Systems Biology Investigation of cAMP Modulation to Increase SMN Levels for the Treatment of Spinal Muscular Atrophy

Spinal muscular atrophy (SMA), a leading genetic cause of infant death worldwide, is an autosomal recessive disorder caused by the loss of SMN1 (survival motor neuron 1), which encodes the protein SMN. The loss of SMN1 causes a deficiency in SMN protein levels leading to motor neuron cell death in the anterior horn of the spinal cord. SMN2, however, can also produce some functional SMN to partially compensate for loss of SMN1 in SMA suggesting increasing transcription of SMN2 as a potential therapy to treat patients with SMA. A cAMP response element was identified on the SMN2 promoter, implicating cAMP activation as a step in the transcription of SMN2. Therefore, we investigated the effects of modulating the cAMP signaling cascade on SMN production in vitro and in silico. SMA patient fibroblasts were treated with the cAMP signaling modulators rolipram, salbutamol, dbcAMP, epinephrine and forskolin. All of the modulators tested were able to increase gem formation, a marker for SMN protein in the nucleus, in a dose-dependent manner. We then derived two possible mathematical models simulating the regulation of SMN2 expression by cAMP signaling. Both models fit well with our experimental data. In silico treatment of SMA fibroblasts simultaneously with two different cAMP modulators resulted in an additive increase in gem formation. This study shows how a systems biology approach can be used to develop potential therapeutic targets for treating SMA.


Introduction
Spinal muscular atrophy (SMA) is an autosomal recessive, neurodegenerative disorder characterized by the progressive loss of a-motor neurons in the anterior horn of the spinal cord; this loss leads to progressive muscle weakness and atrophy [1]. SMA is a leading genetic cause of infant death worldwide with 1 in 5000-10,000 children born with the disease [2,3]. Loss of or mutation in SMN1 (survival motor neuron 1) leads to SMA [4]. In humans and only in humans, SMN1 is duplicated to yield SMN2 [5,6]. There is a single nucleotide change (CRT) within SMN2 exon 7 that causes most of SMN2 mRNAs to lack exon 7 (SMND7). The resultant SMND7 protein is unstable and not fully functional [7,8]. SMN2 can, however, provide some full-length, functional SMN (FL-SMN) protein. The number of SMN2 copies modifies disease severity in SMA patients [9][10][11][12][13][14][15][16]. In transgenic mouse models for SMA, the copy number of human SMN2 modulates the phenotypic severity [17][18][19]. SMN2 is, therefore, an endogenous genetic modifier of disease severity in SMA.
Because of this phenotype modifying property, SMN2 has been the target for numerous drug discovery strategies. Targeting cyclic adenosine monophosphate (cAMP) signaling is of particular interest in developing inducers of SMN2 expression. The cAMP signaling cascade ( Fig. 1) is used by both prokaryotes and eukaryotes to regulate various processes including cell growth, metabolism and stress response [20]. The SMN2 promoter contains at least one cAMP-response element (CRE) that is able to bind to activated CRE-binding protein (phospho-CREB) [21]. The b2-adrenergic agonist salbutamol increases the amount of FL-SMN protein in SMA fibroblasts and leukocytes of SMA patients [22,23]. Forskolin, which stimulates adenylyl cyclase (AC) catalysis to produce cAMP from ATP, increases SMN2 promoter activity [21]. The synthetic analogue dibutyryl cAMP (dbcAMP)-which activates cyclic AMP-dependent protein kinase (PKA)-also increases SMN2 promoter activity [21]. Taken together, these studies show that modulation of cAMP signaling can increase SMN expression from SMN2.
In this study, we will examine the effect of modulating cAMP signaling on SMN expression in SMA cells using a systems biology approach. cAMP signaling will be regulated by one of four possible targets ( Fig. 1): activation of G protein-coupled receptors, activation of AC, activation of PKA and inhibition of phosphodiesterases (PDEs) that break down cAMP. Within the nuclei of most eukaryotic cells, SMN protein localizes to discreet foci known as gems, or gemini of coiled bodies [24]. The number of gems are markedly reduced within the nuclei of cells from SMA patients [9]. Using gem formation as an indicator of the expression of functional, FL-SMN protein, we will develop computational models of interactions between the cAMP pathway and gem formation to investigate how modulating cAMP signaling dynamics affects FL-SMN production. This systems biology approach consists of a synergistic interaction between experimental data and mathematical models. The experimental data and domain knowledge are used to develop the initial models and through a process of iteration, the model assumptions are updated to come up with an improved model [25]. Such a systems modeling approach can ultimately aid in the development and optimization of cAMP signaling-based therapeutic strategies for SMA.

Materials and Methods
Fibroblast Cell Culture GM03813 fibroblasts [26] (Coriell Cell Repositories; Camden, NJ) were derived from a SMA patient with deletion of SMN1 and 2 copies of SMN2. GM03814 fibroblasts [26] (Coriell Cell Repositories) were derived from the carrier mother of GM03813; this line, therefore, carries 1 copy of SMN1. All fibroblast lines were maintained in Dulbecco's modified essential medium (DMEM; Life Technologies, Grand Island, NY) containing 10% fetal bovine serum (FBS; Atlas Biologicals, Fort Collins, CO), 2 mM L-glutamine (Life Technologies) and 1% penicillin/ streptomycin (Life Technologies).

Drug Treatment
Cells were seeded onto gelatinized glass coverslips at a density of 4000 cells/cm 2 . Cells were treated with one of the following compounds (n53/dose): dbcAMP (5- Fig. 1. The cAMP pathway and SMN2 expression. In this signaling cascade, ligand activation of the membrane bound G protein-coupled receptors such as the b-adrenergic receptor (bAR) results in the dissociation of the G a,s subunit from the receptor. G a,s then activates adenylyl cyclase (AC). Once stimulated, AC produces cAMP by cyclizing intracellular ATP. cAMP then activates a serine/threonine kinase known as cAMP-dependent protein kinase-or protein kinase A (PKA). The regulatory subunits of PKA are then released and the catalytic subunit acts on many downstream targets including the cAMP-response elementbinding (CREB) protein. Phosphorylated CREB (phospho-CREB) binds to cAMP response elements (CREs) with the promoter regions of various genes including SMN2. cAMP signaling is attenuated by cyclic nucleotide phosphodiesterases (PDEs) which break down cAMP into AMP. doi:10.1371/journal.pone.0115473.g001 Mathematical Modeling, cAMP Signaling and SMA 500 mM; EMD Millipore, Billerica, MA), epinephrine (1-100 nM; Sigma-Aldrich, St. Louis, MO), forskolin (0.5-50 mM; EMD Millipore), salbutamol (1-100 nM; Sigma-Aldrich), rolipram (0.1-10 mM; Sigma-Aldrich) or vehicle. ddH 2 O was utilized as the vehicle for the dbcAMP treatments while DMSO was the vehicle for the remaining compounds. Test compounds were added to the medium at a 1:1000 dilution. Medium was changed daily and fresh compound was added for 5 days.

Immunofluorescence
Immunostaining of fibroblast cells was accomplished as described previously [27]. Briefly, cells grown on gelatinized coverslips were fixed with Fixative Buffer (2% paraformaldehyde, 400 mM CaCl 2 , 50 mM sucrose in 100 mM sodium phosphate buffer, pH 7.4) for 30 min at room temperature, thoroughly rinsed with phosphate-buffered saline (PBS) and permeabilized with ice-cold acetone for 10 min. After drying for at least 30 min at room temperature, the cells were rehydrated with PBS for 10 min at room temperature and then blocked with 56BLOCK for 60 min at room temperature. The cells were incubated overnight with primary antibody solution (mouse anti-SMN mAb (MANSMA2 (8F7); Developmental Studies Hybridoma Bank, Iowa City, IA [28]) diluted 1:200 in 16BLOCK) at 4˚C. The cells were then washed extensively (3610 min) with PBS and incubated with secondary antibody solution (biotinylated goat anti-mouse IgG (Jackson ImmunoResearch) diluted 1:400 with 16BLOCK) for 60 min at room temperature. The cells were then washed with PBS (3610 min) and then incubated with AlexaFluor 594-conjugated streptavidin (Life Technologies) diluted 1:200 with PBS for 60 min at room temperature. Cells were then counterstained with Hoescht 33342 (1 mg/mL; Life Technologies) in PBS for 5 min. After thorough washing with PBS, coverslips were mounted onto glass slides with ImmuMount (Shandon Lipshaw) and stored at 4˚C until analysis.

Gem Count Analysis
SMN immunostaining in fibroblasts was visualized using a DMRXA2 epifluorescence microscope (Leica Microsystems) with an ORCA-ER cooled camera (Hamamatsu, Hamamatsu City, Japan) and Volocity 6.1.1 software (Perkin-Elmer). For gem counting, the following parameters were measured in 100 randomly selected nuclei: the number of gems, the number of cells with gems and the number of cells with more than 1 gem. The gem counts were converted into a concentration value (in mM) using an approximate average cell volume (2.68610 213 L). This conversion assumes that all cells are of equal volume [29].

Development of Mathematical Models
The computational model was visualized and developed in CellDesigner [30]. Each model was then converted into Systems Biology Markup Language (SBML) format [31] and imported into MATLAB using SBToolbox [32]. SBToolbox was used to complete parameter sensitivity and model simulations.

Model Derivation
In order to adapt the Williamson model [33] to our system, their parameters required reworking to be in accordance with the units of our data. The Williamson model was shown to match data from literature [34,35] which is reported in units of nmol per gram wet weight versus minutes. Through careful inspection, the time units of the model were determined to be 20 seconds (s) (i.e. one time unit represents 20 s in the data) with the concentration units remaining the same as the data. The data points of the model results presented in Williamson were extracted using WebPlotDigitizer v.2.6 (http://arohatgi.info/ WebPlotDigitizer) and converted into the proper units.
Our simplified model consists of three ordinary differential equations (ODEs; Equations 1-3) and two conservation equations (Equations 4 & 5). Equation 1 represents the rate of change in the active form of the G protein receptor (GP a ) in the presence or absence of a stimulatory hormone or agonist. Equation 2 models the instantaneous changes in active PKA (PKA a ) as a result of cAMP production. Equation 3 captures both cAMP production from ATP by AC and degradation into AMP via PKA a -stimulated PDE activity. The conservation equations demonstrate the balance between the active and inactive forms of both GP and PKA.
In order to further simplify the system, the two PDE terms from the Williamson et al. model [33] were combined into one term. As evinced in the Williamson et al. study [33], PDE2 does not have a significant effect on cAMP concentration, especially when compared to PDE1. Since there are multiple isoforms of PDEs in humans [36], we generated a general PDE term to model the overall inhibitory action of PDEs in the cells. The model parameters were defined as in [33] and their descriptions are summarized in Table 1.
The model was then fit to the converted experimental data using the optimization algorithms detailed below. The optimized parameters determined from this model fitting are listed in Table 1.
The experimental data utilized by Williamson et al. [33] represented concentration in units of nmol per gram wet weight (gww). However, the glucose pulse used in this study was in units of mM. In order to convert the data into mM concentrations, the following equation was used: where C(nM) is concentration of cAMP in milimolar, C w is the conversion factor to grams dry weight (0.15) and V c is the volume of 10 7 cells (2.68610 26 L; approximately 10 7 cells in 1 gww). The equation and constant values were adapted from the equation detailed in Williamson et al. [33]. The parameters marked with an asterisk (*) were carried over from the simplified cAMP model.

Parameter estimation
Parameters for the base model were estimated by fitting our modified model to the data extracted from the Williamson results through a simulated annealing algorithm [37,38], which is efficient at finding the global minimum for optimization. The algorithms were taken from Systems Biology Toolbox (SBToolbox) [32] in MATLAB and the estimation was run using the SBparameterestimation function from SBToolbox as well as the main estimation functions listed in additional files.  9) and the self-assembly of FL-SMN into gems (Equation 10). SMN2 activation was modeled using the Hill equation while the rest of the parameters were based on mass action kinetics. The conservation relationship detailed in Equation 11 represents the total CREB molecules in the cell. Each model parameter is defined in Table 1. Our model used units of min for time and mM for concentration.
½totalCREB~½CREB p z½CREB ð 11Þ Both salbutamol and epinephrine directly activate G proteins by binding with their receptors outside the cell. In our model, both compounds were directly substituted for the hormone concentration term in Equation 1: ½Hormone~½Salbutamol~½Epinepherine ð 12Þ In addition to activating the SMN2 promoter, salbutamol also alters the splicing of SMN2 mRNA causing an increase in FL-SMN production over SMND7 [22]. The interaction of salbutamol with the splicing machinery was modeled as proportional increase in the transcription rate of SMN2 mRNA given in Equation 8: Treatments with the AC activator forskolin were modeled as an increase in basal AC activity proportional to the dosage of forskolin: AC basal Ã~A C basal zFk a ½Forskolin ð 14Þ For the treatments with dbcAMP, the dose concentration was added directly to the existing cAMP concentration in the system: Rolipram is a well-known PDE inhibitor, which indirectly causes an increase in cAMP. The inhibition interaction was modeled as reversible and competitive in Michaelis-Menten kinetics. The presence of the inhibitor alters the apparent Michaelis constant for the binding of cAMP to PDE: where [R] represents the concentration of rolipram and K i represents the inhibitor dissociation constant.

Parameter Estimation
Since the gem count data was collected after a treatment window of 5 days, the concentrations were treated as steady state values for the system. The steady state assumption allowed the model equations to be set to zero and solved for their constituent model states giving a system of algebraic equations. Due to the highly conserved nature of the cAMP pathway, the parameter values derived from the base model were carried over in order to reduce the parameter space to be optimized. A system of equations was derived through the steady state assumption on the full cAMP:SMN2 model. Parameter estimation was completed through a sign squared error (SSE) analysis between the gem steady state concentrations derived from the gem count data and the full cAMP:SMN2 model calculations for each compound and dose. The parameter space was covered by generating a multidimensional matrix encompassing the possible combinations of parameter values over a specified range for each parameter to be estimated. For an easier model fit, the two controls were assumed to be identical and their data was averaged together.

Model Development
An alternate pathway has been suggested in the literature [39] which shows active PKA directly stimulating the self-assembly of SMN into gems. Gems are much more stable than monomeric SMN so increasing the gem formation rate would increase the overall SMN concentration over time. Burnett et al. also found no noticeable increase in SMN mRNA levels coinciding with increased PKA a levels suggesting that transcription is not involved. In order to examine the implications of the alternate pathway, a new model was developed by modifying our full cAMP:SMN2 model.
Equations 1, 2 and 3 from the full cAMP:SMN2 model were also used for this model. The key modifications made were the elimination of the CREB and transcription terms, simplification of translation to a constant rate, T, and the addition of PKA a concentration to the gem formation term. The elimination of the CREB term also allowed for removal of the related conservation equation form the model. The alternate cAMP:SMN2 model parameters are defined in Table 3.
½totalGP~½GP a z½GP i ð 26Þ ½totalPKA~½PKA a z½PKA i ð 27Þ The modifications made for each of the compounds were identical to the full cAMP:SMN2 model, except that the effect of salbutamol on splicing was represented as a proportional increase in the translation rate (Equation 28):

Sensitivity Analysis
Steady state sensitivity analysis was completed according to the following equation: where Sn ij is the normalized sensitivity of species i with respect to parameter j, Xss i is species i at steady state, p j is parameter j, and Dp j is the change in parameter j. The sensitivities of gem concentration and FL-SMN concentration to changes in each of the system parameters were calculated.

Statistical Analysis
All quantitative data were expressed as mean ¡ standard error. Comparisons made between quantitative data were made using one-way ANOVA with a Bonferonni post hoc test. A p-value less than or equal to 0.05 was considered statistically significant. Statistical analyses of quantitative data were completed using SPSS v.22.

Effect of Modulating cAMP Signaling on Gem Localization in SMA Fibroblasts
Fibroblasts derived from a type II SMA patient (GM03813; [26]) were treated with increasing doses (n53/dose) of one of the following modulators of cAMP signaling: epinephrine, salbutamol, forskolin, dbcAMP and rolipram. Fig. 1 shows how each compound modulates cAMP signaling. All 5 of the cAMP signaling modulators tested increased SMN immunostaining in the nucleus as well as in the cytosol of SMA fibroblasts (Fig. 2). Further analysis of SMN localization to gems showed that all 5 of the cAMP signaling modulators increased the number of gems in 100 randomly selected nuclei (Fig. 3A), the proportion of cells containing gems (Fig. 3B) and proportion of cells containing multiple gems (Fig. 3C) in a dosedependent manner relative to vehicle-treated SMA fibroblasts. While none of the compounds attained gem counts similar to those observed in fibroblasts (GM03814) derived from the mother of GM03813-i.e. carrier fibroblasts, the number of gems/100 nuclei in SMA fibroblasts treated with the highest doses of dbcAMP, forskolin, salbutamol and rolipram reached at least 50% of the gem counts found in carrier fibroblasts.

Development of a Computational Model for the Effect of cAMP Signaling on SMN2 Expression
We developed a computational model of cAMP signaling in humans by modifying a previously published model of the cAMP pathway in yeast [33]. Because of the highly conserved nature of cAMP signaling, essential features of the cAMP pathway are common between humans and yeast and can be modeled with limited changes between species. The original model in yeast consists of 3 ordinary differential equations (ODEs) and 16 parameters [33] (Fig. 4A). By modeling only those functions essential to cAMP and likely conserved between yeast and humans, our base model of the cAMP pathway contained 3 differential equations and 8 parameters (Fig. 4B). Even with this simplified model, we were able to capture the essential dynamics of cAMP signaling reported previously [33] ( Fig. 4C). Therefore, our computational model represents an essential set of relationships that are likely at work in humans and clinically relevant. We then extended this simplified model of cAMP signaling to include production of FL-SMN through CREB and SMN2 (Fig. 5A). We also added pathways through which treatments to modify cAMP levels may affect FL-SMN production. We used the number of gems/100 nuclei as our experimental dataset-after being converted to concentration (S1 Table)-to determine how well our model fits with observed data. Except for those found in the literature, the parameters between cAMP production and gem formation within the computational model were fit to these experimental data by minimizing the sum of squared error (SSE) between simulation and experiment. After preliminary simulation, select parameters from the base equations were optimized to better capture the dynamics observed in the human system ( Table 1). By comparing model simulations to our experimental data, we can predict which treatments act through the pathways we proposed. The full cAMP:SMN2 model accurately predicted the response of SMA fibroblasts to treatments with forskolin (Fig. 5B), dbcAMP (Fig. 5C), and rolipram (Fig. 5D). Therefore, it is likely that the overall effects of these drugs act through the cAMP signaling cascade as modeled. Both epinephrine (Fig. 5E) and salbutamol (Fig. 5F) treatments, however, showed deviations from model predictions. The full cAMP:SMN2 model predicted a nearly linear, dose-dependent increase in gem formation while the data predicted a sharp increase in gem formation followed by a plateau. The data suggest saturation of the G protein-coupled receptors that bind both epinephrine and salbutamol. These compounds may act through additional, cAMP-independent pathways to give their full effect on gem formation or may have additional levels of regulation that were not simulated.
Having built and tested a computational model of FL-SMN production, we next used a local sensitivity analysis to identify which targets in the cAMP signaling pathway may be most beneficial to optimally increase FL-SMN    production and gem formation. Gem concentrations at steady-state were used as output measures to identify the sensitivities of FL-SMN production to perturbations in each model parameter ( Table 2). The Hill coefficient for the binding of phospho-CREB to the CRE present in the SMN2 promoter had the most impact on the final gem concentration in the full cAMP:SMN2 model. Since the Hill coefficient affects the rate of SMN2 transcription, the sensitivity analysis suggests that the transcription of SMN2 has the greater impact on cAMP signaling-induced gem formation and functional, FL-SMN expression.

Using Full cAMP:SMN2 Mathematical Model to Predict the Effects of Combination Treatments on SMN2 Expression
As previously discussed, the full cAMP:SMN2 model accurately predicts the effects of treatment by rolipram, forskolin and dbcAMP. We used the full cAMP:SMN2 model to examine the effect of a simultaneous treatment with two of these three compounds: rolipram + dbcAMP, forskolin + dbcAMP and rolipram + forskolin. All three combinations demonstrated synergistic responses yielding higher steadystate gem concentrations with each increasing dose. However, both combinations with dbcAMP hit a maximum gem concentration around 6.0 pM (Figs. 6A and 6B) while the combination of rolipram and forskolin peaks around 6.7 pM (Fig. 6C). Since the gem concentration in carrier fibroblasts is approximately 7.0 pM (S1 Table), these results suggest that manipulation of the cAMP signaling pathway at multiple points in the cascade can optimally increase SMN2 expression.

Development of an Alternate Model for the Effect of cAMP Signaling on SMN2 Expression
Previous work has shown that activation of PKA directly affects gem formation independent of SMN2 transcription [39]. Based on this observation, we also developed an alternate model of the interplay between cAMP signaling and the expression of functional FL-SMN and gem formation (the alternate cAMP:SMN2 model; Fig. 7A). We fit the alternate cAMP:SMN2 model to the available gem concentration data (S1 Table) as described for the full cAMP:SMN2 model. The downstream parameters as well as select simplified model parameters were included for optimization ( Table 3). Similar to the full cAMP:SMN2 model, the alternate cAMP:SMN2 model predicted responses due to treatments with forskolin ( Fig. 7B), dbcAMP (Fig. 7C) and rolipram (Fig. 7D); the alternate cAMP:SMN2 model also yielded deviations for salbutamol (Fig. 7E) and epinephrine (Fig. 7F) treatments.
With the alternate cAMP:SMN2 model fully optimized, we conducted a normalized local sensitivity analysis in order to reveal the interactions most important for gem production within the alternate pathway. The alternate cAMP:SMN2 model sensitivity results show that both the gem formation and degradation rates have a significant influence on final gem concentration, as would be expected (Table 4). Furthermore, their sensitivities are three orders of magnitude greater than the corresponding sensitivity to the Hill coefficient in the full cAMP:SMN2 model. The estimated gem formation rate for the alternate cAMP:SMN2 model is approximately five orders of magnitude larger than that of the full cAMP:SMN2 model, thus making this parameter the key differentiator between the two proposed cAMP:SMN2 models.
We also developed and analyzed a combination model which encompasses the effects of cAMP signaling on the upregulation of SMN2 promoter activity and transcription (the full cAMP:SMN2 model) as well as the direct stimulation of gem formation by PKA (the alternate cAMP:SMN2 model). The fit of this combination cAMP:SMN2 model to the experimental data, however, was significantly weaker than for the fits of either the full cAMP:SMN2 and alternate cAMP:SMN2 models (data not shown). Therefore, this combinatorial effect of cAMP signaling on the expression of functional SMN2 is far less likely to be biologically accurate.

Discussion
In this study, we use a systems biology approach with mathematical models to characterize the regulation of SMN2 expression by cAMP signaling. This is the first time, to our knowledge, that a systems biology approach has been used to develop SMA therapeutic strategies. We focused on the interaction between cAMP signaling and SMN2 expression in this study since there is ample evidence in the literature showing that induction of cAMP signaling increases SMN2 expression [21][22][23]. The cAMP signaling treatment data were used to generate two distinct mathematical models-full cAMP:SMN2 and alternate cAMP:SMN2 models-for the interaction of cAMP signaling and SMN2 expression. Simulated data from both models match very well with experimental data suggesting that either model is robust. The mathematical models can also be used to predict the effects of drug combinations on cAMP-mediated regulation of SMN2 expression. This study will also guide future investigations into the mechanisms by which cAMP signaling regulated SMN2 expression.
Gem formation serves as an indicator of the expression of fully functional, FL-SMN protein in this study. Reduced gem formation correlates with SMN protein expression and disease severity in fibroblasts derived from SMA patients [9]. Numerous studies have identified drug compounds that increase the number of gems in SMA patient cells [27,[40][41][42][43][44][45][46][47][48][49]. In these studies, drug-induced changes in gem formation are verified by corresponding changes in SMN protein levels in SMA fibroblasts measured by immunoblot or enzyme-linked immunosorbent assays (ELISAs). Some of these gem inducers also increase SMN protein levels in the central nervous system and can ameliorate the phenotype in SMA mouse models [47,[50][51][52]. These observations support the rationale for using gem formation as an indicator of SMN expression in our mathematical models.
Activation of cAMP signaling increases SMN2 expression but there is debate as to how this signaling cascade regulates SMN2. Some groups report that the regulation of SMN2 promoter activity and mRNA transcription are influenced by cAMP signaling [21][22][23] but others suggest that the regulation of SMN2 expression by cAMP signaling occurs post-transcriptionally, i.e. by influencing FL-SMN protein stability [39]. The two mathematical models generated in this study for the interaction between cAMP signaling and SMN2 expression-full cAMP:SMN2 and alternate cAMP:SMN2 models-differ by whether or not cAMP signaling affects SMN2 transcription. Either model fit very well with the experimental data. However, when the two models were combined, the fit with the experimental data was not strong suggesting that only one model correctly simulates the interaction between the cAMP signaling cascade and SMN2 expression. At present, we cannot determine which mathematical model more accurately simulates cAMP signaling-dependent regulation of SMN2. A detailed examination of the time course of gem formation-as well as other levels of SMN2 regulation-in response to cAMP signaling modulators would permit model discrimination and refinement. The regulation of SMN expression by cAMP signaling is complex and multifaceted. As a result, some facets of the interaction between cAMP signaling and SMN gene expression were not included in our mathematical models. For example, PKA has been shown to directly phosphorylate SMN in vitro [39,53]. This PKA-dependent phosphorylation of SMN may modulate its interactions with components of the core SMN:gemins macromolecular complex including gemin-2 (SIP1), gemin-5 and gemin-8 [39,53]. Since the effects of PKA phosphorylation of SMN on its function and localization are not yet known, we could not factor this variable in our mathematical models. Also, activation of NMDA-type, glutamatergic receptors increases SMN expression in the spinal cord by AKTmediated phosphorylation of CREB and repression of ERK-activated Elk-1 [54,55]. It remains to be determined whether cAMP signaling-independent phosphorylation of CREB would affect SMN expression in our model system. Once we have a better understanding of how these events affect SMN expression and function, direct PKA phosphorylation of SMN and the intersection of other signaling pathways-like AKT and MAP kinase (ERK)-can be integrated into mathematical models of the interactions of cAMP signaling on SMN expression and function.
In summary, we have demonstrated that increasing cAMP activation increases FL-SMN production, as measured by gem formation, in human cells using a systems biology approach, We generated data-driven, mathematical models describing the interactions between cAMP signaling and functional FL-SMN production (gem formation) from SMN2. These models can be used to identify the components of the cAMP signaling cascade that may be most effective at increasing SMN levels in SMA cells as well as to predict the effects of combination treatment strategies. Development of cAMP signaling-based therapeutic strategies using a combination of biological data and mathematical modeling will be essential for treating SMA.
Supporting Information S1