Integration of modeling with experimental and clinical findings synthesizes and refines the central role of inositol 1,4,5-trisphosphate receptor 1 in spinocerebellar ataxia

A suite of models was developed to study the role of inositol 1,4,5-trisphosphate receptor 1 (IP3R1) in spinocerebellar ataxias (SCAs). Several SCAs are linked to reduced abundance of IP3R1 or to supranormal sensitivity of the receptor to activation by its ligand inositol 1,4,5-trisphosphate (IP3). Detailed multidimensional models have been created to simulate biochemical calcium signaling and membrane electrophysiology in cerebellar Purkinje neurons. In these models, IP3R1-mediated calcium release is allowed to interact with ion channel response on the cell membrane. Experimental findings in mice and clinical observations in humans provide data input for the models. The SCA modeling suite helps interpret experimental results and provides suggestions to guide experiments. The models predict IP3R1 supersensitivity in SCA1 and compensatory mechanisms in SCA1, SCA2, and SCA3. Simulations explain the impact of calcium buffer proteins. Results show that IP3R1-mediated calcium release activates voltage-gated calcium-activated potassium channels in the plasma membrane. The SCA modeling suite unifies observations from experiments in a number of SCAs. The cadre of simulations demonstrates the central role of IP3R1.

The SCA modeling suite is a collection of well-mixed (compartmental) and spatial (1D, 3D) computational models that simulate the biochemical and electrophysiological properties of the cerebellar Purkinje neuron involving various calcium signaling and ion channel molecules in constructed or experimentally derived geometries (Supplemental Material, Supplemental Figure  S1 and Supplemental Table S1). The SCA suite examines the role of IP3R1 in SCA pathophysiology , with potential for translational studies.

NOVEL PREDICTIONS FROM THE SCA MODELING SUITE COINCIDENCE DETECTION TIME WINDOW AT SPINE IP3R1
Cerebellar Purkinje neurons receive input from more than 150,000 granule cell axons (parallel fibers), leading to hydrolysis of PIP2 and subsequent IP3-mediated calcium release from the endoplasmic reticulum (ER) (Finch and Augustine, 1998;Takechi et al., 1998;Berridge et al., 2000;Cohen, 2003) (Figure 1). Models 1-7 explored PIP2 signaling and IP3 production (Xu et al., 2003;Hernjak et al., 2005;Brown et al., 2008). Results from Models 4-7 indicated that baseline PIP2 levels are insufficient for requisite IP3 production in the spine, even with apparent anomalous lateral diffusion of PIP2 from the neighboring dendrite . On average, the Purkinje neuron has approximately 14 spines per micron of dendrite (Harris and Stevens, 1988). Each spine is attached to the dendrite branchlet by a neck with diverse morphology (Harris and Stevens, 1989) (see Supplemental Material, S3 IP3R1 in dendritic formation and spine morphology). Model 6 results showed that spine necks of varying radii and lengths also restricted diffusion of produced IP3 out of the spine head (Brown et al., 2008). This supported experimental results from Santamaria et al. with IP3 diffusing more slowly in spiny dendrites than in aspiny dendrites (Santamaria et al., 2006). This suggested that spines might compartmentalize IP3 via spine necks. Simulation results from Model 2 suggested local PIP2 sequestration as a likely source of sufficient PIP2, to fine-tune an experimentally observed (Wang Phosphatidylinositol 4,5-bisphosphate, a plasma membrane phospholipid of the inner leaflet that gives rise to DAG and IP3 when hydrolyzed; PLC, phospholipase C, an enzyme that hydrolyzes PIP2 when activated by G-βγ from mGluR; mGluR or Grm1, metabotropic glutamate receptor type 1 (Guergueltcheva et al., 2012); T, other glutamate transporters and receptors including Grid2, Excitatory amino-acid transporter type 1 (EAAT1; mutated in Episodic Ataxia type 6, de Vries et al., 2009), Excitatory amino-acid transporter type 4 (EAAT4; Spectrin β, an anchor for EAAT4 and Grm1 is mutated in SCA5, Ikeda et al., 2006), and AMPAR; B, calcium-binding proteins or buffers including calbindin and parvalbumin (Supplemental Material, S1 Calcium buffers in SCA and Supplemental Figure S2); mAtaxin, mutant ataxin proteins including Ataxin-1 through Ataxin-7; ICpeptide, peptides that resemble the tip of IP3R1 and thereby competitively bind mAtaxin; SERCA, sarcoendoplasmic reticulum calcium ATPase, a transporter for calcium entry from the cytosol to the smooth endoplasmic reticulum (ER); CARP, Carbonic anhydrase-related protein (particularly CARP VIII), an IP3R1 antagonist (Türkmen et al., 2009) (Supplemental Material, S4 IP3R1 suppression by CARP); RYR, ryanodine receptor, a transporter of calcium from the ER to the cytosol in dendrites (but not present in spines) in response to binding of specific ligands such as ryanodine; Dantrolene, a drug that inhibits RYR (Supplemental Material, S2 Calcium-induced calcium release crosstalk); PMCA, Plasma membrane calcium ATP-ase transports calcium out of the cell; Ca Ch, calcium channels including store-operate channels (SOC) for store-operated calcium entry and Cav2.1, which is the main P-type calcium channel in PCs with nonsense/missense mutations causing episodic ataxia type 2, expansion of CAG repeats causing SCA6, and mutations in CavB4 an accessory subunit for Cav2.1 causing EA5 (Escayg et al., 2000); IP3R, inositol trisphosphate receptor (mutated in SCA15/16 and altered sensitivity in SCA1-3, antagonized in QG ataxia), intracellular calcium release channel on the endoplasmic reticulum gated by IP3; PKC, protein kinase C (mutated in SCA14) expressed in Purkinje neurons helps control expression of surface molecules including AMPAR. Adapted from Hernjak et al. (2005Hernjak et al. ( ). et al., 2000Sarkisov and Wang, 2008) time window between PF and climbing fiber (CF; from the inferior olive) activation of the Purkinje neuron spine. Stimulation from a single CF innervating the Purkinje neuron cell body and proximal dendrites leads to calcium influx across the plasma membrane, through voltage-gated calcium channels (Ito et al., 1982) (Figure 1). Calcium binding of IP3R1 increases open probability of the receptor (Fiala et al., 1996). IP3R1 serves as the gate-keeper for IP3-induced calcium release. Thus, coincidence detection at IP3R1 leads to more calcium release than with activation of IP3R1 by IP3 or calcium alone (Wang et al., 2000;Hernjak et al., 2005;Ogasawara et al., 2008;Sarkisov and Wang, 2008;Brown et al., 2011).

BK CHANNEL IN IP3R1-ASSOCIATED ATAXIA BIOCHEMICOELECTROPHYSIOLOGICAL MODEL
IP3R1 interacts closely with the large conductance calciumactivated voltage-gated potassium (BK) channel in glioma cells (Weaver et al., 2007). BK channels appear in lipid rafts in the plasma membrane apposed to the smooth ER (sER). IP3R1 also functionally activates the BK channel in arterial smooth muscle cells (Zhao et al., 2010). It is thought that in other cell types, including neurons, BK channels may form physical complexes with various plasma membrane calcium channels, resulting in a proximity of only a few nanometers from the calcium channel pores (Dai et al., 2009).
In Purkinje neurons, BK channels contribute to repolarization of membrane potential transients in dendrites (Miyasho et al., 2001) and afterhyperpolarization of action potentials at the soma (Sausbier et al., 2004). BK channels are involved in several ataxias that converge on IP3R1-dependent signaling. BK knockout mice are ataxic and show markedly decreased spontaneous firing (tonic and bursting) of Purkinje neurons, with longer interspike intervals due to lack of BK contribution to afterhyperpolarization of the sodium (action potential) spikes which would normally help to reset the sodium channels in wild type mice (Sausbier et al., 2004;. BK channels are activated by the P/Q-type calcium channels (Walter et al., 2006), which are mutated in episodic ataxia 2 (EA2) (Guida et al., 2001;Mantuano et al., 2004;Tonelli et al., 2006;Walter et al., 2006) and spinocerebellar ataxia 6 (SCA6) (Ishikawa et al., 1997;Bürk et al., 2014). In the SCA modeling suite (Models 8-9, 13-15), BK channels plays a key role in mediating the effects of IP3R1-mediated calcium release on electrophysiological signals . Combining electrophysiology with detailed biochemistry leads to emergent properties (altered firing of the Purkinje neuron in Models 13-15) that are not possible to simulate in purely electrophysiological or biochemical models .

BIOCHEMICAL-ELECTROPHYSIOLOGICAL MODELING
There are other calcium channels that functionally couple with IP3R1. The small conductance calcium-activated potassium (SK) channels are not voltage-gated, but contribute to precision timing (Womack and Khodakhah, 2003;Womack et al., 2004;Walter et al., 2006;Alviña and Khodakhah, 2010a,b). Targeted overactivation of SK channels in SCA2 mice restores regular pacemaking activity . Isolated underactivation of SK channels without a counteracting mutation also yields ataxic mice (Alviña and Khodakhah, 2010a). Addition of this channel to the SCA models (Models 8-9, 13-15) will help mediate the influence of biochemical calcium release on electrophysiology.

PKC IMPACT ON BK CHANNEL ACTIVITY
Phosphorylation by PKC also inhibits neuronal BK channel activity (Shipston and Armstrong, 1996). Decreased PKC levels could therefore attenuate BK inhibition. This would balance suppression of BK channel activation by lower calcium transients in IP3R1-deficient Purkinje spines. Merging Models 13 and14 with Model 16 could illustrate contributions of BK regulation by PKC phosphorylation to SCAs. Protein kinase A (PKA) (Hall and Armstrong, 2000;Widmer et al., 2003) and PIP2 activation of BK and other potassium channels (Hilgemann et al., 2001;Falkenburger et al., 2010;Zhang et al., 2010) could also be added to these models.

SCA MOUSE MODELS
In addition to SCA1, SCA2, and SCA3 mice (Colomer Gould, 2012;Hansen et al., 2013;Hearst et al., 2014;Switonski et al., 2014), there are other mouse models available for testing SCA modeling suite predictions. The IP3R1 +/− mice can most be likened to IP3R1 haploinsufficiency in humans with SCA15/SCA16 (Ogura et al., 2001;van de Leemput et al., 2007;Hara et al., 2008;Iwaki et al., 2008;Di Gregorio et al., 2010;Novak et al., 2010b;Castrioto et al., 2011;Marelli et al., 2011;Obayashi et al., 2012) (Model 10). The ITPR1 opt/opt mice also have reduced IP3R1. However, IP3R1 is likely misregulated in these mice, as evidenced by IP3R1-mediated calcium transients that paradoxically show less attenuation to repeated stimulation than wild type mice (Street et al., 1997). If IP3R1 sensitivity is increased in ITPR1 opt/opt mice, then these mice could serve as an additional candidate model for polyQ ataxias or other ataxias with decreased expression of supersensitive IP3R1 (see Model 11). Similarly, the reported SCA15 mouse model ITPR1 18/ 18 shows reduced levels of IP3R1, but the 18 bp mutation is in the regulatory region of IP3R1 (van de Leemput et al., 2007). Calcium release and membrane electrophysiology need to be probed in these mice to ascertain whether they match the anticipated physiology of SCA15. Human SCA29 has missense mutations in the regulatory domain of IP3R1  and would also need such studies in any corresponding mouse model.

EXPERIMENTALLY AVAILABLE ICpeptides
A number of synthetic experimental peptides resembling sections of the C-terminal of IP3R1 are available for competitive binding in SCA mouse models. The IC4 peptide (also reported as IC1, Q2714-A2749; Tang et al., 2003;Tu et al., 2004) is available for competitive inhibition of PP1α in ataxias with reduced levels of IP3R1 (simulated in Model 10). IP3R1 dephosphorylation by protein phosphatase alpha (PP1α) decreases IP3R1 sensitivity to IP3 (Tang et al., 2003). IC4 (ICpeptide, Figure 1) resembles the tip of the C-terminal of IP3R1 that encodes the PP1α-binding domain. All these peptides can be used to validate and confirm predictions from the SCA modeling suite. The IC-G2736X and IC-10 peptides  are available for competitive inhibition of mutant Ataxin in ataxias with supersensitive IP3R1 (IC-G2736X simulated in Model 11). Peptide-based therapeutic approaches (Lucchese and Kanduc, 2014) could use viral vectors, as explored for Huntington's disease (HD) .

CLINICAL TRANSLATION
The SCA modeling suite is poised for continued use in translational studies (Brown et al., 2015). Cerebellar IP3R1 levels (Ogura et al., 2001;van de Leemput et al., 2007) in various SCA mouse models could be experimentally correlated with levels of peripheral lymphocyte IP3R1 from the same mice. The two sets of values could be plotted against each other. Levels of peripheral lymphocyte IP3R1 from ataxic individuals (van de Leemput et al., 2007) could then potentially be compared with corresponding levels in mice to estimate cerebellar levels in humans. In one study of SCA15, Western blot showed variably reduced IP3R1 levels in peripheral lymphocytes from three affected members of the same family relative to an unaffected family member (van de Leemput et al., 2007). Measuring peripheral blood lymphocyte levels of IP3R1 would be relatively noninvasive for humans. Correlated estimates of cerebellar IP3R1 would be useful to help guide therapy, particularly in presymptomatic patients who have undergone genetic testing and counseling (Supplemental Material, S1.6 Presymptomatic staging to consider calbindin modulation).
Other tissues such as smooth muscle, which has 75% of IP3R as IP3R1 (De Smedt et al., 1997), and peripheral lymphocytes, in which the major IP3R isoform is also type 1 (deSouza et al., 2007), likely have compensatory mechanisms involving 25% of IP3R as IP3R2 and IP3R3 to overcome IP3R1 deficits. In addition, there are two regulatory domain phosphorylation site splice variants of IP3R1 (Tu et al., 2002;Wagner et al., 2003). S(II) is favored in the brain (Wagner et al., 2003). Other tissues, such as smooth muscle and peripheral lymphocytes, may differentially phosphorylate their IP3R1 at S(I) (Tang et al., 2003) in response to insufficient levels of the receptor.
Further, there is a high density of sER containing IP3R1 in Purkinje spines (calculated average of ∼15% of spine volume from Harris and Stevens, 1988), relative to hippocampal spines (reported as <5% of spine volume from Harris and Stevens, 1989) (Supplemental Material, S6 IP3R1 in hippocampal spines), which are important for synaptic plasticity involved in cognitive learning and memory. This suggests that IP3R1 on sER preferentially serves particular functions in Purkinje spines that may manifest differently in other cell types.
All of these reasons underlie the observation that in IP3R1 mutations, and in several human ataxias with biochemical and electrophysiological signals that converge on IP3R1-dependent signaling (Mikoshiba, 2007;Schorge et al., 2010), the primary clinical manifestation is spinocerebellar ataxia.

SCA IN COMPUTATIONAL SYSTEMS NEUROBIOLOGY
Spatial quantitative models have given some insight into how cerebellar Purkinje neuron intracellular processes work together as an efficient system. A computational foundation for studying a wide array of spinocerebellar ataxias that involve mutations in various calcium and potassium channels, kinases, and other molecules, including IP3R1 was developed (Supplemental Material, Supplemental Figure S1). The result is a practical application of Computational Systems Neurobiology . Using these models to study various ataxias will help us to explain a wide array of experimental observations, elucidate cellular causes of these ataxias in mice and humans, and further understand the relationship between cytosolic calcium and membrane electrophysiology. The SCA modeling suite can help characterize the cellular pathophysiology of IP3R1-associated ataxia. That will help us to understand the biochemical and electrophysiological coupling in excitable membranes, since IP3R1 is highly expressed in the brain, and enriched in the cerebellum (Furuichi et al., 1989;De Smedt et al., 1997;Mikoshiba, 2007).

AUTHOR CONTRIBUTIONS
Sherry-Ann Brown conceived of, analyzed, designed, drafted, critically revised, approved, and agreed to be accountable for this submitted work. Leslie M. Loew analyzed, designed, drafted, critically revised, approved, and agreed to be accountable for this submitted work.

ACKNOWLEDGMENT
We are grateful to Dr. Louise McCullough for reading and editing this manuscript.