Figure 1.
A typical allosteric activation via a bi-stable switch.
A node in the cellular network is illustrated by only two populated states, active and inactive, separated by a sizeable but surmountable free energy barrier. Before activation, the inactive state dominates the population as indicated by the relative basin depth in the free energy landscape and a balance level. Within a narrow increment range in ligand concentration, the allosteric activation event shifts the population in favor of the active state. The activation is highlighted in the embedded plot with a typical sigmoid transition from the inactive to the active state.
Figure 2.
The simplest allosteric two-state model (ATSM).
(A) The two-state model presents an equilibrium between two states, and
, with the relative population defined by the equilibrium constant,
, and their binding to an allosteric ligand,
. For the inactive state, the binding equilibrium constant is given by
, and for the active state, by
. Due to the complete circle of equilibrium, the equilibrium constant between
and
is automatically deduced as
with the previous three mass equations. Also, the forward reaction
with
implies a population shift due to the allosteric binding event. In this schematic allostery description, the conformation selection scheme emphasizes that the microscopic path of
dominates the equilibrium process in contrast to the induced-fit scheme which implies the
path prevails. (B) A typical sigmoid response-concentration curve in the allosteric two-state model. If we accept the assumption that a measured biological response is proportional to the fraction of receptors in the activated state,
as defined in the ATSM, manipulation of the three equilibrium equations in ATSM (Figure 2A) deduces the response,
, as a function of ligand concentration with three independent parameters,
,
, and
. The sigmoid response-concentration curve of ATSM is established by three quantities, the basal activity as
,
, the maximum activity
,
, and the activity at the middle point of the transition,
which corresponds to ligand concentration at
.
Figure 3.
The simplest free energy landscape presentation of the thermodynamic view of allostery.
At the bottom of the folding funnel, an apo protein is optimized to populate two states, (inactive) and
(active), with each basin representing an ensemble of conformations and their relative populations as determined by the relative depth of the local basins. Allostery is clearly seen by a population shift from the inactive state dominated by apo (light green) to the active state prevailing in the complex (pale orange) through allosteric ligand binding.
Figure 4.
The classification of allosteric ligands with ATSM.
Given an experimental sigmoid response-concentration curve with full biological response, we can determine the three independent parameters ,
, and
in ATSM. Full agonist, corresponding to
, produces a full biological response. Partial agonist even at saturating concentration can only produce a partial biological response with
. Inverse agonist suppresses basal activity with
. Neutral antagonist with
does not impose any biological response.
Figure 5.
The thermodynamic and free energy landscape of the population shift views, the structural view of the allosteric two-state model, and an extension of the model to two allosteric sites and one functional site.
(A) The free energy landscape presentation of ATSM. Before binding, the relative free energy between the inactive () and active (
) states is given by
, which is
according to the ATSM as depicted by the light green curve. After binding, the relative free energy between
and
is given by
, which under a saturating ligand concentration becomes
, as drawn by the orange curve. The extent of population shift as measured by the free energy change due to binding,
, is equal to
. This result implies that the allosteric effect is solely determined by the allosteric efficacy, α, but not the absolute ligand affinity.
can also be expressed by the difference between the active conformation stabilization energy,
(red arrow), and inactive conformation destabilization energy,
(blue arrow). (B) The structural view of allostery according to the ATSM. The allosteric communication between the allosteric and functional sites is indicated by the arrow with the coupling specified by the allosteric efficacy
. Unlike the thermodynamic view, the structural view emphasizes that the conformations of two sites breathe dynamically in a concerted motion through a set of mutually interacting residues. Without such a propagation channel between sites,
is always the case, no matter the changes at the allosteric site. Thus, while a preexisting channel (or allosteric networks of correlated residues) is a required condition, by itself the communication through the channel does not determine the allosteric efficacy. (C) The structural view of allostery according to the extended ATSM. In the drawing, the two allosteric communication channels between the two allosteric sites and the functional site are indicated by the blue double arrows with the coupling specified by the allosteric efficacy
,
from the extended ATSM. The communication between the two allosteric sites is linked with a coupling specified by the binding cooperativity,
, which is shown not to affect the allosteric efficacy directly. The activation cooperativity
is the sum of the allosteric effect of site 1 toward coupling
(pale green arrow) plus allosteric site 2 toward allosteric coupling α (orange arrow). As in the simplest ATSM, it is the ligand binding itself that puts forth the allosteric communications through existing propagation channels and determines the allosteric efficacy and the activation cooperativity either positively or negatively.
Figure 6.
The extended ATSM with two allosteric ligands.
(A) The model has ten species related by four equilibrium cycles with seven parameters. The first equilibrium cycle (orange) specified by the ,
, and
is exactly the same as in the simplest ATSM (Figure 2A), giving
the equilibrium constant between the two states,
the binding affinity of ligand
bound to inactive
, and
the allosteric intrinsic efficacy of ligand
. The second equilibrium cycle
(pale green) describes the second ligand binding similar to the first ligand binding, assigning
and
respectively as the binding affinity and the allosteric intrinsic efficacy of ligand
. In the third equilibrium cycle
(cyan), the sixth parameter
administers the binding cooperativity between ligand
and
upon the formation of the ternary complex
. Similarly, the seventh parameter
governs the activation cooperativity between ligand
and
through the formation of
in the fourth equilibrium cycle
(red). (B) The complete equilibrium cycles of the extended ATSM. The four essential equilibrium cycles of the extended ATSM in (A) are combined into a cubic shape of a complete cycle. To guide the visualization, the two corners of the complete cycle are highlighted by colored equilibrium arrows for species
and
and colored parameters for referencing back to the individual essential equilibrium cycle. (C) The structural view of allostery with two allosteric site and two (independent) functional sites. The drawing is based on two assumptions. First, the populations of the two functional sites are regulated independently by two distinct allosteric sites. Second, the two functional conformations coexist. The allosteric coupling set (
,
, and
) for functional site 1 and a duplicated set of independent allosteric efficacies (
,
, and
) for functional site 2 are similar to the description in Figure 6B. These two sets of coupling are linked by a shared binding cooperativity γ, coupling the two allosteric sites.
Table 1.
Agonist classification by the simplified structural view of allostery.