaystyle X_{I}<X_{S}\quad\text{(simple antiporter)}$ (8)

is required for transport, i.e., the electrochemical gradient of the driving
ion must be steeper and more negative than that of the substrate. In other
words, the amount of available free energy per driving ion translocation event
must be larger (more negative) than the substrate gradient against which $S$
is moved because out of equilibrium not all free energy can be transformed
into useful work and a fraction always increases the entropy of the universe
in the form of heat, as required by the second law. The condition Eq. 7 can
also be fulfilled with $J_{I}>0$, $X_{I}>0$, i.e., a spontaneous flux of ions
from the inside to the outside. In this case the transporter would need to
operate as a symporter to move driving ion and substrate _together_ —energetic
coupling cannot happen in separate cycles (Hill, 1989)).

For a simple symporter with $X_{I}<0$, $X_{S}>0$ and $J_{I}=J_{S}<0$, the
condition equivalent to Eq. 8 reads

$\displaystyle X_{I}<-X_{S}\quad\text{(simple symporter)}.$ (9)

We will come back to the question of the relationship between symporters and
antiporters in Section VI where we will see that one can write a universal
kinetic scheme that encompasses symporters, antiporters, and uniporters.

##  IV Inverted repeat symmetry

The alternating access model together with the thermodynamic cycle analysis
explains how transporters function in principle, i.e., they describe the
physical constraints under which any transporter protein has to operate.
However, understanding _how_ these principles are embodied in an actual
biomolecule requires structural atomic-resolution data, primarily provided by
X-ray crystallography and electron microscopy. The most important requirement
of the alternating access model is the existence of _two states_ that make
binding sites accessible to the outside _or_ the inside, generally referred to
as an _outward facing (OF) conformation_ and an _inward facing (IF)
conformation_. It has been hypothesized that a viable evolutionary path to
create a switchable two-state system in a single protein molecule can be based
on an internal two-fold structural symmetry, so-called _inverted repeats_.
This deep insight into a fundamental principle of transporter function was
only recently discovered by Forrest  _et al._ (2008) and since then broadly
recognized as nearly universal (Forrest, 2013, 2015).

###  IV.1 Inverted repeat structures

Structural symmetry is well represented among membrane proteins. These
symmetries can arise due to oligomerization, often seen in cyclically
symmetric channels and pores, or due to the presence of internal repeats
within the protein sequence (Forrest, 2015). Notably, internal repeats occur
more frequently in membrane protein super-families than overall (Myers-
Turnbull  _et al._ , 2014); in the case of secondary active transporters, most
known structures show an _inverted repeat symmetry_ (Bai, Moraes, and
Reithmeier, 2017; Shi, 2013)—that is, internal repeats which adopt similar
folds but start on opposite sides of the membrane, giving rise to $C_{2}$
pseudosymmetry about an axis parallel to the membrane plane. Further common to
most secondary active transporters is the presence of two bundles or domains,
with the substrate binding sites located near the interface and often
involving discontinuous helices (Shi, 2013). The exact number of transmembrane
helices and distribution of the inverted repeats over the two domains differs,
with several common folds observed (Figure 4):

Figure 4: Representative structures of common secondary active transporter
folds, highlighting the inverted repeats. In each case, the protein is first
shown whole, then with the repeats separated translationally, and finally with
the second repeat rotated and overlayed on the first. A: LacY (inward facing,
MFS fold; PDB ID IPV6) B: Mhp1 (outward facing, LeuT fold; PDB ID 2JLN) C:
ASBTNM (inward facing, NhaA fold; PDB ID 3ZUY). Images were produced with VMD
(Humphrey, Dalke, and Schulten, 1996).

##### (3 + 3) + (3 + 3): Major Facilitator Superfamily (MFS).

The core MFS fold contains 12 transmembrane helices (TMs) (Law, Maloney, and
Wang, 2008; Yan, 2013). An N- and C-domain are each formed from a pair of 3 TM
inverted repeats, and are themselves two-fold pseudosymmetric. The MFS is one
of the largest transporter families found across multiple organisms; the first
structures were reported for lactase permease LacY (Abramson  _et al._ , 2003)
and glycerol-3-phosphate transporter GlpT (Huang  _et al._ , 2003), with many
determined since.

##### (5 + 5): LeuT fold.

The LeuT fold consists of 5 TM inverted repeats, with the first two helices
from each repeat forming a core bundle (i.e. TMs 1, 2, 6, 7), while the next
two (TMs 3, 4, 8, 9) form a scaffold/hash domain; TMs 5 and 10 may act as
gates (Kazmier, Claxton, and Mchaourab, 2017). First observed in the
neurotransmitter/sodium symporter LeuT (Yamashita  _et al._ , 2005), several
other transporters have been found to adopt this fold, including the
sodium/hydantoin transporter Mhp1 (Weyand  _et al._ , 2008).

##### (5 + 5): NhaA fold.

Also consisting of 5 TM repeats, the NhaA fold is observed in sodium/proton
antiporters (e.g. NhaA (Hunte  _et al._ , 2005)) and the apical sodium
dependent bile acid transporter (ASBT) family (e.g. ASBTNM (Hu  _et al._ ,
2011)). The first two helices of each repeat (TMs 1, 2, 6, 7) form a panel or
dimer domain, with the remaining three (TMs 3-5, 8-10) forming a core domain
(Fuster and Alexander, 2014; Padan, 2014).

##### (7 + 7): 7-TM inverted repeat (7TMIR) fold.

Relatively recently identified, transporters with this fold include the
proton/uracil symporter UraA and chloride/bicarbonate antiporter AE1; four
helices from each repeat (TMs 1-4, 8-11) for a core domain, while the
remaining three (TMs 5-7, 12-14) form a gate domain (Chang and Geertsma,
2017).

Internal repeats such as these have been speculated to arise from the
duplication of an ancestor gene and subsequent fusion event, in this case
following a flip of one duplicate relative to the membrane; possible
candidates showing these initial “half” folds have been identified in the DedA
(for the LeuT fold) and SWEET (for the MFS fold) families (Keller, Ziegler,
and Schneider, 2014). The EmrE multidrug transporter is proposed to come
together as an antiparallel dimer and function through an exchange of
asymmetrical structures similar to that described below (Korkhov and Tate,
2009; Morrison  _et al._ , 2012), and represents a possible pre-fusion step in
the proposed duplication-and-fusion evolutionary process of inverted repeat
symmetry.

Distinct inward- and outward-facing conformations arise from asymmetry in the
exact conformations of the repeats composing the two domains (discussed in
Section IV.2), which changes the relative locations/orientations of these
domains. Several mechanisms for this relative motion have been proposed (Drew
and Boudker, 2016; Forrest, Krämer, and Ziegler, 2011): the domains may rotate
about the substrate binding site to alternatively expose it to each side of
the membrane, as in the _rocker-switch_ (where the domains are structurally
symmetric, proposed for MFS transporters (Radestock and Forrest, 2011)) and
_rocker-bundle_ (where the domains are distinct, e.g. for LeuT fold
transporters (Kazmier, Claxton, and Mchaourab, 2017)) mechanisms; or, as in
the _elevator mechanism_ , one domain predominantly containing the binding
site may move perpendicular to the membrane, moving the binding site against
to relatively fixed second domain to expose it to each side of the membrane in
turn (proposed for NhaA fold transporters (Padan, 2014; Drew and Boudker,
2016)).

###  IV.2 Asymmetry and alternating access

While inverted repeats share an overall fold, they are found to take on
different conformations, giving rise to an asymmetry that allows the substrate
binding site to be exposed to one side of the membrane while blocked from the
other. By exchanging conformations between the two repeats—with the first
repeat adopting the conformation of the second and vice versa—the protein is
thus able to switch between an inward facing and an outward facing state
(Forrest, Krämer, and Ziegler, 2011) (Figure 5). By breaking the symmetry
between the two inverted repeats in a symmetrical fashion, two conformational
states are naturally created.

Figure 5: Cartoon showing how symmetry-broken inverted repeats generate the
two major conformations in the alternating access mechanism. Each repeat
(labeled A and B) may take on one of two conformations (shown as 1 and 2 in
the inset), giving rise to 2 x 2 = 4 possible conformations, though two
(occluded and “leak” states, shown inset) are not part of the basic
alternating access mechanism.

Exchanging conformations in this way is hypothesized to require no or little
net energetic change in the overall protein structure from the inward-to-
outward or outward-to-inward transitions (Forrest, 2015). The presence of two
possible conformations for each of the two repeats also brings up the question
of whether the repeats can possess the same conformation at a given time; such
overall conformations might form occluded (closed at both side) or leaky (open
on both sides) states of the transporter (Figure 5; inset). The presence of
occluded and leak states in the transport cycle is discussed further in
Section V.

The above described _repeat swapping_ has been taken advantage of to generate
homology models of transporters in different states, given a structure in only
one state: the conformation of each repeat is used as a template for the
other, forcing the exchange of conformations (Vergara-Jaque  _et al._ , 2015).
This method was first applied to LeuT (Forrest  _et al._ , 2008), producing a
structure that latter proved to be consistent with an experimental structure
(Krishnamurthy and Gouaux, 2012), and has since been used to generate
structures for a range of secondary active transporters, with subsequent
experimental validation obtained in several cases; including the glutamate
transporter GltPh (Crisman  _et al._ , 2009; Reyes, Ginter, and Boudker,
2009), LacY (Radestock and Forrest, 2011), CcdA (Zhou and Bushweller, 2018),
and NhaA (Schushan  _et al._ , 2012).

##  V Transporters as gated pores

Läuger (1980) envisaged ion channels as pores with a single free energy
barrier, which can be identified with the gate of the channel that controls
ion flow in response to external stimuli (Hille, 2001). He could model
transporters as pores with two coupled barriers (Läuger, 1980); motivated by
the suggestive original “gated pore model” (Klingenberg, 1979) (which was more
precisely renamed the “single binding center gated model” (SBGP) (Klingenberg,
2007)) one may also call these two barriers gates (Figure 6) (Abramson and
Wright, 2009; Krishnamurthy, Piscitelli, and Gouaux, 2009; Forrest, Krämer,
and Ziegler, 2011). Such a gate should be thought of as a switch or bi-stable
element that can exist in two states that are generally called “open” and
“closed” although it might also carry the meaning “outward facing” or “inward
facing”. The gate picture reduces the nuanced view of free energy barriers
with variable barrier height to one in which either a very high barrier exists
(“closed”) or the barrier is small compared to thermal fluctuations (“open”).
This simplification allows one to broadly enumerate and categorize states and
make general (but necessarily approximate) statements for whole classes of
proteins. It also allows one to create simple cartoons of transporter states
that summarize transporter conformations succinctly. As will be shown below,
the cartoon is a useful abstraction because gates correspond to physical
molecular domains in transporter proteins (i.e., they have a molecular
identity) and thus states generated from the gate picture directly correspond
to observable protein conformations.

Figure 6: Ion channels and transporters as gated pores. In this simplified
picture, ion channels contain a single gate that is controlled by external
stimuli. Transporters can implement alternating access by the coordinated
movement of two or more gates. The number of gates $N$ determines the total
number of distinct states, $2^{N}$. Not all states might be physiologically
observed, and some, such as the leak states, will prevent energy transduction.

In ion channels, a change in membrane potential or binding of a signaling
molecule opens the gate and ions spontaneously flow through the open pore down
their electrochemical gradient (Hille, 2001), as shown for a pore with $N=1$
gate in Figure 6.333Describing a channel with a single gate is an
oversimplified picture because many ion channels contain an activation gate
and a separate inactivation gate, which switches the channel into a relatively
long lasting inactive state (Hille, 2001). These gates are typically coupled
to some degree, e.g., the inactivation gate might only close when the
activation gate has closed but the coupling is presumably different from the
coupling between gates that enables energy transduction in transporters. In
the “transporters as gated pores” picture, the coordinated movement of two (or
more) gates creates the conformations of the alternating access model (Section
II). The outward facing open state is formed when the outer gate opens while
the inner gate remains closed. Conversely, the inward facing state consists of
the outer gate closed, while the inner one is open, as shown for a transporter
with $N=2$ gates in Figure 6. Simultaneous opening of both gates must be
avoided—a “leak” state (see Figure 6)—to prevent leakage of the driving ion
and dissipation of the ionic gradient. The coordination of the gates is termed
“coupling”. Furthermore, conformational changes (i.e., changes in the gates)
must also be coupled to the binding/dissociation of driving ion(s) and
substrate(s), a point that will be revisited below and explicitly included in
Section VI. For simplicity, we will focus on the different conformational
states of the protein while keeping in mind that the presence of ions and/or
substrates will likely change the structure to some degree.

It has been observed experimentally that under certain conditions transporters
can also function as channels (DeFelice and Goswami, 2007), a view that fits
naturally in the picture of a transporter whose gates are not fully
coordinated so that leak states may occur (see Figure 6) although many
questions remain in this somewhat under-explored area. Channel-like behavior
is characterized by spontaneous energetically downhill diffusion of ions (or
substrates) in a non-stoichiometric and burst-like fashion, which differs from
the leak cycles that can occur in the standard cycle due to loose coupling
(Henderson, Fendler, and Poolman, 2019) in that the latter still only move
individual particles. Even for the channel-like behavior of transporters, it
is not necessarily clear that the canonical transport pathway is used. It is
possible that alternative pathways through the protein are responsible
(Vandenberg, Huang, and Ryan, 2008).

Nevertheless, the “transporters as gated pores” picture is more than just a
convenient cartoon model because as we will discuss below, the gates generally
represent a molecular reality, i.e., secondary transporters contain
distinguishable parts that function as gates. Therefore, conformational states
that are predicted from the gated pore model generally correspond to
conformations with distinct structural arrangements of the corresponding
gates.

###  V.1 Gates as molecular building blocks

Since X-ray crystallography has revealed the molecular structures of a range
of transporters, various authors have identified domains of these proteins
that regulate access to binding sites with gates, as summarized by Forrest,
Krämer, and Ziegler (2011). A particular terminology of _thin_ and _thick_
gates originated in the structural analysis of LeuT-like transporters
(Krishnamurthy, Piscitelli, and Gouaux, 2009; Abramson and Wright, 2009). Thin
gates are generally considered to be parts of the protein whose movement can
prevent the exchange of ions or substrates with the intra- or extracellular
solution. Perhaps somewhat confusingly, the conformational transition that is
responsible for alternating access, or rather the sum of moving structural
elements, is sometimes considered the thick gate. In other transporter
families, such as the MFS transporters, no special distinction between thin
and thick gates is commonly made.

Although there is some ambiguity in how to define gates, they are nevertheless
recognizable molecular entities. Diallinas (2014) concludes, based on work in
the purine transporter UapA, that physiological transport properties are
determined by intramolecular interactions between binding sites and gating
elements, similar to ones present in channels. LeVine  _et al._ (2016)
quantitatively analyzed the mechanism of the LeuT transporter with a
particular emphasis on the allosteric coupling between ions, substrate, and
the protein. Based on experimental and simulation data, they concluded that
LeuT is best described with an _allosteric gated pore alternating access
mechanism_ in which gate movement is strongly coupled to binding and the other
gates.

We will illustrate the physical reality of gates in transporters in an
example, the Mhp1 transporter (a member of the LeuT-like family of APC (amino
acid-polyamine-organoCation) transporters (Västermark  _et al._ , 2014)), and
in Section V.2, where also members of the major facilitator superfamily (MFS)
(Marger and Saier, 1993) will be included.

#### Thin and thick gates in Mhp1

Figure 7: The three gates in Mhp1. A: Mhp1 in the membrane. The hash motif
(helices 3, 4, 8, 9) is shown in yellow, the bundle (helices 1, 2, 6, 7) in
red, flexible (thin gate) helices 5 and 10 in blue, and C-terminal helices 11
and 12 in gray. The views on the gates (B–D) are indicated by broken
rectangles. B: extracellular thin gate (formed by TM10). C: thick gate,
quantified by the distance across the Na2 sodium binding site. D:
intracellular thin gate (TM5). Images were produced with VMD (Humphrey, Dalke,
and Schulten, 1996).

The hydantoin permease Mhp1 from _Microbacterium liquefaciens_ is a
nucleobase-sodium symporter (Suzuki and Henderson, 2006), a member of the NCS1
family. It co-transports one sodium ion with one 5-substituted hydantoin. It
shares a five-helix inverted repeat architecture with other members of the
superfamily of LeuT-like transporters (Cameron, Beckstein, and Henderson,
2013). X-ray crystallographic structures of Mhp1 in outward facing and inward
facing conformations together with computer simulations, mass spectometry, and
electron paramagnetic resonance (EPR) measurements revealed the structural
basis for the alternating access mechanism in this secondary transporter
(Weyand  _et al._ , 2008; Shimamura  _et al._ , 2010; Zhao and Noskov, 2013;
Simmons  _et al._ , 2014; Kazmier  _et al._ , 2014a; Calabrese  _et al._ ,
2017; Li, Zhao, and Tajkhorshid, 2019). The transporter can be understood as a
gated pore with two thin and one thick gate (Krishnamurthy, Piscitelli, and
Gouaux, 2009), i.e., as a pore with three gates: The thick gate regulates the
passage through the center of the membrane by means of the large
conformational change that switches the transporter from its outward facing to
its inward facing conformation. In Mhp1 it consists of the hash motif (formed
by helices TM3, TM4 and their inverted-repeat counterparts TM8 and TM9; see
Figures 7A, C and 4B) that can rotate by about $30^{\circ}$ on an axis
parallel to TM3 relative to the four-helix “bundle” (TM1, TM2 and TM6, TM7)
(Shimamura  _et al._ , 2010). Thin gates are formed by the N-termini of the
pseudo-symmetry related helices TM5 and TM10 and the linker to each preceding
helix (Shimamura  _et al._ , 2010). The extracellular (EC) thin gate (TM10;
Figure 7B) governs access to the substrate binding site from the periplasmic
medium while the intracellular (IC; Figure 7D) gate fulfills the symmetrical
role of controlling the pathway to the cytosol.

The sodium binding site is formed between bundle and hash motifs, so opening
of the thick gate, i.e., the alternating-access transition, opens up the
sodium binding site and weakens ion binding to ensure rapid diffusion of the
ion into the cytosolic compartment and opening a pathway for the substrate to
follow (Shimamura  _et al._ , 2010; Zhao and Noskov, 2013).

The role of the thin gates in Mhp1 appears to be more subtle (and might well
differ from the role of thin gates in related NSS-like transporters such as
LeuT (Kazmier  _et al._ , 2014a, b; Kazmier, Claxton, and Mchaourab, 2017)).
In Mhp1, the whole N-terminus of TM10 moves together with the linker between
TM9 and TM10 (Weyand  _et al._ , 2008; Shimamura  _et al._ , 2010; Kazmier
_et al._ , 2014a), thus forming a distinct gate structure that is mirrored in
TM5 and the TM 4-5 linker, which are related to TM9/10 through the inverted-
repeat symmetry as described in Section IV and shown in Figure 4B.

Figure 8: The putative role of the extracellular (EC) gate of Mhp1 is to
prevent a sodium leak when the thick gate is open. The left four panels show a
cut through the electrostatic solvation free energy (Born energy) landscape of
a Na+ ion inside Mhp1 for different conformations of the transporter, computed
with the Poisson-Boltzmann equation. Red ($-10$ kJ$\cdot$mol-1) to yellow
($+10$ kJ$\cdot$mol-1) regions can be considered accessible for sodium ions
under typical conditions. (The Na+ Born energy was calculated as described
previously (Stelzl  _et al._ , 2014).) The gate cartoons in A–C represent some
of the states for the triple-gated transporter in Figure 6; the cartoon in D
symbolizes a leaky state that was artificially modeled by removal of the EC-
gate portion of TM10. A: Outward facing open conformation (EC gate open, thick
gate closed). B: Inward facing open conformation (EC gate closed, thick gate
and IC gate open). The solvent accessible surface (cyan) is shown from the
side in the context of the protein helices (view on the surface from the top).
The color scheme for the helices is the same as in Figure 7, except that the
N-terminal half of the EC gate (TM10) is shown in black. The closed EC gate
prevents a continuous sodium pathway. C: Outward facing occluded conformation
(EC gate closed, thick gate closed). D: Simple model for a hypothetical inward
facing open, leaky conformation with IC gate and thick gate open and EC gate
removed. The solvent accessible surface representation and the electrostatic
free energy show a sodium pathway through the membrane-spanning portion of the
transporter. Images were produced with UCSF Chimera (Goddard, Huang, and
Ferrin, 2007) and PyMOL (Schrödinger, LLC, ).

As discussed in Section II, a protein that functions according to the
alternating access mechanism cannot function if it presents a continuous,
leaky pathway (Tanford, 1983) [or if it allows too many non-productive leak
cycles to occur (Section III)]. The EC gate appears to prevent Mhp1 from
leaking the driving ion, Na+, as demonstrated by modeling: Figure 8B shows
that in the inward facing conformation, with the EC gate closed, the solvent
accessible surface only extends from the IC side into the binding site at the
center of the protein. However, when the EC gate is removed (the atoms were
deleted from the structure as a simple model of a hypothetical inward facing
conformation with an open EC gate) a pathway opens up through the membrane
(Figure 8D). The calculated electrostatic solvation free energy (Born energy)
in the volume of the pathway shows that Na+ ions could traverse the membrane
because a low-energy path is visible (Figure 8D). On the contrary, in all
other states, no low energy path can be found for a sodium ion (Figures 8A–C)
because either the thick gate or the EC gate blocks the passage. Thus, the EC
gate fulfills an important role in preventing a sodium ion leak when the thick
gate is in its open, i.e., inward facing state. When the thick gate is closed
(outward facing), the EC gate only regulates access to the binding site from
the extracellular compartment.

Additionally, the EC gate is involved in substrate selectivity (Simmons  _et
al._ , 2014). Mhp1 transports 5-substituted hydantoins where the substituent
must be a bulky hydrophobic moiety such as a benzyl or indolylmethyl group.
However, if the 5-substituent is too voluminous such as a naphtyl group,
transport is inhibited even though the molecule binds tightly. A crystal
structure of outward-facing Mhp1 with 5-(2-naphthylmethyl)-L-hydantoin bound
revealed that the EC gate was trapped in an open conformation due to a steric
clash of the naphtyl ring with Leu363 (Simmons  _et al._ , 2014). A Leu363Ala
mutant of Mhp1, which removes the clash, was competitive for transporting
5-(2-naphthylmethyl)-L-hydantoin. These results strongly suggest that closure
of the EC gate is required for the alternating access transition to occur. In
the language of the gated pore view, the thin EC gate is coupled to the thick
gate. Structural comparison suggests that this coupling is due to the
geometrical architecture and the direct connection of the rotating hash motif
to the EC gate through the 9-10 linker. The thick gate cannot move into the
space occupied by the open EC gate and therefore is prevented from closing.
Conversely, the open thick gate appears to latch the EC gate in its closed
position (Shimamura  _et al._ , 2010), possibly helped by changes in the
extracellular EL4 loop (Song and Zhu, 2015).

###  V.2 Gate states

Thinking of transporters as consisting of $N$ gating elements that can
individually switch between two states (such as open and closed as in Figure
6) suggests a simple count to enumerate the possible number of conformations
of the transporter,

$\displaystyle n_{C}=2^{N}.$ (10)

For a transporter with two gates, four states are possible, and eight states
for $N=3$.444We equate a state with a conformation of the transporter,
assuming that each state is formed by an distinguishable ensemble of
conformers near the specific conformation. This typically implies that there
is a kinetic separation between states. Although this is not necessarily
always the case in practice, we will nevertheless use state and conformation
interchangeably to keep the discussion simple. The simple count ignores the
fact that gate movement must be coordinated in some fashion. The type of
coupling will depend on the individual molecule and may even depend on the
substrate (Henderson, Fendler, and Poolman, 2019) but for canonical transport
one might want to assume that a leak state with all gates open plays no
important role and so $n_{C}=2^{N}-1$.555One could write $n_{C}=2^{N}-F$ where
$0\leq F<2^{N}$ is the number of “forbidden” conformations if one knew through
other means which conformations were not accessible.

The primary advantage of such a simple enumeration is to provide a framework
in which to place experimentally or computationally observed conformations.
Forrest, Krämer, and Ziegler (2011) proposed a similar classification with
eight states, consisting of different conformations and with differing
substrate occupancy. Their scheme makes use of thin gates but places central
importance on the major conformational switch between inward and outward
facing conformations. It has been successfully used to, for instance,
categorize the wealth of structural data for the APC transporter BetP, for
which crystal structures have been obtained for most of the states (Ressl  _et
al._ , 2009; Perez  _et al._ , 2012, 2014), and to analyze simulated
transitions for four LeuT-fold transporters (Jeschke, 2013).

An almost trivial prediction of the gated pore model is the existence of
_occluded states_. In an occluded state, the transporter obtains a
conformation in which the binding sites are not accessible from either
compartment. In the doubly-gated pore, the occluded state naturally arises
when the two gates are closed ($N=2$ in Figure 6). The alternating access
model and the associated kinetic and thermodynamic analysis do not require
occluded states for energy transduction and vectorial transport. Therefore,
the existence of occluded states, which are not strictly necessary for
function, could be interpreted as a consequence of the structural constraints
of the implementation of alternating access (via inverted repeat symmetry) in
proteins. Below we will show some structural evidence for occluded states. But
it is also noteworthy to point out that molecular dynamics (MD) computer
simulations have been able to generate occluded states when started from
crystallographic conformations corresponding to inward or outward facing
states: For example, Latorraca  _et al._ (2017) simulated the LbSemiSWEET
transporter with unbiased MD and observed full transitions from outward to
inward facing states that passed through an occluded state. The simulation
spontaneously reached experimentally determined structures for inward open and
occluded LbSemiSWEET. They found that the transitions were driven by favorable
inter-helical interactions when either the extracellular or the intracellular
gate closed and and unfavorable helix configuration when both gates were
closed. The two gates became tightly coupled, which prevented simultaneous
gate opening, which would result in a leak state. Other simulation examples
are discussed below, which all point to the insight that molecular gates are a
simple way to generate alternating-access states. In the absence of specific
coupling that prevents two gates from closing at the same time, occluded
states will occur.

####  V.2.1 MFS transporters: two gates

The MFS transporters all share a common fold with four inverted repeats
(Figure 4A). It was originally believed that alternating access would proceed
by a rigid body movement whereby the two halves of the protein would move
relative to each other in a “rocker switch” manner (Law, Maloney, and Wang,
2008). The discussion concentrated on LacY for which an alternative model
described the protein as more flexible, with cytoplasmic and periplasmic
openings governing access to the binding site, effectively describing gates
(Kaback  _et al._ , 2007). The existence of an occluded state in LacY would
corroborate the gated pore model for its mechanism. Stelzl  _et al._ (2014)
hypothesized that LacY functioned as a pore with two coupled gates that could
both close at the same time. With this assumption they could perform biased MD
simulations to generate a model of occluded LacY with both gates closed. The
model broadly agreed with experimental electron-electron resonance (DEER)
spectroscopy data. More recently, experimental evidence for an occluded apo
intermediate of LacY (based on sugar accessibility to cysteine cross-linked
mutant) (Smirnova, Kasho, and Kaback, 2018) corroborated the occluded model.

Figure 9: Conformational state of MFS transporters from a survey of crystal
structures. The gray rectangles approximately indicate classification of the
structures as outward open, occluded, or inward open. A Minimal pore radii $R$
computed with HOLE (Smart  _et al._ , 1996) near the periplasmic and
cytoplasmic entrance. A conformation is classified as occluded if both $R\leq
1.2$ Å. B Gate distances $d$, calculated as the minimum distance between the
Cα atoms of the relevant pairs of helix tips H1,2,7,8 (periplasmic gate) or
H4,5,10,11 (cytoplasmic gate) (Fowler  _et al._ , 2015). A conformation is
classified as occluded for both $d\leq 9$ Å. Figure drawn after Fowler  _et
al._ (2015).

The MFS transporter PepTSo is a proton-coupled bacterial symporter for which
only inward facing crystal structures are known (Newstead  _et al._ , 2011;
Fowler  _et al._ , 2015). An open question has been the nature and molecular
mechanism of the conformational transition between inward and outward
conformation. Fowler  _et al._ (2015) used an array of experimental and
computational techniques, including X-ray crystallography, DEER, and MD, to
elucidate the dynamics of PepTSo. They found that PepTSo is representative for
a large number of MFS transporters in that the ends of the first two helices
in each of the four inverted repeats (see Figure 4A) form gates at the EC and
IC entrance. A wealth of structural data exists for the MFS transporters (Yan,
2013) with many transporter structures having been solved to atomic resolution
in different conformations. Fowler  _et al._ (2015) analyzed 33 MFS structures
in terms of the minimal pore radius near the periplasmic (extracellular, EC)
and cytoplasmic (intracellular, IC) entrance (Figure 9). The structure could
neatly be categorized as outward facing, inward facing, or occluded, based
either on geometrical constriction radius (Figure 9A) or on the distances of
the inverted-repeat gates (Figure 9B).

Using multiple MD simulation with a Markov state model, Selvam, Mittal, and
Shukla (2018) sampled conformational transitions from the inward facing
conformation through an occluded state to an outward facing conformation of
PepTSo. Their computational results were validated by comparison of simulated
with experimental DEER spectroscopy data. The occluded state formed by closure
of both ends of the protein. In a computed free energy landscape, the occluded
conformation occupied a stable local minimum, as expected for a thermodynamic
state.

Overall, the evidence suggests that MFS transporters can be described as
transporters with two gates. The gates are related to their internal repeat
symmetry. Coupling allows occluded states to occur, which were found to exist
in crystal structures and MD simulations.

####  V.2.2 Mhp1: three gates

Figure 10: Molecular dynamics simulations sample an inward facing occluded
state of Mhp1. A Gate distances (see Figure 7) from 100-ns MD trajectories of
Mhp1 with a Na+ ion in the Na2 site (simulations from Shimamura  _et al._
(2010) and additional unpublished data). Contour lines are drawn at 20%
increments of probability density. The shaded area indicates the full extent
of order parameters explored in the simulation. Simulations started from
crystal structures (circles) in three different conformational states
(represented by the PDB ID), except for the magenta trajectories, which were
started from a frame of the _inward facing open_ simulation (gray) that showed
an almost closed intracellular gate. Data for three independent simulations
each starting from the outward facing states (blue and red) are shown together
with one from the inward facing open (gray) and two from the inward facing
occluded (magenta) states. B, C Putative inward-facing occluded conformation
of Mhp1 (snapshot from the high-probability region of the _inward facing
occluded_ trajectory (magenta) in A). The cut through the transporter is shown
in the same way as the crystal structures in Figure 2. D Inward facing open
crystal structure (PDB ID 2X79) with the open IC gate. Molecular images were
drawn with PyMOL (Schrödinger, LLC, ).

As an example of a transporter that can be described with three gates we look
at Mhp1 again. The crystallographic structures in Figure 2 show an occluded
state (Weyand  _et al._ , 2008; Simmons  _et al._ , 2014) in addition to the
outward (Weyand  _et al._ , 2008) and inward facing states (Shimamura  _et
al._ , 2010) that are necessary for alternating access. Given the definition
of the three gates (see Figure 7), the crystallographic occluded structure is
in an outward-facing occluded conformation because the thick gate is closed
(outward facing) and both thin gates are also closed. MD simulations had shown
that the thin gates could change conformations on the 100-ns time scale
(Shimamura  _et al._ , 2010). A detailed analysis of the simulations in terms
of the gate distances (Figure 10A) showed that the EC gate was mobile when the
thick gate was closed (outward facing conformation) and the simulations
sampled both outward open and outward occluded conformations. The IC thin gate
remained locked, though. Conversely, once the thick gate was open (inward
facing conformation), the EC gate was locked and the IC gate could sample open
and closed conformations. The dynamic behavior of the thin gates reflects the
two-fold symmetry that is imposed by the inverted repeat symmetry (Figure 4B).
Using site-directed spin labeling and DEER spectroscopy, Kazmier  _et al._
(2014a) showed that the IC gate formed by TM5 undergoes motions between open
and closed conformations, in agreement with the computational results.

The crystallographic inward facing structure(Shimamura  _et al._ , 2010) (PDB
ID 2X79) shows the IC gate in a wide open position666The crystals that
produced the inward facing open structure with PDB ID 2X79 only formed when
cells were grown on minimal medium with seleno-L-methionine (Shimamura  _et
al._ , 2010). The electron density map of 2X79 contains a blob of unidentified
density in the inward facing cavity that appears to have wedged open the IC
gate and stabilized the IF conformation. It is possible that the unidentified
molecule(s) held the IC gate in an especially wide open position from which it
relaxes in the MD., corresponding to an inward open structure. The MD
simulations with the thick and both thin gates closed showed that a second
occluded state might exist (Figure 10B,C), as predicted by a pore with three
gates (Figure 6). Thus, the MD simulations sampled one additional conformation
predicted for a triple-gated pore, bringing the total observed to 4 out of 7
(discounting the leak state). They also suggest that some other conformations
are not observable because of coupling between thick and thin gates. For
example, opening of the thick gate while the EC gate was open was
experimentally ruled out (Simmons  _et al._ , 2014) (see also the discussion
in Section V.1); conversely the MD suggested that the EC gate will remain
closed when the thick gate is open. These observations rule out two more
putative states (EC open/thick open/IC closed and the leak state, EC
open/thick open/IC open). The remaining two states (EC closed/thick closed/IC
open and EC open/thick closed/IC open) seem unlikely based on the MD, which
showed that the IC gate is locked when the thick gate is closed, so that a
closed thick gate prevents an open IF gate. Based on this analysis, only 4 out
of 8 possible states, namely the three crystallographic conformations (OF
open, OF occluded, IF open) and the MD-based prediction for IF occluded,
should be the observable conformations for Mhp1. Further experiments and
simulations will be necessary to confirm the coupling between the three Mhp1
gates as predicted from qualitative observations.

An analysis based on gate states is general but limited in important details
and must be augmented with additional information about the relative stability
of the states. For example, under physiological conditions, the inward facing
conformation is more prevalent than the outward facing one although this can
be changed with the addition of substrate (Kazmier  _et al._ , 2014a;
Calabrese  _et al._ , 2017). The DEER experiments suggest that some
conformations such as the inward facing occluded one might be much shorter
lived than other ones (Kazmier  _et al._ , 2014a). Such quantitative
information is crucial in order to interpret kinetic reaction diagrams based
on the predicted states, as discussed in the next section.

##  VI Unified transport cycle model

Figure 11: Unified picture of transporter function for a hypothetical
transporter with a 1:1 stoichiometry between driving ion (red circle) and
substrate (blue square) and two gates. All combinations of conformational
states with bound ion and/or substrate are listed. Leak states are omitted for
simplicity. When an ion or substrate is shown, the corresponding binding or
dissociation reaction is implied. Depending on the physiological function
(symbol on the right), only certain sequences of states are visited (in the
idealized case) while others (grayed out) are not part of the cycle. A
Symporter. (The cycle drawn here corresponds to the one in Figure 1A; the
alternative binding sequences 1$\leftrightarrow$2$\leftrightarrow$4 and
9$\leftrightarrow$11$\leftrightarrow$12 might also occur.) B Antiporter. (The
cycle corresponds to the one in Figure 1B; the alternative binding sequences
2$\leftrightarrow$4$\leftrightarrow$3 and
10$\leftrightarrow$12$\leftrightarrow$11 might also occur.) C Uniporter. D
Unified transport cycle with all possible kinetic paths.

In our enumeration of gate states we have implicitly assumed that these states
do not depend on the binding of driving ions or substrate. Such an assumption
is not warranted. For instance, the symporter in Figure 1A must avoid leak
cycles that involve a slippage transition between the inward- and outward-
facing transporter conformations when only the ion is bound or it would just
dissipate the ion gradient. Mechanistically, the absence of the substrate when
the ion is present must be changing the free energy landscape of the
transition (Läuger, 1980) in such a way that the ion-only transition faces a
much higher barrier than the fully loaded transporter. In other words, binding
of an ion _and_ a substrate unlocks the transporter and enables the
conformational transition to occur as experimentally found for the aspartate-
sodium symporter GltPh (Akyuz  _et al._ , 2015). A similar argument can be
made for the antiporter cycle in Figure 1B where the transition between the
empty inward and outward-facing states needs to be suppressed to avoid leak
cycles that only dissipate the ion. In this case, binding of the ion _or_ the
substrate unlocks the transporter. In both cases it is clear that presence or
absence of bound ion and/or substrate corresponds to a protein with different
energetics from, say, the unloaded conformation.

Consequently, the number of available states of a transporter will be the
product of the number of conformational states $n_{C}$ with the number of ways
to bind driving ions and substrates. We can estimate $n_{C}$ from the gate
model as $n_{C}=2^{N}-1$ for $N$ gates and a leak state excluded. Assuming an
ion:substrate stoichiometry of $\nu_{I}$:$\nu_{S}$ and making the simplifying
assumption that there are $\nu_{I}$ ion binding sites and $\nu_{S}$ substrate
binding sites, there are
$n_{j}=\sum_{k=0}^{\nu_{j}}\binom{\nu_{j}}{k}=2^{\nu_{j}}$ ways to distribute
zero to $\nu_{j}$ particles over $\nu_{j}$ binding sites. Hence the number of
states in the model is

$\Omega(N,\nu_{I},\nu_{S})=n_{C}n_{I}n_{S}=(2^{N}-1)\,2^{\nu_{I}+\nu_{S}}$
(11)

(If ions and substrates compete for overlapping binding sites then $\Omega$ is
less than the value given by Eq. 11.)

For example, for the transporters in Figure 1, $\nu_{I}=\nu_{S}=1$ and with
$N=2$, $\Omega=3\times 4=12$ different states should be considered, as shown
in Figure 11. In principle, all theoretically possible transitions between
states (arrows in Figure 11) contribute to an overall transport process (Hill,
1989). In our example, occluded states are included for completeness. However,
occluded states (numbers 5–8) cannot exchange with each other and their effect
could be replaced with an effective rate constant between the outward facing
and inward facing conformations that are connected by the occluded state.

If we follow Zuckerman (2019) and consider three different idealized
processes, in which certain transitions are suppressed by virtue of low
kinetic rate constants (Hill and Eisenberg, 1981) (grayed out in Figure 11),
then we recognize the transport cycle for a symporter (Figure 11A) and for an
antiporter (Figure 11B). The same observation had been made by Robinson  _et
al._ (2017), who postulated a _free exchange model_ for the EmrE transporter.
Furthermore, by suppressing transitions that involve the driving ion and only
retaining a cycle that contains the alternating-access transition with either
substrate bound or the empty transporter, a simple uniporter model emerges
(Figure 11C). In this case, no energy coupling occurs and the substrate will
move down its electrochemical gradient by facilitated diffusion.

The idealized cycles could be made more realistic by retaining all transitions
related to ion and substrate binding (1–4 and 9–12 in Figure 11) while still
suppressing the undesirable conformational transition (e.g., the ion leak
pathway 2$\leftrightarrow$11 for the symporter in Figure 11A). With these
additional transitions included, different sequences of binding or
dissociation reactions would be included in the models for the symporter and
antiporter. A uniporter might be able to bind a driving ion but not transport
it. Overall, the three physiologically very different types of transporters
only differ in which of the alternating-access transitions is forbidden (or
strongly suppressed). One can imagine that mutations may differentially change
the transition rates and so switch the function of transporter from, say, a
symporter to a uniporter (as seen in the MFS sugar transporters (Madej  _et
al._ , 2014)) or an antiporter to a symporter as reviewed by Henderson,
Fendler, and Poolman (2019). Occluded states are now seen as a possible
control point to tune the function: for instance, in order to block an
outward$\leftrightarrow$inward transition, only one partial transition to or
from the occluded state needs to be blocked.

The unified view of transporter function (also known as the free exchange
model) has recently been investigated in more detail. The Henzler-Wildman
group ran computational models that indicated that, given the known parameters
of the EmrE transporter (Robinson  _et al._ , 2017), the protein should be
able to switch between symport and antiport mode based on external
concentrations (Hussey, Thomas, and Henzler-Wildman, 2020). In a commentary on
the EmrE work, Grabe, Zuckerman, and Rosenberg (2019) outlined how slippage
processes should be considered an important part of transporter function. They
then went on to demonstrate computationally how slippage pathways can provide
a form of proof-reading and a new kind of selectivity mechanism for
transporters (Bisignano  _et al._ , 2020). Specifically, they showed how the
bacterial vSGLT sodium:sugar symporter might be able to discriminate
carbohydrate substrates from very similar toxic compounds and under certain
conditions even export toxins. Furthermore, Zuckerman and co-workers employed
a systematic approach to explore the space of all transport reactions (Figure
11D) to computationally engineer transporters with specific functions such as
antiport or symport with specific selectivities (George  _et al._ , 2020).
Overall, there is increasing evidence that the unified transport cycle model
is a useful and comprehensive framework in which to understand the continuum
of secondary transporter function.

##  VII Conclusion

We provided a perspective on broad and general principles that apply to
secondary active transporters. Transporters are seen as catalysts or “physical
enzymes” that enable transport across the cell membrane against an
electrochemical gradient by transducing free energy from the electrochemical
gradient of a driving ion. Energy transduction requires cyclical reactions
that include both driving ion and transported substrate. The alternating
access model provides a simple scheme through which such cycles can be
established. The protein must exist in at least two distinct conformations in
which the binding sites are exposed only to either the outside or the inside
solution. Importantly, no energy transduction is possible if a continuous pore
is established. The two protein conformations that are needed for the two
alternating access states are related by a structural two-fold pseudo symmetry
that originates in inverted repeats in the protein’s genetic sequence. A
description of transporters as gated pores is fruitful in many cases because
gates (two state switches) can be identified with structural elements in the
transporter. Enumerating all distinct gate states naturally includes occluded
states in the alternating access picture and also suggests what kind of
protein conformations might be observable. By connecting the possible
conformational states and ion/substrate bound states in a kinetic model, a
unified picture emerges in which symporter, antiporter, and uniporter function
are extremes in a continuum of functionality.

Many open questions remain. For example, the molecular mechanism of coupling
between conformational changes and ion/substrate binding and allosteric
interactions between gates need to be evaluated for most known transporters.
General theories of allosteric coupling will likely be helpful to define the
specific quantitative questions that need to be asked (LeVine  _et al._ ,
2016). Occluded states were explained as a consequence of the existence of
gates in transporters, so a natural question to ask is if all transporters
have occluded states, and if so, are they ultimately a consequence of the
symmetries of the inverted repeats? It is tempting to speculate that occluded
states are the fully symmetrical high energy conformations whose energy is
lowered by symmetry breaking. There remain classes of transporters for which
we do not have sufficient structural evidence to answer the question although
simulations (as shown here) have started filling this gap. The unified model
indicates that transporter function forms a continuum. However, how difficult
is it to move through this continuum, what are the minimal changes to change
physiological function? Could such changes be achieved with allosteric
modulators (small molecules) or changes in external conditions such as
membrane tension, pressure, temperature, or transmembrane voltage?

More broadly speaking, it has also been recognized that channels and
transporters form a spectrum (Gadsby, 2009; Henderson, Fendler, and Poolman,
2019), or as expressed by Läuger (1980): “Channel and carrier [transporter]
models should therefore not be regarded as mutually exclusive possibilities,
but rather as limiting cases of a more general mechanism.” There seems to be
value in stepping back and asking what the general principles are under which
a class of proteins has to operate.

_Data availability_ The data that support the findings of this study are
available from the corresponding author upon reasonable request.

###### Acknowledgements.

We thank Philip Fowler for providing us with the data for Figure 9. Research
reported in this work was supported by the National Institute Of General
Medical Sciences of the National Institutes of Health under Awards Number
R01GM118772. Some of the work was supported by the European Community’s
Seventh Framework Programme FP7/2007–2013 under grant agreement No
HEALTH-F4-2007-201924, European Drug Initiative for Channels and Transporters
(EDICT) Consortium.

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