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MAPs dimerize
(
Fig. 23.1
C): In this model, A can exist either as a monomer or as
a dimer, both of which can bind the MTs with dissociation constants
K
AMT
and
K
AAMT
, respectively. The dissociation constant for the A-A dimerization is
K
AA
.
Pseudocooperativity
: Because the standard model of cooperative biding (i.e., that
of hemoglobin) cannot be applied to polymers and models commonly used for poly-
mers do not fit well into the mathematical framework of MTBindingSim, we have
implemented a “pseudocooperativity” model. In this model, each A that binds to
an MT site with a dissociation constant of
K
AMT
alters a second MT site so that it
becomes MT*, which has a dissociation constant for A of
K
AMT*
.
MAPs bind MT-bound MAPs
(
Fig. 23.1
D): In this model, the binding of A to an
MT with a dissociation constant of
K
AMT
creates a new binding site for another A to
bind to the previous MT-bound A with a dissociation constant of
K
AA
. This allows a
second A to bind without taking up another MT site.
Two MAPs bind MT-bound MAPs
(
Fig. 23.1
E): This model is an extension of the
“MAPs bind MT-bound MAPs” model, where the binding of A to an MT with a dis-
sociation constant of
K
AMT
then allows two more As to bind to the MT-bound A with
a dissociation constant of
K
AA
. An examination of this model and the “MAPs bind
MT-bound MAPs” model shows that further A-A binding on the MT surface will
follow a similar pattern, ultimately resulting in a nonconvergent infinite series,
which cannot be modeled by the equations used in MTBindingSim (this would be
a polymerization).
Two binding sites
: In this model, there are two independent binding sites on the
MT for an A with dissociation constants
K
AMT1
and
K
AMT2
.
23.4
USING MTBindingSim EXAMPLE 1: TAU-MT BINDING
Tau is a MAP that binds all along the length of MTs and stabilizes the MT structure.
Despite multiple investigations into the binding of Tau to MTs, it is unclear how
many tubulin dimers one Tau protein binds to or what is the Tau-MT dissociation
constant (
K
D
) because different publications report different answers. For example,
measured
K
D
values range from
M(
Ackmann, Wiech, &
Mandelkow, 2000; Goode, 1994; Gustke, Trinczek, Biernat, Mandelkow, &
Mandelkow, 1994; Kar, Fan, Smith, Goedert, & Amos, 2003; Makrides, Massie,
Feinstein, & Lew, 2004
).
Ackmann et al. (2000)
and more recently
Duan and Goodson (2012)
have shown
that the amount of Tau that binds to 1
100 nM up to
1
<
>
m
M MTs continues to rise as the Tau concen-
tration is increased (data fromDuan and Goodson are shown in
Fig. 23.2
A). If a bind-
ing ratio of 1 Tau:1 tubulin dimer is assumed, the data appear to show that Tau is
supersaturating the MTs (the concentrations of cosedimented Tau end up being
greater than the concentrations of total MTs).
Ackmann et al. (2000)
suggested that these observations could be explained by
the idea that Tau binds to MT-bound Tau. Further experimental support for this idea
was provided by cross-linking and AFM experiments by
Makrides et al. (2003)
.In
this proposed model, Tau binds to the MT and a second Tau protein is then able to
m
