mechanistic view of allostery for deciphering allosteric coupling in
enzymes, receptors, antibodies, and other protein structures [10–
12, 21].
Our model of allostery is designed to predict if a mechanical
perturbation of rigidity and a change in conformational DOF
(mimicking a binding event) at a given site A on a protein can
percolate and transmit across a protein structure and result in a
change and transmission in rigidity and available conformational
DOF at a second remote site B. A key step is to introduce the local
perturbation of rigidity at site A by adding extra constraints (edges)
to site A up to its rigidification. (Note that in the description of
RTA algorithm below, no actual edges need to be added, but the
same effect can be obtained, which is mathematically verified.)
Upon the initial perturbation (rigidification) of site A, if this results
in a reduction of conformational DOF at site B, then A “transmits
degrees of freedom’ (DOF) to B and the two sites are in ‘rigiditytransmission communication.” The maximum possible reduction
in DOF in site B quantifies the strength of the allosteric transmission signal, where larger the reduction, the stronger the allosteric
transmission signal. As a mechanistic description, the presence of
rigidity-transmission allostery (transmission of DOF) between sites
A and B can be mathematically verified to be equivalent to a
statement that a change in shape (conformation) in site A (i.e.,
mechanically change the shape as binding might) will lead to rearrangement and change of shape and conformation of the second
site B [8]. Thus, rigidity-based allostery captures the essence of
coupled conformational change between distant sites inherent in
allosteric communication.
In Fig. 3b, c we have illustrated the concept of DOF transmission and a change in shape propagation between two remote sites in
a 2-dimensional bar and joint framework toy model, which is built
with bars (rods) which fix the distance between the connecting
flexible joints. This framework has a single internal DOF and
responds specifically to a stimulus at a second distant site. When
we introduce a subtle change in the distance between the two joints
in site A (analogous to simulating ligand binding), this initial shape
change propagates across the framework and results in a change in
shape and conformation at the distant site B. Equivalently, fixing
the distance between the end joints in A (i.e., insert a bar connecting u and v) and rigidifying site A will in turn rigidify site B,
stopping the motion in B. Hence, there is a transmission of one
DOF between A and B. As an analogy to allostery in a hypothetical
protein, a small ligand that fits in site A can pull on the two vertices,
which in turn leads to a change in conformation and a closing
motion at site B, allowing site B to more likely dock its binding
ligand partner (i.e., a hypothetical analogue to positive allosteric
modulation).
Probing Allosteric Mechanism with Rigidity Transmission
67
enzymes, receptors, antibodies, and other protein structures [10–
12, 21].
Our model of allostery is designed to predict if a mechanical
perturbation of rigidity and a change in conformational DOF
(mimicking a binding event) at a given site A on a protein can
percolate and transmit across a protein structure and result in a
change and transmission in rigidity and available conformational
DOF at a second remote site B. A key step is to introduce the local
perturbation of rigidity at site A by adding extra constraints (edges)
to site A up to its rigidification. (Note that in the description of
RTA algorithm below, no actual edges need to be added, but the
same effect can be obtained, which is mathematically verified.)
Upon the initial perturbation (rigidification) of site A, if this results
in a reduction of conformational DOF at site B, then A “transmits
degrees of freedom’ (DOF) to B and the two sites are in ‘rigiditytransmission communication.” The maximum possible reduction
in DOF in site B quantifies the strength of the allosteric transmission signal, where larger the reduction, the stronger the allosteric
transmission signal. As a mechanistic description, the presence of
rigidity-transmission allostery (transmission of DOF) between sites
A and B can be mathematically verified to be equivalent to a
statement that a change in shape (conformation) in site A (i.e.,
mechanically change the shape as binding might) will lead to rearrangement and change of shape and conformation of the second
site B [8]. Thus, rigidity-based allostery captures the essence of
coupled conformational change between distant sites inherent in
allosteric communication.
In Fig. 3b, c we have illustrated the concept of DOF transmission and a change in shape propagation between two remote sites in
a 2-dimensional bar and joint framework toy model, which is built
with bars (rods) which fix the distance between the connecting
flexible joints. This framework has a single internal DOF and
responds specifically to a stimulus at a second distant site. When
we introduce a subtle change in the distance between the two joints
in site A (analogous to simulating ligand binding), this initial shape
change propagates across the framework and results in a change in
shape and conformation at the distant site B. Equivalently, fixing
the distance between the end joints in A (i.e., insert a bar connecting u and v) and rigidifying site A will in turn rigidify site B,
stopping the motion in B. Hence, there is a transmission of one
DOF between A and B. As an analogy to allostery in a hypothetical
protein, a small ligand that fits in site A can pull on the two vertices,
which in turn leads to a change in conformation and a closing
motion at site B, allowing site B to more likely dock its binding
ligand partner (i.e., a hypothetical analogue to positive allosteric
modulation).
Probing Allosteric Mechanism with Rigidity Transmission
67