1
A Multi-State Model of the CaMKII Dodecamer Suggests a Role for Calmodulin in Maintenance
of Autophosphorylation
Matthew C. Pharris
1
, Thomas M. Bartol
2
, Terrence J. Sejnowski
2,3,4
, Mary B. Kennedy
5
, Melanie
I. Stefan
2,6,7,8*
, and Tamara L. Kinzer-Ursem
1*
1
Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA
2
Salk Institute for Biological Studies, La Jolla, CA, USA
3
Institute for Neural Computation, University of California San Diego, La Jolla, CA, USA
4
Division of Biological Sciences, University of California San Diego, La Jolla, CA, USA
5
Division of Biology and Biological Engineering, California Institute of Technology, Pasadena,
CA, USA
6
EMBL-European Bioinformatics Institute, Hinxton, UK
7
Centre for Discovery Brain Sciences, The University of Edinburgh, Edinburgh, UK
8
ZJU-UoE Institute, Zhejiang University, Haining, CN
* Corresponding authors
E-mail: melanie.stefan@ed.ac.uk, tursem@purdue.edu
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2
1
Abstract
2
Ca
2+
/calmodulin-dependent protein kinase II (CaMKII) accounts for up to 2 percent of all brain
3
protein and is essential to memory function. CaMKII activity is known to regulate dynamic shifts in the
4
size and signaling strength of neuronal connections, a process known as synaptic plasticity. Increasingly,
5
computational models are used to explore synaptic plasticity and the mechanisms regulating CaMKII
6
activity. Conventional modeling approaches may exclude biophysical detail due to the impractical
7
number of state combinations that arise when explicitly monitoring the conformational changes, ligand
8
binding, and phosphorylation events that occur on each of the CaMKII holoenzyme’s twelve subunits. To
9
manage the combinatorial explosion without necessitating bias or loss in biological accuracy, we use a
10
specialized syntax in the software MCell to create a rule-based model of the twelve-subunit CaMKII
11
holoenzyme. Here we validate the rule-based model against previous measures of CaMKII activity and
12
investigate molecular mechanisms of CaMKII regulation. Specifically, we explore how Ca
2+
/CaM-
13
binding may both stabilize CaMKII subunit activation and regulate maintenance of CaMKII
14
autophosphorylation. Noting that Ca
2+
/CaM and protein phosphatases bind CaMKII at nearby or
15
overlapping sites, we compare model scenarios in which Ca
2+
/CaM and protein phosphatase do or do not
16
structurally exclude each other’s binding to CaMKII. Our results suggest a functional mechanism for the
17
so-called “CaM trapping” phenomenon, such that Ca
2+
/CaM structurally excludes phosphatase binding
18
and thereby prolongs CaMKII autophosphorylation. We conclude that structural protection of
19
autophosphorylated CaMKII by Ca
2+
/CaM may be an important mechanism for regulation of synaptic
20
plasticity.
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3
21
Author summary
22
In the hippocampus, the dynamic fluctuation in size and strength of neuronal connections is
23
thought to underlie learning and memory processes. These fluctuations, called synaptic plasticity, are in-
24
part regulated by the protein calcium/calmodulin-dependent kinase II (CaMKII). During synaptic
25
plasticity, CaMKII becomes activated in the presence of calcium ions (Ca
2+
) and calmodulin (CaM),
26
allowing it to interact enzymatically with downstream binding partners. Interestingly, activated CaMKII
27
can phosphorylate itself, resulting in state changes that allow CaMKII to be functionally active
28
independent of Ca
2+
/CaM. Phosphorylation of CaMKII at Thr-286/287 has been shown to be a critical
29
component of learning and memory. To explore the molecular mechanisms that regulate the activity of
30
CaMKII holoenzymes, we use a rule-based approach that reduces computational complexity normally
31
associated with representing the wide variety of functional states that a CaMKII holoenzyme can adopt.
32
Using this approach we observe regulatory mechanisms that might be obscured by reductive approaches.
33
Our results newly suggest that CaMKII phosphorylation at Thr-286/287 is stabilized by a mechanism in
34
which CaM structurally excludes phosphatase binding at that site.
35
Introduction
36
CaMKII is a protein of interest because of its crucial role in synaptic plasticity [1-5]. In the
37
hippocampus, synaptic plasticity in the post-synapse occurs within mushroom-shaped protrusions called
38
dendritic spines [6]. Synaptic plasticity is dependent on calcium ion (Ca
2+
) flux through N-methyl-D-
39
aspartate receptors (NMDARs) located on the dendritic spines of the post-synaptic neuron [7]. Depending
40
on the magnitude, frequency, and location of Ca
2+
flux, synaptic plasticity may produce increases or
41
decreases (or neither) in synaptic strength [8, 9]. Large, higher-frequency Ca
2+
spikes can induce an
42
enduring up-regulation of synaptic strength, called long-term potentiation (LTP); while weak, lower-
43
frequency Ca
2+
spikes can induce an enduring down-regulation of synaptic strength, called long-term
44
depression (LTD) [9, 10]. Whether Ca
2+
spikes induce LTP or LTD depends on relative activation of
45
intracellular protein signaling networks. When Ca
2+
first enters the dendritic spine, it interacts with a
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4
46
variety of buffer and sensor proteins, chiefly calmodulin (CaM), which has many protein targets in the
47
spine, including CaMKII [5, 11, 12].
48
The CaMKII holoenzyme contains at least twelve subunits [13-16] arranged as two rings of six.
49
As shown in Fig 1, each CaMKII subunit features an N-terminal kinase domain and C-terminal hub
50
domain [17]. Between the kinase and hub domains is a flexible regulatory domain which lends to the
51
subunit a wide range of movement away from the holoenzyme’s central hub. A crystal structure of human
52
alpha-CaMKII expressed in
E. coli
published by Chao
et al
. (2011) shows CaMKII subunits as able to
53
rapidly and stochastically pivot between a “docked” and “undocked” conformation, seemingly mediated
54
by residues on the kinase domain’s activation loop and a spur structure on the hub domain (see Fig 3C in
55
[17]), such that a docked subunit may be inaccessible to CaM binding. In contrast, a more recent work
56
using electron microscopy with rat alpha-CaMKII expressed in Sf9 cells suggests that less than 3 percent
57
of subunits exhibit a compact (or docked) conformation [18]. Given the uncertainty in the field, we
58
include subunit docking and undocking in our model, allowing for future exploration of this possible
59
subunit functionality. In addition to docking and undocking, each subunit can be in an “inactive”
60
conformation when the regulatory domain is bound to the kinase domain (Fig 1B), or an “active”
61
conformation when this binding is disrupted by the binding of Ca
2+
/CaM or phosphorylation at Thr-286
62
[17, 19]. In the active conformation the catalytic domain of a subunit is able to bind and phosphorylate
63
enzymatic substrates. A subunit may spontaneously return to an inactive conformation in the absence of
64
Ca
2+
/CaM or phosphorylation at Thr-286 [19].
65
Fig 1. Schematic of CaMKII Subunit Structure.
(A) Map of amino acid residues in a CaMKII subunit.
66
The N-terminal kinase domain (blue) approximately spans residues 1-274. The regulatory domain
67
(residues 275-314, yellow) binds to the kinase domain autoinhibiting the kinase activity of the each
68
CaMKII subunit. The putative phosphatase binding site is also shown purple. The Ca
2+
/CaM binding site
69
is shown in orange. Subunits self-associate via the hub domain (residues 315-475, green) to form
70
multimeric complexes of 12-14 subunit holoenzymes. (B) The “inactive” CaMKII subunit (PDB: 3SOA)
71
in which the regulatory domain (yellow) is closely associated with the kinase domain (blue). (C) A
72
schematic of the “active” CaMKII subunit. The regulatory domain (yellow) is not bound to the kinase
73
domain (blue). This schematic was generated by manually modifying PDB entry 3SOA to illustrate how
74
the regulatory domain may be available for Ca
2+
/CaM binding and the kinase domain open for substrate
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75
binding. (D) Cartoon depiction of all protein species in our model, in which Ca
2+
/CaM (orange) or
76
phosphatase (purple) may bind to the regulatory domain (yellow) of a CaMKII subunit.
77
78
CaMKII activity can become Ca
2+
/CaM-independent through phosphorylation at Thr-286, which
79
is required for LTP [3, 20]. Importantly, this phenomenon is an autophosphorylation: it is thought to
80
occur when an active subunit phosphorylates neighboring subunits within the same holoenzyme [21, 22].
81
Autophosphorylation at Thr-286 (“pThr-286”) is thought to provide structural stability to a subunit’s
82
active conformation (reviewed in [23]) [24]. Because CaMKII plays a key role in the induction of LTP,
83
and ultimately learning and memory (reviewed in [4, 8]), we seek to better understand the biochemical
84
regulation of CaMKII activation and autophosphorylation via computational modeling.
85
To characterize the spatiotemporal regulation of CaMKII, experimental studies are increasingly
86
complemented by computational models [15, 17, 25, 26]. Computational models of Ca
2+
-dependent
87
signaling implicate competition, binding kinetics, feedback loops, and spatial effects in regulating enzyme
88
activation [7, 12, 24, 27, 28]. However, fully characterizing these and other mechanisms of CaMKII
89
regulation is impeded by the challenge of accurately portraying the CaMKII holoenzyme. As described by
90
previous work, combinatorial explosion applies to models of CaMKII (and similar biomolecules) because
91
the protein exhibits a large number of functionally significant and not necessarily inter-dependent states
92
[24, 26, 29-31]. The large number of possible states of CaMKII can neither be explicitly specified nor
93
efficiently evaluated with conventional mass action-based methods. Indeed, for just one CaMKII hexamer
94
ring, we estimate a state space of ~32 billion states, and for the full dodecamer approximately 10
20
95
possible states (See S1 Appendix). The numbers of possible CaMKII states far exceeds the number of
96
CaMKII molecules in a dendritic spine, suggesting that some states never occur and are therefore not
97
functionally important. Previous models leverage this observation to reduce the model state space and
98
provide valuable insight to CaMKII binding and autophosphorylation dynamics [24, 31-34]. However, for
99
CaMKII it remains unclear which states functionally participate in synaptic plasticity. Reduced models
100
can inadvertently obscure key mechanisms regulating CaMKII activation and autophosphorylation. To
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101
elucidate complex regulatory mechanisms, it may be necessary for models to provide for all possible
102
states
ab initio
.
103
In this work, we use rule-based model specification and particle-based rule evaluation methods to
104
overcome combinatorial explosion [26, 30, 35]. Rules are conditions, based primarily on experimental
105
observations, that prescribe when an implicitly-defined reaction may occur. At a given iteration, only
106
states that matter for the execution of a particular rule are explicitly declared. States that do not matter to a
107
particular rule can be omitted, a principle that has been paraphrased as “don’t care, don’t write” [36]. We
108
use rule- and particle-based methods within the spatial-stochastic software MCell 3.3 [28, 37] to present a
109
comprehensive multi-state model of the CaMKII dodecamer
.
Other simulation platforms can also
110
overcome combinatorial explosion through rule-based model specification (e.g. BioNetGen [38]) or
111
network-free approaches (e.g. NFsim [39]). Unlike other platforms, MCell 3.3 provides both spatial-
112
stochastic and rule-based modeling, although multi-state molecules in MCell 3.3 cannot diffuse. We use
113
MCell 3.3 in anticipation of future MCell versions accounting for multi-state molecule diffusion, and to
114
eventually build on simulations with physiological dendritic spine geometries such as those by Bartol
et
115
al
. (2015) [40].
116
Here, we validate this rule-based MCell model of CaMKII regulation against current descriptions
117
of the Ca
2+
frequency-dependence of CaMKII activation. By varying the rules and model parameter
118
values we can simulate different experimental manipulations of CaMKII interaction with Ca
2+
/CaM and
119
phosphatase and thereby explore various mechanisms regulating CaMKII activity. In particular, we show
120
that Ca
2+
/CaM is important not only for regulating activation of CaMKII but may also contribute to the
121
maintenance of CaMKII phosphorylation at Thr-286. We hypothesize that by limiting access of
122
phosphatases to CaMKII Thr-286 (perhaps by steric hindrance), Ca
2+
/CaM may prolong the lifetime of
123
the auto-phosphorylated state.
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124
Results
125
Model Development
126
Molecular Species.
The model contains three protein species: CaM, protein phosphatase, and CaMKII.
127
Ca
2+
/CaM facilitates CaMKII activation, which leads to autophosphorylation at Thr-286, and phosphatase
128
activity facilitates de-phosphorylation at Thr-286. Both protein phosphatase 1 (PP1) and protein
129
phosphatase 2A (PP2A) have been shown to dephosphorylate Thr-286, though in different subcellular
130
fractions (reviewed by [21, 41-43]). Here we refer to them generally as protein phosphatase (PP).
131
CaM and PP are modeled in MCell as conventional cytosolic molecules. CaM is modeled as
132
having one of two states: un-bound apo-CaM and fully-saturated Ca
2+
/CaM (four Ca
2+
bound to CaM).
133
Although we and others have described the importance of sub-saturated Ca
2+
/CaM states with fewer than
134
4 Ca
2+
[12, 24, 31, 44-46], the dynamics of Ca
2+
-CaM binding and the binding of sub-saturated Ca
2+
/CaM
135
to CaMKII are beyond the scope of this current work. Indeed, accounting for sub-saturated Ca
2+
/CaM
136
would here require a multi-state representation, and because multi-state molecules cannot diffuse in
137
MCell 3.3, we simplify our Ca
2+
/CaM model to allow CaM and CaMKII to interact. Thus, similarly to
138
previous models [27, 47], we assume that apo-CaM has a negligible affinity for CaMKII; only fully-
139
saturated Ca
2+
/CaM binds CaMKII. In contrast to CaM, PP is modeled as single-state protein that is
140
constitutively active and able to bind auto-phosphorylated CaMKII subunits. Our representation of
141
constitutively active PP is consistent with previous models such as that by Lisman and Zhabotinsky
142
(2001) [48].
143
CaMKII is modeled as a multi-subunit complex, defined using a specialized model syntax for
144
complex molecules (COMPLEX_MOLECULE) in MCell 3.3 [49]. This syntax allows for explicit
145
representation of individual CaMKII dodecamers with distinguishable subunits. As shown in Fig 2, the
146
holoenzyme is arranged as two directly-apposed, radially-symmetric rings each with six subunits. Each
147
subunit features five “flags”, each standing for a particular state that each CaMKII subunit can adopt.
148
Flags are used in rule evaluation, which occurs at each time step and for each individual subunit. That is,
149
MCell repeatedly evaluates model rules against a given subunit’s flags (and those of the neighboring
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8
150
subunits) to determine which state transitions a subunit undertakes at each time step. In the following sub-
151
sections, we describe all CaMKII model flags, the state transitions that apply to each flag, the conditions
152
and rate parameters for each state transition, and related model assumptions. In Fig 2, we visually convey
153
how CaMKII subunits transition between states according to our model’s rules. In S1 Appendix we
154
summarize the state transition rules and rate parameter values.
155
Fig 2. CaMKII holoenzyme state transitions.
(A) CaMKII has twelve subunits arranged in two radially
156
symmetric, directly apposed rings. Subunits may spontaneously undock/extend from the central hub or
157
dock/retract (if inactive). When undocked, subunits may spontaneously open/activate. (B) If two
158
neighboring subunits are active, one may auto-phosphorylate the other at Thr-286. If auto-phosphorylated
159
(pThr-286), a subunit may remain active even upon un-binding of CaM. A pThr-286 subunit un-bound to
160
CaM may additionally phosphorylate at Thr-306, blocking subsequent re-binding of Ca
2+
/CaM. A pThr-
161
286 subunit may also bind and become de-phosphorylated by PP (purple).
162
163
Flag 1: Subunit docking.
Docking is a binary flag that describes subunits as either “docked” or
164
“undocked” to the CaMKII central hub. Subunits are instantiated in a docked state but may undergo
165
numerous transitions between docked and undocked over the course of a simulation. At each time step,
166
we assess a rule governing the subunit’s transition from a docked to undocked state. If this rule is
167
satisfied, meaning that the subunit’s docking flag is verified as “docked”, then the transition is considered.
168
Similarly, we assess a separate rule governing a transition from an undocked to docked state, which
169
requires that the subunit not be bound to CaM and not phosphorylated at Thr-306 [17].
170
Subunit docking follows the structural model of Chao
et al
., who showed that a subunit cannot
171
bind CaM as long as the subunit is in a compact conformation, docked to its central hub [17]. Docking
172
implies a two-step process in which the subunit must first un-dock before subsequent CaM-binding,
173
which accounts for the reported difference in binding rate for CaM to CaMKII-derived peptide (1 × 10
8
174
M
-1
s
-1
[50]) and for CaM to full-length CaMKII-T286A (1.8 × 10
6
M
-1
s
-1
[51]). Taking the ratio of these
175
two rates gives an equilibrium constant for docking of 0.018, which is consistent with estimates by Chao
176
et al
., who assumed K
docking
to fall between 0.01 and 100 [17]. With this equilibrium constant, we estimate
177
kinetic rates for docking and undocking. For this estimation, we first note that subunit docking involves a
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178
structural conformation change on a relatively large scale. Referring to a separate, and notably smaller-
179
scale, conformational change in our model, in which CaM quickly transitions from an initially- to fully-
180
bound state (see Flag 3: CaM Binding), we assume the docked-to-undocked transition to proceed at an
181
order of magnitude slower. We therefore arrive at an assumed rate for k
dock
of 35 s
-1
. In turn, this gives an
182
undocking rate k
undock
=k
dock
× K
docking
of 0.63 s
-1
, which lies within the range of 0.01 s
-1
and 100 s
-1
for
183
k
undock
assumed by Chao
et al
.
184
Flag 2: Subunit activation.
The activation flag describes subunits as either “active” or “inactive”. An
185
inactive subunit has no catalytic activity because the regulatory domain is bound to the subunit’s catalytic
186
site; others may refer to it as a closed subunit. Conversely, an active subunit has catalytic activity because
187
the regulatory domain’s inhibition of the kinase domain is disrupted; in other words, an active subunit is
188
an open subunit. When a subunit is active, Ca
2+
/CaM and/or other proteins may access and bind CaMKII.
189
In our model, the transition reaction from inactive to active (opening) involves no explicit rules (but
190
rather occurs unconditionally and as governed by rates described below). In contrast, two rules inform the
191
conditions for subunit inactivation: that the subunit is 1) not fully-bound to CaM, and 2) not
192
phosphorylated at Thr-286.
193
To assign rate parameters for this flag, we first note that subunits can fluctuate between inactive
194
and active states rapidly in the absence of Ca
2+
/CaM (on the order of hundreds of nanoseconds) [19, 52].
195
Noting this, we set the rate parameter for subunit inactivation at 1 × 10
7
s
-1
. Further, Stefan
et al
.
196
determined that the activation probability (in the absence of CaM and phosphorylation) is 0.002, leading
197
us to set our activation rate parameter to 2 × 10
4
s
-1
[29]. Thus, we arrive at a model in which CaMKII
198
subunit activation is unstable until stabilized by CaM-binding or autophosphorylation.
199
Flag 3: CaM binding.
CaM binding is a ternary flag meaning that each CaMKII subunit displays one
200
of three states, where CaM may be “unbound”, “initially-bound”, or “fully bound”. Our model adapts
201
previous work by Stefan
et al
. (2012)
to describe CaM-binding to CaMKII as a two-step process [29].
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202
First, CaM binds to the regulatory domain of a CaMKII subunit (residues 298-312), resulting in a low-
203
affinity “initially bound” CaMKII state, which is compatible with both the closed and open subunit
204
conformation. Second, if the initially bound CaMKII opens it may transition to a “fully bound” state that
205
describes the complete, higher-affinity interaction between CaM and CaMKII along residues 291-312
206
(see Figure 5 in [29]). We specify three rules to govern the transition from an unbound to initially bound
207
state: the subunit must be 1) undocked, 2) not PP-bound, and 3) un-phosphorylated at Thr-306. The
208
transition reaction from initially bound to a fully bound state is governed by a single rule that the subunit
209
already be active/open. Dissociation of CaM from a fully bound CaM-CaMKII state proceeds through the
210
initially bound state before becoming completely unbound from CaMKII.
211
In order to determine the parameters governing initial binding of CaM to CaMKII, we use data on
212
CaM binding to CaMKII-derived peptides, rather than full-length CaMKII. This is done to separate the
213
intrinsic binding constants from the parameters governing subunit activation/inactivation and
214
docking/undocking. The microscopic k
on
for CaM binding to CaMKII has been measured, using a
215
CaMKII peptide and fluorescently labeled DA-CaM, as 1 × 10
8
M
-1
s
-1
[50]. For the K
D
governing initial
216
CaM binding, we use the K
D
reported by Tse
et al
. for CaM binding to a low-affinity peptide (CaMKII
217
residues 300-312), which is 5.9 × 10
-6
M [53]. From these two parameters, we can compute the
218
dissociation rate of initially-bound CaM from CaMKII: k
off_CaM_ini
= K
d_CaM_ini
× k
on_CaM
= 590 s
-1
.
219
In order to determine the parameters governing the transition from initially-bound to fully-bound
220
CaM to CaMKII, we note that this transition involves a structural compaction of the CaM molecule,
221
which has been measured using fluorescent labels [50, 51]. Using fluorescent labels to analyze the
222
structural compaction of CaM is convenient in its exclusion of effects due to conformational changes
223
within CaMKII subunits or the CaMKII holoenzyme. Thus, we use these measurements as a proxy for
224
CaM binding to a CaMKII peptide and to estimate parameters governing the transition between initially-
225
and fully-bound CaM-CaMKII. Based on experiments by Torok
et al
., we identify a transition rate from
226
initially- to fully-bound CaM-CaMKII of 350 s
-1
and from fully- back to initially-bound CaM of 4 × 10
-3
.
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11
227
s
-1
[50]. This means that, in the absence of obstructions to binding, the likelihood of a bound CaM
228
molecule being in the initial binding state (rather than the fully bound state) is 4 × 10
-3
/ 350 = ~1.1 × 10
-5
.
229
This is consistent with a probability of CaM being bound to the high-affinity site of 0.99999 which was
230
derived by Stefan
et al
. (2012) [29].
231
Flag 4: Phosphorylation at Thr-286.
Phosphorylation at the residue Thr-286 is a ternary flag that
232
describes this site as either “un-phosphorylated (uThr-286)”, “phosphorylated (pThr-286)”, or
233
“phosphatase-bound”. We specify three rules to govern the reaction that transitions a subunit from uThr-
234
286 to pThr-286: the subunit 1) be uThr-286, 2) be active, and 3) have an active neighbor subunit in the
235
same holoenzyme ring. The neighboring subunit’s activation flag is considered because
236
autophosphorylation is facilitated by its catalytic site. Our model only considers the counter-clockwise
237
neighbor subunit because, in the absence of experimental observations to the contrary, we assume that
238
steric effects cause autophosphorylation to occur in only one direction about a CaMKII ring, similar to
239
previous work [54, 55]. The rate of autophosphorylation, 1 s
-1
, at Thr-286 is taken from an earlier study of
240
CaMKII autophosphorylation in the presence of CaM [44].
241
De-phosphorylation of pThr-286 is facilitated by binding and enzymatic activity of protein
242
phosphatases PP1 and PP2A, here referred to generally as PP [41, 42]. Two rules govern PP binding to a
243
CaMKII subunit (the transition from pThr-286 to a phosphatase-bound state): that the subunit be 1) pThr-
244
286 and 2) un-bound to CaM. It has been shown that a majority of autophosphorylated CaMKII in the
245
PSD is dephosphorylated by PP1 [56, 57]; while in brain extracts autophosphorylated CaMKII is mostly
246
dephosphorylated by PP2A [41]. The requirement that CaM be unbound from CaMKII in order for PP to
247
bind to CaMKII is motivated by the observation that simultaneous binding of CaM and PP to the CaMKII
248
regulatory domain may be mutually exclusive due to steric hindrance. CaM, having molecular weight 18
249
kDa, binds to the CaMKII regulatory domain around residues 290–309 [54, 58, 59], which is at least 4
250
residues, and at most 23 residues away from Thr-286 (again, see also Figure 5 in [29]). To the best of our
251
knowledge, the peptide binding footprint of neither PP (PP1 nor PP2A) onto CaMKII is not yet fully
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The copyright holder for this preprint
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12
252
described. However, both PP1 and PP2A are widely known to target pThr-286 [56, 57, 60] and de-
253
phosphorylate threonine residues nearby alpha helices in other substrates [61, 62]. Additionally, the
254
catalytic subunit of PP1 has a molecular weight of 37 kDa, which is nearly twice that of CaM and more
255
than half that of a CaMKII subunit. Taken together, we hypothesize that the PP binding footprint likely
256
overlaps with the CaM binding site, such that the presence of bound PP likely structurally excludes or
257
impedes upon a subsequent binding of CaM to CaMKII. Similarly, the presence of bound Ca
2+
/CaM
258
structurally would exclude coincident binding of PP. In S1 Appendix, we further discuss the quantitative
259
basis of this structural exclusion hypothesis in light of the crystal structure of the PP1-spinophilin
260
interaction (PDB: 3EGG) [63]. In short, PP1 tends to bind substrates at a site >20Å from the PP1 active
261
site. Thus, if the PP1 binding footprint does not actually contain T286, then the furthest likely CaMKII
262
residue of PP1 binding (at least on the hub domain side of T286) is G301, well within the CaM binding
263
footprint (S1 Appendix). We examine the regulatory implications of this hypothesis by relaxing the rules
264
of PP binding and requiring only that the subunit be pThr-286. The association, dissociation, and catalytic
265
rates of PP for CaMKII are taken from Zhabotinsky (2000), using a Michaelis constant of 6
μM
and a
266
catalytic rate of 2 s
-1
[47].
267
Flag 5: Phosphorylation at Thr-306.
Phosphorylation at the residue Thr-306 is a binary flag that
268
describes this site as either un-phosphorylated (“uThr-306”) or phosphorylated (“pThr-306”). We model
269
the transition from uThr-306 to pThr-306 using three rules: that that the subunit be 1) uThr-306, 2) active,
270
and 3) un-bound by CaM. Our model uses a forward rate parameter 50-fold slower than that of
271
phosphorylation at Thr-286, based on past experimental measurements [33, 64]. Over the course of our
272
simulation times, we observe very few pThr-306 transitions and therefore exclude the reverse transition
273
reaction describing de-phosphorylation of pThr-306 into uThr-306.
274
Stimulation frequency correlates with subunit activity
275
To validate our model, we assessed a variety of model outputs under various regimes of
276
Ca
2+
/CaM stimulation. As a first assessment, we simulated a persistent Ca
2+
/CaM bolus, similar to
.
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It is made available under a
(which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint
.
http://dx.doi.org/10.1101/575712
doi:
bioRxiv preprint first posted online Mar. 12, 2019;
13
277
experiments by Bradshaw
et al
. (2002), who monitored CaMKII autophosphorylation over time [55]. In
278
Fig 3 we simultaneously monitored the time-course concentration of CaMKII subunit flags indicating:
279
initially-bound Ca
2+
/CaM, fully-bound Ca
2+
/CaM, active CaMKII, and pThr-286. In the persistent,
280
continuous presence of Ca
2+
/CaM, the concentration of subunits with initially-bound Ca
2+
/CaM (orange
281
trace) is noisy and consistently low, implying that Ca
2+
/CaM transiently binds subunits in an initially-
282
bound conformation. That is, initially-bound Ca
2+
/CaM seems rapidly to either dissociate or proceed to a
283
fully-bound conformation. Fully-bound Ca
2+
/CaM (red trace) subunit concentrations closely follow those
284
of active CaMKII subunits (dark blue trace) over time, providing evidence that Ca
2+
/CaM stabilizes
285
CaMKII activation. Indeed, because the difference in concentrations of fully-bound Ca
2+
/CaM and active
286
CaMKII is always small, we observe that although unbound CaMKII may spontaneously activate, these
287
activated subunits rapidly return to an inactive state and are not likely to progress to a phosphorylated
288
(pThr-286) state. We next observe that the increase of CaMKII autophosphorylation at Thr-286 (cyan
289
trace) over time is strongly associated with increases in the number of subunits that are fully-bound to
290
Ca
2+
/CaM and active subunits (dark blue and red traces, respectively). This is consistent with previous
291
work showing that Ca
2+
/CaM must be bound to CaMKII for pThr-286 to occur [54] and CaMKII Ca
2+
-
292
independent activity is strongly associated CaMKII autophosphorylation at Thr-286 [17, 51, 65, 66].
293
Furthermore, we observe in Fig 3A that more than 80 percent of CaMKII subunits are autophosphorylated
294
at t=20sec, which is of similar magnitude and timescale as observed by Bradshaw
et al
. (see Figure 2A in
295
[55]).
296
Fig 3. Validation of the Rule-based Model.
Bold traces (A-C) and solid circles (D) are the average of N
297
= 50 executions. For each species (A-C), six representative traces are also shown (semi-transparent lines).
298
(A) Model output resulting from stimulation with a large continuous bolus of Ca
2+
/CaM. Concentrations
299
of active (red), initially CaM-bound (yellow), fully CaM-bound (blue), and pThr-286 (cyan) subunits. (B)
300
Time-course average concentration (bold trace) of active subunits stimulated by 5 Hz or 50 Hz Ca
2+
/CaM.
301
(C) Time-course concentration of pThr-286 subunits stimulated continuously by 5 Hz or 50 Hz
302
Ca
2+
/CaM. (D) Frequency-dependent activation (red) and pThr-286 (cyan) of CaMKII subunits, with
303
SEM error bars. Black dotted traces are linear fits.
304
305
Next, we assessed model behavior under low- and high-frequency stimulating conditions.
306
CaMKII activation and autophosphorylation at Thr-286 in response to 5Hz and 50Hz Ca
2+
/CaM is plotted
.
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(which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint
.
http://dx.doi.org/10.1101/575712
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14
307
in Figure 3B and 3C, respectively; 50 seeds were run for each condition, with 6 representative traces
308
(transparent lines) and the average response (bold) plotted. As expected, the data showed significantly
309
greater levels of CaMKII activation and autophosphorylation at 50Hz [12, 20]. Indeed, we compared our
310
result in Fig 3C to work by Shifman
et al.
(2006), who observed much lower autophosphorylation at low
311
Ca
2+
/CaM concentrations (less than 2
μM)
than at high concentrations (see Figure 4D in [44]). Therefore,
312
because our 50Hz model cumulatively exposes CaMKII to approximately ten times as much Ca
2+
/CaM
313
per second as our 5Hz model, our results in Fig 3C are consistent with Shifman
et al
., showing much
314
higher autophosphorylation at 50Hz than 5Hz.
315
To further determine how stimulation frequency affects CaMKII activity, the model was
316
stimulated at frequencies ranging from 1Hz to 50 Hz. At each frequency, models were sampled at 20
317
seconds of simulation time. We observe a nearly linear correlation between both subunit activation (R
2
=
318
0.99) and pThr-286 (R
2
= 0.96) and stimulation frequency (Fig 3D). This result is consistent with
319
computational results from Chao
et al
., who developed a stochastic model that also yielded a linear
320
relationship between pThr-286 and stimulation frequency for frequencies greater than 1 Hz [15]. Taken
321
together, these results (Fig 3) show that our model behaves as expected and is able to produce CaMKII
322
activity and autophosphorylation behaviors similar to previous computational and experimental results.
323
Exploring Switch-like Behavior in CaMKII
324
CaMKII has long been theorized to exhibit switch-like or bistable behavior, which could underlie
325
the importance of pThr-286 to learning and memory formation [4, 47, 48, 67, 68]. However, experimental
326
efforts have struggled to identify a bistability between CaMKII and phosphatase activity. Though
327
recently, Urakubo
et al
. used the chelator EGTA to control single pulses of Ca
2+
in a mixture of CaM,
328
CaMKII, PP1, and NMDAR peptides, leading to what seemed to be the first direct observation of
329
CaMKII bistability [69]. Referring to Urakubo
et al
., we explored whether a spatial stochastic model of
330
the CaMKII dodecamer would exhibit near bistability or switch-like behavior for concentration
331
parameters of Ca
2+
, CaM, CaMKII, and PP known to exist in hippocampal spines. To explore this
.
CC-BY 4.0 International license
It is made available under a
(which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint
.
http://dx.doi.org/10.1101/575712
doi:
bioRxiv preprint first posted online Mar. 12, 2019;