Monomeric α‐synuclein activates the plasma membrane calcium pump

Abstract Alpha‐synuclein (aSN) is a membrane‐associated and intrinsically disordered protein, well known for pathological aggregation in neurodegeneration. However, the physiological function of aSN is disputed. Pull‐down experiments have pointed to plasma membrane Ca2+‐ATPase (PMCA) as a potential interaction partner. From proximity ligation assays, we find that aSN and PMCA colocalize at neuronal synapses, and we show that calcium expulsion is activated by aSN and PMCA. We further show that soluble, monomeric aSN activates PMCA at par with calmodulin, but independent of the autoinhibitory domain of PMCA, and highly dependent on acidic phospholipids and membrane‐anchoring properties of aSN. On PMCA, the key site is mapped to the acidic lipid‐binding site, located within a disordered PMCA‐specific loop connecting the cytosolic A domain and transmembrane segment 3. Our studies point toward a novel physiological role of monomeric aSN as a stimulator of calcium clearance in neurons through activation of PMCA.

Appendix Figure S3.Supplementary PMCA activity assays A. The activity of PMCA1-ΔC relipidated in brain PC lipids.Ca 2+ titrations were performed in parallel in absence of the activating partner (basal activity), in the presence of 2.8 μM alpha-synuclein or in the presence of 1.2 μM CaM.B. The effect of oligomeric aSN on the PMCA activity.PMCA1d fold activation by titrated fulllength monomeric and oligomeric aSN.The assay was performed in presence of 1.8 μM free Ca 2+ and brain lipid extract was used for the PMCA relipidation.Monomeric aSN data, presented here for comparison, is the same as in Figure 4. Oligomeric aSN experiment was performed in four independent replicates, where PMCA originated from single expression culture and aSN oligomers from two independent preparations.All data shown as mean ± SEM. C. The effect of full-length and C-terminally truncated aSN (1-95) on the calcium-dependent activity of PMCA1d.On the left -the calcium titration experiment was performed simultaneously in absence of activating partner (empty circles), in presence of the full-length monomeric a-SN (filled circles) and C-terminally truncated aSN (1-95) (filled squares).The pump was relipidated in brain lipid extract (BE).The lines are the best fit given by the Hill equation.On the right -apparent Kd Ca2+ values calculated from the fitted Hill plots with the apparent Kd values (μM) for Ca 2+ as follows: PMCA1d basal (without aSN) -0.347 ± 0.059, with aSNwt -0.189 ± 0.028, with aSN (1-95) -0.142 ± 0.026.The measurements were performed in three independent replicates, where the proteins originated from single expression culture.D. The activity of C-terminally truncated PMCA4x (lacking the autoinhibitory domain) was measured as a function of monomeric a-SN concentration in presence of 1.8 μM free Ca 2+ .PMCA was relipidated with brain extract (BE).The measurement was performed in independent duplicates, where proteins originated from single expression culture Appendix Figure S7.Pull-down of aSN with PMCA immobilized by Calmodulin-sepharose.
In this experiment pure protein preparations were used.

A model for aSN-dependent calcium regulation
In order to conceptualize the findings of aSN-mediated PMCA activation and its influence on the Ca 2+ concentration in the presynaptic terminal, we adapted an existing ODE-model published by Erler et al. (Erler, Meyer-Hermann et al., 2004), hereafter named the Erler-model, to take into account the new dependence of PMCA on aSN.
Here we briefly introduce the Erler model, before introducing the changes applied to take into account the aSN-dependence of PMCA.
The Erler-model describes Ca 2+ -fluxes through PMCA, the H + /Ca 2+ exchanger NCX and the voltage gated Ca 2+ channel VGCC and studies calcium dynamics during action potentials in absence and presence of external Ca 2+ buffers like Ca 2+ -fluorophores (Erler et al., 2004).Erler et al. made use of the Hodgkin-Huxley model (Hodgkin & Huxley, 1952, Keener & Sneyd, 2009) to describe the membrane potential dynamics during an action potential.The dynamics of the cytosolic Ca 2+ ion concentration was described by the following differential equation: Where   denotes the influx of Ca²⁺ through voltage gated Ca²⁺ channels,   and   denote Ca²⁺ effluxes mediated by PMCA and NCX respectively and   denotes a leakage flux of Ca²⁺ ions across the membrane down its electrochemical gradient.
Where the opening probability reaches its asymptotic value  ∞ () with time constant .The asymptotic value  ∞ () can be described by a sigmoidal function: Where  ℎ is the half activation voltage and  is the steepness at the inflection point of  ∞ ().
The calcium ion efflux through PMCA and NCX are modeled as Hill equations: Where   and   are the specific surface densities,   and   are the universal maximum activity rates,   and   are the half activation concentrations, and   and   are the Hills coefficients of PMCA and NCX respectively. is the leakage surface current density, which is determined by the steady state conditions, and ensures that the model can maintain equilibrium when unperturbed.
To account for the aSN concentration dependency of the PMCA activity, the flux through PMCA used by Erler et al. was replaced by another kinetic rate law, which can be derived from the following binding scheme, which allows for description of non-essential activation as seen by aSN.: • Where  , is the dissociation constant of calcium,  , is the dissociation constant of aSN,   is the catalytic constant of PMCA,  is the reciprocal allosteric coupling constant, and  is the factor by which aSN affects the catalytic constant.
The resulting equation is (Baici, 2015): In order to determine the kinetic parameters, the kinetic for PMCA was fitted to the PMCA1 activity in dependence of [Ca 2+ ] and [aSN] (Figure 2A left and Figure 2B), using the minimize function from scipy.optimize (VirtanenGommers et al., 2020) and the cost function: With   being the standard error of the mean corresponding to the data point   .
The optimal parameter set was given by:  ,() = 1.93

𝑒𝑒𝑚𝑚𝑚𝑚𝑙𝑙 𝑃𝑃𝑖𝑖
µ    = 0.29  = 4.31  , = 5.5 µM  , = 0.29 µM The resulting fit is shown in Appendix Figure S8.Note that the data points for high calcium concentrations were excluded from the fitting process.

Calculation of dependent parameters
The parameter  ,() obtained by the fitting process is given in  And finally: .

Complete ODE System
Finally, the entire system of ODEs is given by:  S1.
Appendix Table S1.Initial values and parameters for the calcium regulation model.

Computer Code -Transcriptomics analysis
The original code written in R for the purpose of the analysis of transcriptomics data.

𝐺𝐺 in µ𝑚𝑚⁻¹ representing the surface to volume ratio, the ion valence 𝑧𝑧 𝐶𝐶𝐶𝐶 , and Faraday's constant 𝐹𝐹 in 𝑃𝑃𝑚𝑚 𝑚𝑚𝑚𝑚𝑙𝑙 . As the term 1 1+𝑇𝑇 𝑒𝑒𝑒𝑒 +𝑇𝑇 𝑒𝑒𝑒𝑒 is unitless, all fluxes 𝐽𝐽 are defined in units of 𝐶𝐶𝑃𝑃 µ𝑚𝑚² . The term 1 1+𝑇𝑇 𝑒𝑒𝑒𝑒 +𝑇𝑇 𝑒𝑒𝑒𝑒 represents calcium ion buffering through endogenous and exogenous buffers, where 𝑇𝑇 𝑙𝑙𝑒𝑒 (𝑐𝑐) =
(Erler et al., 2004) concentration are given in Where   denotes the surface density of VGCCs,   denotes the voltage dependent opening probability,   is the open pore conductivity,  is the membrane potential, and   is the reversal potential, described by the Nernst equation:Where  is the molar gas constant,  is the temperature, [²⁺]  is the external calcium ion concentration and   is a correction factor for the linear approximation used for the single channel open current   (  − )(Erler et al., 2004).The time dependence of voltage dependent opening probability is modeled by a single exponential approximation: , +  , +  , +  , ≡ 0 With  , ,  , and  , being the fluxes mediated by PMCA, NCX and VGCC at equilibrium and (Keener & Sneyd, 2009) modeled as GHK-flux equation(Keener & Sneyd, 2009), which depends on the permeability of the membrane for Ca 2+ (  ), which was calculated using the steady state assumption:  = ( , +  , +  , ) ⋅