Familial Alzheimer’s disease (FAD)-causing mutant presenilins (PS) interact with inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) Ca2+ release channels resulting in enhanced IP3R channel gating in an amyloid beta (Aβ) production-independent manner. This gain-of-function enhancement of IP3R activity is considered to be the main reason behind the upregulation of intracellular Ca2+ signaling in the presence of optimal and suboptimal stimuli and spontaneous Ca2+ signals observed in cells expressing mutant PS. In this paper, we employed computational modeling of single IP3R channel activity records obtained under optimal Ca2+ and multiple IP3 concentrations to gain deeper insights into the enhancement of IP3R function. We found that in addition to the high occupancy of the high-activity (H) mode and the low occupancy of the low-activity (L) mode, IP3R in FAD-causing mutant PS-expressing cells exhibits significantly longer mean life-time for the H mode and shorter life-time for the L mode, leading to shorter mean close-time and hence high open probability of the channel in comparison to IP3R in cells expressing wild-type PS. The model is then used to extrapolate the behavior of the channel to a wide range of IP3 and Ca2+ concentrations and quantify the sensitivity of IP3R to its two ligands. We show that the gain-of-function enhancement is sensitive to both IP3 and Ca2+ and that very small amount of IP3 is required to stimulate IP3R channels in the presence of FAD-causing mutant PS to the same level of activity as channels in control cells stimulated by significantly higher IP3 concentrations. We further demonstrate with simulations that the relatively longer time spent by IP3R in the H mode leads to the observed higher frequency of local Ca2+ signals, which can account for the more frequent global Ca2+ signals observed, while the enhanced activity of the channel at extremely low ligand concentrations will lead to spontaneous Ca2+ signals in cells expressing FAD-causing mutant PS.
Aberrant Ca2+ signaling caused by IP3R gating dysregulation is implicated in many neurodegenerative diseases such as Alzheimer’s, Huntington’s, Spinocerebellar ataxias, and endoplasmic reticulum stress-induced brain damage. Thus understanding IP3R dysfunction is important for the etiology of these diseases. It was previously shown that FAD-causing mutant PS interacts with the IP3R, leading to its gain-of-function enhancement in optimal Ca2+ and sub-saturating IP3 concentrations. Here, we use data-driven modeling to provide deeper insights into the upregulation of IP3R gating in a wide range of ligand concentrations and quantify the sensitivity of the channel to its ligands in the presence of mutant PS. Our simulations demonstrate that these changes can alter the statistics of local Ca2+ events and we speculate that they lead to Ca2+ signaling dysregulations at the whole cell level observed in FAD cells. These models will provide the foundation for future data-driven computational framework for local and global Ca2+ signals that will be used to judiciously isolate the primary pathways causing Ca2+ dysregulation in FAD from those that are downstream, and to study the effects of upregulation of IP3R activity on cell function.
Citation: Mak D-OD, Cheung K-H, Toglia P, Foskett JK, Ullah G (2015) Analyzing and Quantifying the Gain-of-Function Enhancement of IP3 Receptor Gating by Familial Alzheimer’s Disease-Causing Mutants in Presenilins. PLoS Comput Biol 11(10): e1004529. https://doi.org/10.1371/journal.pcbi.1004529
Editor: Kim T. Blackwell, The Krasnow Institute for Advanced Studies, UNITED STATES
Received: April 9, 2015; Accepted: August 26, 2015; Published: October 6, 2015
Copyright: © 2015 Mak et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Data Availability: All relevant data are within the paper and its Supporting Information files.
Funding: This work was supported by a startup grant from College of Arts and Sciences at University of Florida to GU, a National Institutes of Health grant MH059937 to JKF, and a National Institutes of Health grant GM065830 to DODM. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Alzheimer’s disease (AD) is a fatal neurodegenerative disease that leads to cognitive, memory, and behavioral impairments followed by progressive cell death. The symptoms of AD include the extracellular deposition of amyloid β (Aβ) plaques and intracellular neurofibrillary tangles—aggregates of microtubule-associated protein τ . According to the amyloid hypothesis, the accumulation of Aβ oligomers or plaques due to the imbalance between synthesis and clearance of Aβ is the driving force for AD pathogenesis . However, whether τ and Aβ aggregates are the causes or symptoms of AD remains a matter of debate .
Aβ is produced by the cleavage of amyloid precursor protein (APP), an integral membrane protein. APP is cleaved sequentially by β and γ-secretases to generate Aβ monomers that are released to the extracellular space and form oligomers. The γ-secretase complex contains four different proteins including presenilins (PS) that are synthesized and localized in the ER . Mutations in PS alter the APP processing, thus leading to Aβ oligomarization either through higher production or relatively higher proportion of amyloidogenic Aβ types . It is well established that mutations in PS and APP are the main causes of Familial AD (FAD) . What is not clear is how PS mutations and Aβ accumulation lead to the impairment of brain function and neurodegeneration. The Ca2+ hypothesis of AD, which is based on the enhanced intracellular Ca2+ signaling during AD, accounts for early memory loss and subsequent cell death [6, 7, 8].
There is strong evidence in favor of intracellular Ca2+ signal exaggeration by FAD-causing PS mutations as an early phenotype that could contribute to the pathogenesis of the disease . The exaggerated cytosolic Ca2+ signals are ascribed mainly to the enhanced release of Ca2+ from intracellular endoplasmic reticulum (ER) store due to overloading of ER lumen by up-regulated sarco-endoplasmic reticulum Ca2+-ATPase (SERCA) pump ; disruption of ER-membrane Ca2+ leak channels ; or enhanced gating of IP3R [12, 13, 14, 15], the ubiquitous ER-localized Ca2+ release channel crucial for the generation and modulation of intracellular Ca2+ signals in animal cells . Single channel studies in multiple cell lines show that the sensitivity of IP3R to its agonist IP3 increases significantly in the presence of FAD-causing mutant PS [14, 15], leading to a several fold increase in the open probability (Po) of IP3R channel in subsaturating IP3. These studies were performed in the absence of Aβ, suggesting that the modulation of IP3R is a major mechanism for intracellular Ca2+ signal dysregulation in cells expressing FAD-causing mutant PS. Furthermore, altered IP3R-mediated Ca2+ release has been suggested as the fundamental defect and highly predictive diagnostic feature in AD . Suppression of IP3R-mediated Ca2+ signaling was recently shown to restore normal cell function and memory tasks in M146V (FAD-causing PS mutation) knock-in  and triple-transgenic  mice models of FAD .
IP3R gates in three distinct modes: an “L” mode with very low Po, in which brief openings are separated by quiescent periods with long mean closed channel durations (τc); an “I” mode with intermediate Po, in which the channel opens and closes rapidly with short τc and mean open channel durations (τo); and an “H” mode with high Po, in which the channel gates in bursts . All three modes are observed under all conditions in which the channel gates, and the channel spontaneously switches among all three modes even under constant ligand conditions. The Po of the channel remains remarkably consistent in each gating mode in all ligand conditions so the ligand dependencies of overall channel Po, τo and τc come from the ligand dependencies of the relative prevalence (normalized occupancy) πM of the gating modes (M can be L, I, and H) .
Due to the significant role of IP3R-mediated Ca2+ signaling dysregulation in AD, a comprehensive understanding of the IP3R function is important for both the etiology of the disease and designing effective therapeutic reagents. It was discovered that IP3R channels in cells expressing FAD-causing mutant PS exhibit relatively higher πH and lower πL in comparison to IP3R in cells expressing wild-type PS [15, 14] in non-optimal ligand conditions. πI, on the other hand, remains largely the same. The switch in the prevalence of H and L modes causes the increase in Po of IP3R in the presence of FAD-causing mutant PS.
In this paper, we employ a data-driven modeling approach to gain further insights into the gating behavior of IP3R in the presence of wild-type and FAD-causing PS. We focus on the channel gating behaviors of endogenous IP3R in the presence of human wild-type (PS1-WT) and FAD-causing mutant (PS1-M146L) PS expressed in the Sf9 cells, an insect cell line derived from the moth Spodoptera frugiperda. Other FAD-causing mutant PS1 (PS1-L116P, PS1-G384A) and PS2 (PS2-N141I) have similar effects on IP3R channel gating as PS1-M146L. On the other hand, non-FAD-associated mutant PS1 (PS1-L113P and PS1-G183V), wild-type PS2 and EVER1 (an irrelevant ER transmembrane protein) have little to no effects on IP3R channel gating, like PS1-WT [15, 14]. Therefore, the conclusions from studying IP3R channel in the presence of PS1-WT (IP3RPS1WT) and IP3R channel in the presence of PS1-M146L (IP3RPS1M146L) can be generalized to other FAD-causing mutations as well. We used the data-driven kinetic model developed to describe all observed gating behaviors of the endogenous IP3R channels in Sf9 cells: channel Po, τo and τc distributions in various steady Ca2+ and IP3 concentrations (𝓒 and 𝓘, respectively); modal gating behaviors in various steady 𝓒 and 𝓘; and kinetic response of IP3R channels to abrupt changes in 𝓘 and/or 𝓒  as the starting point of our approach. By modifying a minimum number of model parameters, the data-driven model was applied to fit observed gating behaviors: channel Po, τo, τc, and modal prevalence, in optimal (1 μM) 𝓒 and sub-saturating (100 nM) 𝓘, of the Sf9 IP3RPS1M146L and IP3RPS1WT (used as control)  as well as Po, τo, and τc of IP3RPS1WT in 33 nM and 10μM 𝓘 at 𝓒 = 1μM. In addition to elucidating the kinetics and factors contributing to the gain-of-function enhancement of IP3R activity [14, 15], we extrapolate, using our modified model, the gating behavior of IP3RPS1WT and IP3RPS1M146L for a wide range of 𝓒 and 𝓘. We also quantify and compare the ligand sensitivities of IP3RPS1M146L and IP3RPS1WT. Simulations of local Ca2+-release events based on the results of the data-driven model demonstrate that the gain-of-function enhancement of IP3R activity leads to larger, longer, and more frequent local Ca2+ releases events in cells expressing FAD-causing PS mutants. The models derived here will provide the foundation for developing future data-driven computational framework for global intracellular Ca2+ signals that will be used to judiciously isolate the primary factors causing Ca2+ signaling dysregulation in FAD from those that are downstream, and to study the effects of upregulation of IP3R activity on cell functions such as ATP production.
Materials and Methods
The main experimental data used in this paper for fitting the models were previously published elsewhere . Basic experimental data (Po, τo, and τc) at 𝓘 = 33nM, and 10μM for both IP3RPS1WT and IP3RPS1M146L  were also used to generate our model. The full details of experimental methods are given in  and summarized below.
Two Sf9 cell lines expressing recombinant PS1-WT and PS1-M146L, respectively, were generated and maintained as described in .
Nuclei isolated from transfected Sf9 cells [23, 14] were used for nuclear patch clamp experiments in on-nucleus configuration at room temperature . All experimental solutions contained 140 mM KCl and 10 mM HEPES (pH 7.3). Bath solution contained 90 nM free Ca2+ (buffered by 0.5 mM BAPTA (1,2-bis(2-aminophenoxy)ethane-N,N,N’,N’-tetraacetic acid). Pipette solution contained 1 μM free Ca2+ (buffered by 0.5 mM 5, 5′-dibromo-BAPTA), 0.5 mM Na2ATP and sub-saturating 100 nM IP3.
Segments of current records exhibiting current levels for a single IP3R channel were idealized with QuB software (University of Buffalo) using SKM algorithm [25, 26]. The idealized current traces were further analyzed as described in  to characterized the modal gating behaviors of IP3R channels. Short closing events, presumably caused by ligand-independent transitions , were removed by burst analysis. Gating modes were assigned according to durations of channel burst (Tb) and burst-terminating gaps (Tg) , using a critical Tb of 100 ms and a critical Tg of 200 ms to detect modal transitions.
We fit the twelve-state model previously developed for IP3R in Sf9 cells  (Fig 1) to the channel gating data of Sf9 IP3RPS1WT and IP3RPS1M146L at 𝓒 = 1μM and 𝓘 = 100 nM , following the procedure in [22, 28, 29], which we describe below. Although the scheme in Fig 1 seems to suggest simultaneous binding/unbinding of multiple ligands as the channel goes from one state to another (for instance to , or to ), in reality, there is no such direct transition in our model. Each one of such transitions actually involves one or more intermediate states that are not explicitly shown in order to keep the scheme simple. As discussed in detail in , the simplifying approximations were made by considering the fact that the intermediate states have relatively low occupancy and therefore can be aggregated into the main states. The rates for the composite transitions between those main states explicitly shown in the scheme were actually derived with the intermediate low-occupancy states carefully taken into consideration.
The superscript of each state denote the gating mode that state is in. The two numbers in the subscripts respectively indicate the number of Ca2+ and IP3 bound to the channel in that state. The model has nine closed states: , , , , , , , , and and three open states: , , and . The transition rates between various states and the related flux parameters are listed in Tables 2 and 3 respectively.
First, we derive the optimal parameters specifying the occupancy of various gating states from the mean Po and prevalences of the three modes.
Open Probability: In the following, and represent a closed and open state respectively in the M mode (where M = L, I, or H) with m Ca2+ and n IP3 bound to the channel. Relative to the reference unliganded closed state , the occupancies of and states are proportional to 𝓒m𝓘n, with occupancy parameters and , respectively. The occupancy parameter of a state is equal to the product of equilibrium association constants along any path connecting to that state (). The normalized occupancy of Cmn and Omn are and , respectively, where Z, the total occupancy of all states, is given by (1) The equilibrium Po function is: (2)
Modal Prevelances: The IP3R channel exhibits three distinct gating modes . The relative prevalence, πM, of the gating mode  is given as (3) where ZM is the sum of occupancies of all states in a given mode. For example, for H mode, ZH = .
We fit Po πL, πI, and πH function simultaneously to the Po and prevalence data using the Mathematica routine “NonlinearModelFit” based on least squares fitting. We perform this fit for single channel data from both IP3RPS1WT and IP3RPS1M146L to get the optimal occupancy parameters for IP3R in the presence of wild-type and FAD-causing mutant PS.
Probability flux parameters.
To determine the parameters describing the probability flux between different model states  involved in the transition rates between various states, we performed maximum likelihood fits on current traces of channel gating from IP3RPS1WT and IP3RPS1M146L.
Maximum Likelihood and AIC Calculations: We calculated the “log-likelihood” function for the model in the open-source programming language “Octave” and used the function “nelder_mead_min” in the optimization tool kit to minimize the likelihood score (−log(likelihood(data))) of the time-series data by varying the 18 free flux parameters while holding the occupancy parameters fixed. The log of the likelihood function for the current traces is given as  (4) where πC is the initial probability of closed states being occupied at equilibrium, toi and tci are the ith opening and closing in the time-series respectively, and QCC, QOO, QOC, and QCO are the sub-matrices of the 12 × 12 generator matrix Q. That is, (5) The element of Q at location ij, Qij,i ≠ j is the transition rate from state i to state j. The diagonal entries are given by Qii = −∑j ≠ i Qij, which is an expression of conservation of probability . Thus QCC, QOO, QOC, and QCO are matrices of the transition rates from all closed to all closed, all open to all open, all open to all closed, and all closed to all open states, respectively. Since our model has 9 closed and 3 open states, QCC, QOO, QCO, and QOC are 9 × 9, 3 × 3, 9 × 3, and 3 × 9 matrices respectively. For data obtained at equilibrium, πC = WO QOC/J, with J = WO QOC uC, where uC is a nine—(the number of close states) component vector of all 1’s. WC and WO are diagonal matrices of the equilibrium occupancies of all closed and all open states respectively.
The total log-likelihood of all data used in the fit was calculated as (6) where Nexp is the number of experiments and datai is the data set (time series) from experiment i. A total of 30 and 15 experiments were used in the global fit for the IP3R gating in the presence of PS1-WT and PS1-M146L, respectively.
Mean open and closed times.
The mean open and closed times are given by (7) where J is the total equilibrium flux from the 3 open states to the closed states. The equilibrium flux from a given state to other states is the product of the occupancy of that state and the sum of transition rates from that state to others. Thus, J is given as : (8) where r(S → U) is the transition rate from state S to state U.
Mean modal lifetimes.
The lifetime τX of any aggregate X (mode or other combinations of Markovian states), in an aggregated Markov chain is given by (9) where ZX is the unnormalized occupancy of aggregate X and JX the unnormalized flux out of that aggregate. JX is the sum of all the fluxes from all reactions from all Markovian states contained in the aggregate X to Markovian states not contained in X, so JX = ∑S JS = ∑S(ZS∑U r(S → U)), where ∑S is summing over all Markovian states S in the aggregate X, ∑U is summing over all Markovian states U that are not in X. For example for H mode, , where and .
In the following, we first derive the expressions for the open and closed dwell-time distributions and later generalize them for the dwell-time distributions in any aggregate of states. We define a 12 × 12 diagonal matrix W with Wii equal to the equilibrium occupancy of ith state. We partition the W matrix into WC and WO, where WC and WO are diagonal matrices of the equilibrium occupancies of the 9 closed states and 3 open states respectively in the model. The open time distribution is the probability density for a channel that opened at time 0 to close for the first time at tO. The probability that the channel first closed at time tO is given by (10) which has solution po(to) = πO exp(QOO tO). The probability, FO, that the channel remains open at time tO is the sum of the probability over all the open states and is given as (11) where uO and uC are column vectors of all ones having dimensions equal to the number of open and close states respectively. The probability, GC, that the channel closes for the first time at time tO is GC(tO) = 1−FO(tO). The open dwell-time distribution, fO(tO) is defined by [32, 33, 30, 31]: (12) or fO(tO) = dGC(tO)/dtO so that (13) which can be written as (14) Similarly, the closed time distribution is given as (15) The initial probabilities of open and closed states being occupied at equilibrium are given as (16) (17) where J = WC QCO uO = WO QOC uC is the total flux from all open states to all closed states at equilibrium and vice versa.
Generalizing this result, the dwell-time distributions of aggregates X and Y respectively are given as (18) Similarly, the closed time distribution is given as (19) The initial probabilities of states in X and Y being occupied at equilibrium are given as (20) (21) where J = WY QYX uX = WX QXY uY.
For the open and close dwell-time distributions in a given mode, X and Y consist of all open and close states in the mode respectively. Thus, , for I mode and , for H mode. WY and WX are diagonal matrices of the equilibrium occupancies of all closed states and all open states in the given mode respectively. uX and uY are column vectors of all ones having dimensions equal to the number of open and close states respectively in the mode. The square matrix Q has the dimensions of the number of states in the mode (4 for I mode, 2 for H mode). Sub-matrices QXY of Q has the transition rates from all states in X to all states in Y aggregate in the mode etc. For example for I mode, (22) (23) (24) (25) Similar matrices can be written for H mode where each sub-matrix is of dimension one (one close and one open state each in X and Y).
Stochastic simulations of an IP3R cluster.
To simulate Ca2+ puffs and blips (local Ca2+ release events from the ER due to nearly simultaneous opening of multiple channels and a single channel, respectively, in a cluster of several IP3R channels), we followed a procedure developed in  and consider a cluster of ten IP3R channels arranged in a two dimensional array with an inter-channel spacing of 120 nm. The gating of each channel is given by the twelve-state model shown in Fig 1.
Ca2+ concentration on the cytoplasmic side of the cluster is controlled by diffusion; the flux coming out from the ER through IP3R channels, Jj; and the concentration of free dye, bd. Thus the rate equations for the concentrations of free Ca2+ cj(rj, t) and free Ca2+ dye buffer at distance rj from channel j and time t are described as below: (26) (27) In the above equations, Bd is the total concentration, the forward (binding) rate, and the reverse (unbinding) rate for dye buffer. Dc and Dd are the diffusion coefficients for Ca2+ and dye respectively. δ(rj) is the Dirac delta function and Jj is the Ca2+ flux through the jth channel. (28) Where I = 0.05 pA is the channel current, F is the Faraday’s constant, Δr = 2.5nm, and δV is the volume of the hemisphere over the channel having a radius of rpore . We assume that the Ca2+ pump and leak currents are slow on the time scales considered here and therefore have negligible effects. Various parameters used in Eqs (26) and (27) are given in S1 Text.
The propagation of Ca2+ and dye is simulated throughout a 3D cytosolic space. Considering the spherical symmetry around the channel, the Laplacian of Ca2+ and buffers in spherical coordinates is given as (29) where .
We solved the two differential equations Eqs (26) and (27) using an implicit numerical method based on finite differences for discretizing the system of PDEs on a hemispherical volume of radius 5 μm with a spatial grid size of 5 nm for each channel as described in the S1 Text and summed the contribution of all channels for the instantaneous Ca2+ concentration at a given point in space. The Ca2+ concentration at the location of each channel is updated by adding the contributions from other channels in the cluster (30) Where rji is the distance between channels i and j.
Representative time-series traces of the gating behavior of IP3RPS1WT and IP3RPS1M146L are shown in Fig 2A. Occupancy parameters for the twelve states in the model obtained by fitting the Po (Figs 2B, 3A) and prevalence (Fig 2C) data from IP3RPS1WT and IP3RPS1M146L are given in Table 1. Notice that some of the parameters for IP3RPS1WT are different from those in  because IP3RPS1WT behaves somewhat differently from the IP3R channel in wild type untransfected Sf9 cells (IP3RnoPS1), despite the general similarity in the gating of the two (Fig 3A–3C, triangles for IP3RnoPS1, squares and solid lines for IP3RPS1WT), especially Po at 𝓘 = 100nM and 400 nM < 𝓒 ≤ 1μM. It is remarkable that the occupancy of only 4 states changes in the presence of PS1-M146L as compared to PS1-WT. The four states are , and whose occupancies change by a factor of 4.587, 1.284, 1.718, and 0.018 respectively. Thus IP3RPS1M146L spends relatively more time in the states , and and less time in as compared to IP3RPS1WT. This is consistent with the prevalence data where there is a significant increase in πH (0.345 vs 0.836) at the cost of πL (0.515 vs 0.059) in IP3RPS1M146L as compared to IP3RPS1WT. πI on the other hand does not change significantly (0.14 vs 0.104) (Fig 2C). Thus the increase in Po is mainly due to the significantly less time spent by IP3RPS1M146L in and more time spent in (Fig 2B) as compared to IP3RPS1WT.
Parameters for IP3RPS1M146L are shown in bold if they are different from those for IP3RPS1WT. All other parameters are the same for IP3RPS1WT and IP3RPS1M146L.
(A) Representative idealized experimental (left) and model-simulated (right) time-traces for IP3RPS1WT (top) and IP3RPS1M146L (bottom) at 𝓒 = 1μM and 𝓘 = 100nM, where 0 and 1 represent closed and open states, respectively. (B and C) Experimental (left) and model-simulated (right) Po and πM, respectively, of IP3R channels in the presence of PS1-WT and PS1-M146L. In (C), relative prevalence of the L, I, and H modes are in red, orange and green, respectively.
Experimental values are shown by symbols (filled symbols for data that are used to derive the parameters for our model, open symbols for data not used for parameter derivation), theoretical values calculated from the twelve-state model using corresponding parameters are shown by lines. Mean Po (A), τc (B), and τo (C) of IP3RPS1WT (solid lines and squares) and IP3RPS1M146L (dashed lines and circles) at 𝓘 = 33nM, 100nM, and 10μM (in turquoise, blue, and magenta, respectively) as functions of 𝓒. Data for 𝓘 = 100nM (blue symbols) were published in , and data for 𝓘 = 33 nM and 10 uM (turquoise and magenta symbols, respectively) were published in . (C) Because experimental τo values did not show any strong systematic trend as 𝓘 varied (from 33 nM through 100 nM to 10 μM), theoretical values of τo generated by the models for all 𝓘 (33nM, 100 nM or 10 μM) are the same (shown in black, solid line for IP3RPS1WT and dashed line for IP3RPS1M146L). Prevalences (D) and life-times (E) of the three gating modes (red, orange, and green for L, I, and H modes, respectively) of IP3RPS1WT (solid lines and squares) and IP3RPS1M146L (dashed lines and circles) as a function of 𝓒 at 𝓘 = 100nM. In (D), the open triangles are data for IP3RnoPS1 at saturating 𝓘 = 10μM  showing that modal prevalences of IP3RPS1M146L at 𝓘 = 100 nM are similar to those of IP3RnoPS1 at 𝓘 = 10μM. Error bars represent standard error of the mean.
To derive the probability flux parameters used in the transition rates between different gating states (Table 2), we fit the model to idealized current traces recording openings and closings of IP3RPS1WT and IP3RPS1M146L by minimizing the likelihood score Eq (6) of the data. The flux parameters from the fits are given in Table 3. Only two of the eighteen flux parameters of IP3RPS1M146L are different from IP3RPS1WT (shown in bold). These two parameters are involved in the and transitions and are higher for IP3RPS1M146L as compared to IP3RPS1WT.
In the following jijmn represents the flux parameter (see Table 3) and rsr stands for reciprocal of sum of reciprocals, i.e. rsr(x, y) = 1/(1/x+1/y). For simplicity, we assume that the rates for the & transitions are equal to the rate for transition while those for & transitions are equal to the rate for transition.
jijmn represent a flux parameter between a state with i Ca2+ ions and j IP3 molecules and a state with m Ca2+ ions and n IP3 molecules bound. Superscripts are used to distinguish between different flux parameters that connect different pairs of states that have the same numbers of ligands bound. For example, in both transitions and , the channel is bound to the same number of Ca2+ and IP3. However, the two transitions have different flux parameters because the channel is in different gating modes. The same font convention is used for the parameters as in Table 1.
The mean gating properties of the channel as a function of 𝓒 at different 𝓘 values are shown in Fig 3. Theoretical values of the Po of IP3RPS1WT (Fig 3A, solid lines) and IP3RPS1M146L (Fig 3A, dashed lines) were generated by using Eq (2) and the occupancy parameters in Table 1. The Po of IP3RPS1M146L at 𝓘 = 33nM (turquoise dashed line and turquoise circle) and 100nM (blue dashed line and blue circle) are significantly larger than Po of IP3RPS1WT at 𝓘 = 100nM (solid blue line and blue square). In fact, the Po of IP3RPS1M146L at 𝓘 = 33nM is comparable to Po of IP3RPS1WT (magenta square and solid line) or IP3RnoPS1 (magenta triangles from ) at saturating 𝓘 = 10μM. The Po data for IP3RnoPS1 at saturating 𝓘 = 10μM is shown for comparison to emphasize that IP3RPS1M146L is already maximally activated at a significantly lower 𝓘 of 100nM. This clearly indicates that IP3R in the presence of FAD-causing mutant PS is highly sensitized to activation by IP3, and is maximally activated at significantly lower 𝓘 than IP3RPS1WT or IP3RnoPS1. For 𝓒 > 800nM, Po of IP3RPS1M146L at 𝓘 = 10μM (magenta dashed line and magenta circle) is higher than that of IP3RnoPS1 or IP3RPS1WT at the corresponding 𝓘 and 𝓒, mostly due to the higher saturating Po of IP3RPS1M146L (0.86 ± 0.03) as compared to those of IP3RnoPS1 (0.72 ± 0.03)  and IP3RPS1WT (0.72 ± 0.05) . A close examination of τc (Fig 3B) and τo (Fig 3C) reveals that the increase in Po of IP3RPS1M146L is mostly due to the substantial shortening of τc with relatively modest increase in τo. Theoretical values of τo and τc were calculated using Eq (7) and the parameters in Tables 1 and 3. Gating properties (Po, τo, and τc) of IP3RnoPS1 in 𝓘 = 100nM and 10μM observed in  (triangles in Fig 3A–3C) are similar to theoretical values calculated for IP3RPS1WT, since IP3RPS1WT gating is generally similar to that of IP3RnoPS1, as observed in , albeit with some noticeable differences (Fig 3A–3C). The open triangles in Fig 3A–3C representing data from  of IP3RnoPS1 in wild type Sf9 cells is shown here to demonstrate that the model for IP3RPS1WT can replicate reasonably well the Po, τo, and τc of IP3R channel gating in the absence of PS1.
Next, we calculated with our modified data-driven model the prevalence of the three gating modes using Eq (3) and occupancy parameters given in Table 1 (Fig 3D and 3E). Both experimental (symbols) and theoretical (lines) results show a significant increase in πH (green), and decrease in πL (red) for IP3RPS1M146L (dashed lines and circles) as compared to IP3RPS1WT (solid lines and squares) (Fig 3D) at 𝓒 = 1μM and 𝓘 = 100 nM. πI (orange), on the other hand, remains largely unchanged. Comparison with the prevalence data from IP3R in untransfected Sf9 cells at saturating 𝓘 = 10μM (triangles) from  confirms the saturating activation of IP3RPS1M146L at relatively low 𝓘. The mean life-times of the three gating modes follow a similar trend as seen in their prevalences. τH is longer, τL is shorter, while τI remains unchanged for IP3RPS1M146L as compared to IP3RPS1WT (Fig 3E). The theoretical modal mean life-times were calculated from our modified model by using Eq (9) and parameters in Tables 1 and 3.
The open and closed dwell-time distributions were calculated from the model as described in the Dwell-Time Distributions section Eqs (14) and (15) using occupancy and flux parameters in Tables 1 and 3 respectively. As shown in Fig 4, the model (red lines) fits the observed dwell-time distributions (gray bars) very well. Consistent with the τo observed (Fig 3C), there is a minor right-shift in the open dwell-time distribution of IP3RPS1M146L (Fig 4C) as compared to IP3RPS1WT (Fig 4A). Thus, PS1-M146L does not have significant effect on τo of the IP3R channel. The close dwell-time distribution of IP3RPS1M146L (Fig 4D), on the other hand, shows significant shift to the left when compared to IP3RPS1WT (Fig 4B), leading to the shorter τc and therefore the higher Po observed.
Open (A) and closed (B) dwell time distributions of IP3R in the presence of PS1-WT and open (C) and closed (D) dwell time distributions of IP3R in the presence ofPS1-M146L at 𝓒 = 1μM and 𝓘 = 100nM. Bars and lines respectively represent experimental data and model.
The Dwell-Time Distributions section also describes the derivation of the open and closed dwell-time distributions in H and I modes from the model. The dwell-time distributions from the model for 𝓒 = 1μM and 𝓘 = 100nM in the H (Fig 5A–5D) and I (Fig 5E–5H) modes calculated by using Eqs (18) and (19) and parameters in Tables 1 and 3 are given by red lines. The experimental data are presented by the gray bars for comparison. A close inspection of the modal open and closed dwell-time distributions of IP3RPS1WT and IP3RPS1M146L provides useful insight into the modal behavior of the channel. In line with the over-all open dwell-time distribution, the open dwell-time distributions in the H (Fig 5A, 5C) and I (Fig 5E, 5F) modes do not change significantly. The closed dwell-time distributions in the two modes in IP3RPS1M146L (Fig 5D, 5H) on the other hand, shift significantly to the left as compared to IP3RPS1WT (Fig 5B, 5G). Furthermore, the shift in the closed dwell-time distribution in the H mode is more significant (Fig 5B, 5D). This suggests that the relatively shorter time spent by IP3RPS1M146L in the H mode’s closed state plays a major role in the shortening of τc and hence enhancement of Po of the channel in the presence of FAD-causing mutation as compared to wild-type PS1.
Top and bottom rows are for IP3RPS1WT and IP3RPS1M146L respectively. Open (A, C) and closed dwell-time distributions (B, D) in H mode. Open (E, F) and closed dwell-time distributions (G, H) in I mode. Bars are the experimental values and lines are the model fits.
To gain further insights and quantify the extent of IP3R sensitization due to PS1-M146L, we extrapolate the Po, τc, and the mean modal properties of IP3R at different values of 𝓒 and 𝓘 from our model using parameters tabulated in Tables 1 and 3. Fig 6A shows Po of IP3RPS1WT (black solid lines) and IP3RPS1M146L (blue dashed lines) as a function of 𝓒 at different 𝓘, calculated using Eq (2). Even at 𝓘 = 8nM, Po of IP3RPS1M146L is already higher than that of IP3RPS1WT at 𝓘 = 100nM (thick solid black line) for all 𝓒. Thus, whereas IP3RPS1WT in 8 nM IP3 are minimally active (Po ∼ 0.005) in resting 𝓒 (∼ 70 nM), IP3RPS1M146L under the same ligand conditions can have sufficient activity (Po > 0.04) to initiate intracellular Ca2+ signals.
The lines are from the model while the squares in panels (C, E, and F) are the experimental values for IP3RPS1WT at 𝓒 = 1μM and 𝓘 = 100nM. The increasing thicknesses of the lines in (A) and (B) represent increasing IP3 concentration. (A) Po of IP3RPS1WT at 𝓘 = 8nM and 100nM (black solid lines) and IP3RPS1M146L at 𝓘 = 4nM, 8nM, 16nM, 40nM, and 100nM (blue dashed lines) as a function of 𝓒. (B) The τc of the channel from simulations in (A) where the thicknesses, colors, and styles of the lines have the same meanings as in (A), τc of IP3RPS1WT at 𝓘 = 8nM is not shown. (C) The Po (black) and τc (red) of IP3RPS1M146L as a function of 𝓘 at 𝓒 = 1μM. The vertical and horizontal black and red dotted lines respectively represent the 𝓘 value (∼ 8nM) at which the Po and τc of IP3RPS1M146L cross the Po and τc of IP3RPS1WT at 𝓒 = 1μM and 𝓘 = 100nM. (D) The ratio of the Po of IP3RPS1M146L to that of IP3RPS1WT as a function of 𝓘 at 𝓒 = 70nM (red), 100nM (yellow), 250nM (green), 500nM (blue), 1μM (purple), and 2μM (black). (E) and (F) show the prevalences and mean life-times respectively of L (red), I (orange), and H (green) modes of IP3RPS1WT (solid lines) and IP3RPS1M146L (dashed lines) as a function of 𝓘 at 𝓒 = 1μM. Squares represent values observed in .
The τc of the channels from simulation Eq (7) in Fig 6B correlate well with the Po values (notice that at fixed 𝓘, Po decreases as τc increases and vice versa). This close correlation between the Po and τc is the consequence of the lack of dependence of the τo on 𝓘 (see Eq (7) and Fig 3C). Thus for 𝓘 > 8 nM, τc of IP3RPS1M146L (blue dashed lines) is shorter than that of IP3RPS1WT at 𝓘 = 100nM (black solid line) for all physiological 𝓒 values. Whereas the strong Ca2+ activation of IP3RPS1M146L between 𝓒 = 0.01 and 0.5 μM remains the same as 𝓘 is raised from 16 to 100 nM, channel Po for higher 𝓒 does increase as 𝓘 increases from 16 nM to 1 μM, confirming the higher saturating Po of IP3RPS1M146L as described above (Fig 3A) and is in line with observations (Table S1 in ).
To quantitatively compare the sensitivity of IP3RPS1WT and IP3RPS1M146L to activation by IP3, we plot in Fig 6C the Po of IP3RPS1M146L as a function of 𝓘 at fixed 𝓒 = 1μM (black line) and the experimentally observed Po of IP3RPS1WT at 𝓒 = 1μM and 𝓘 = 100 nM (black square). The plot reveals that Po of IP3RPS1M146L at 𝓘 = 8 nM already exceeds that of IP3RPS1WT at 𝓘 = 100 nM (see black dotted lines). In contrast, Po of IP3RPS1WT is negligible at 𝓘 = 8nM and 𝓒 = 1μM (Fig 6A, black thin solid line). Correspondingly, τc of IP3RPS1M146L (red line in Fig 6C) becomes shorter than the observed τc of IP3RPS1WT (red square) at 𝓘 = 100nM as 𝓘 is raised beyond 8nM.
In Fig 6D, we show the ratio of simulated Po of IP3RPS1M146L to that of IP3RPS1WT as a function of 𝓘 at 𝓒 = 70nM, 100nM, 250nM, 500nM, 1μM, and 2μM. For 𝓘 < 200nM, IP3RPS1M146L is more than twice as active as IP3RPS1WT for all 𝓘 and 𝓒 values. For physiological resting 𝓒 = 70nM, IP3R channel activity is enhanced by 265% in cells expressing PS1-M146L relative to that in PS1-WT expressing cells. For optimal 𝓒, IP3RPS1M146L exhibits a gain-of-function enhancement by over 100 folds as compared to IP3RPS1WT, with maximum enhancement occurring around 𝓘 = 7–8 nM IP3. The drop in the Po ratio for 𝓘 > 8nM is due to the fact that Po of IP3RPS1M146L peaks much faster than IP3RPS1WT as a function of 𝓘.
At fixed 𝓒 = 1μM, the theoretical πL Eq (3) of IP3RPS1M146L decreases for 2nM < 𝓘 < 100nM and plateaus outside this window (Fig 6E, dashed red line). πH of IP3RPS1M146L (dashed green line) changes in the opposite direction for 2nM < 𝓘 < 100nM. πI of IP3RPS1M146L (dashed orange line), on the other hand, remains largely constant. Around 𝓘 = 8 nM, both the πL and πH curves of IP3RPS1M146L crosses the observed πL (red square) and πH (green square) levels, respectively, of IP3RPS1WT measured at 𝓘 = 100nM and 𝓒 = 1μM. πI of IP3RPS1M146L gets close to but does not exceed that of IP3RPS1WT observed at 𝓘 = 100nM and 𝓒 = 1μM (orange square). This indicates that the increase in Po of IP3R in the presence of PS1-M146L is mainly due the switching of the channel from L to H mode. Interestingly, the 𝓘 value (∼ 10nM) where πL and πH cross each other is almost the same as where Po reaches half (0.41) of its peak value (0.82) (see black line in Fig 6C). This is in line with the observations that mode switching is the major mechanism of ligand regulation of IP3R . Our results confirm that the mechanism of ligand regulation of IP3R is mainly due to the switching of the channel between L and H modes with minimal contributions from I mode . Furthermore, switching of IP3RPS1M146L from L to H mode in comparison to IP3RPS1WT translates into the gain-of-function enhancement of IP3R gating. Fig 6E also shows how theoretical values of the prevalences of the three gating modes for IP3RPS1WT vary with 𝓘 at 𝓒 = 1μM (solid lines).
Theoretical values of the mean life-times of I (orange) and H (green) mode calculated using Eq (9) at 𝓒 = 1μM remain largely unchanged for all values of 𝓘 > 3nM (Fig 6F). In that range of 𝓘, τH of IP3RPS1M146L (dashed green line) is shorter than τH of IP3RPS1WT (solid green line), while τI of IP3RPS1M146L (dashed orange line) remains almost the same as τI of IP3RPS1WT (solid orange line). For 𝓘 < 4nM, τI of IP3RPS1M146L drops below the observed value for IP3RPS1WT at 𝓘 = 100nM. Simulated τL of IP3RPS1M146L (dashed red line), on the other hand, decreases significantly as 𝓘 increases. As 𝓘 increases beyond 15 nM, simulated τL of IP3RPS1M146L becomes shorter than that of IP3RPS1WT measured at 𝓘 = 100nM (red square). Relatively speaking, this does not correlate very closely with the 𝓘 = 8nM where the Po of IP3RPS1M146L crosses the observed Po of IP3RPS1WT (Fig 6A) when compared to the prevalences where this critical value of 𝓘 is 8nM. Nevertheless, the shorter τL will increase the Po of IP3RPS1M146L. Thus the shorter τL and longer τH contribute to its increased sensitivity to IP3 as compared to IP3RPS1WT.
To investigate how the remodeling of single IP3R channel gating kinetics in the presence of mutant PS1-M146L affects the dynamics of IP3R-mediated Ca2+ release events, we simulated such events at a Ca2+-release site consisting of a cluster of ten IP3Rs as described in the Methods Section. 400 s-long records of Ca2+ blips and puffs (Ca2+-release events involving just one, or multiple IP3R channels in the cluster, respectively) from the IP3R cluster were generated, and statistics about these Ca2+-release events were derived as described previously . In line with observations reported in [35, 12], the site produces significantly potentiated puffs in the presence of FAD-causing PS1. As shown in Fig 7, the behavior of puffs and blips arising from a cluster of IP3RPS1M146L (dashed lines with circles) is significantly different from that of a IP3RPS1WT cluster (solid line with squares). Puffs from a IP3RPS1M146L cluster have significantly larger amplitudes (Fig 7A), longer life times (Fig 7B), and take longer to terminate (Fig 7C). Furthermore, puff frequency in cells expressing PS1-M146L is significantly higher than that in PS1-WT-expressing cells (10.33/sec versus 1.83/sec) (Fig 7D). Interestingly, the statistics of Ca2+ blips are very similar in both case. Although the life times of blips in PS1-M146L-expressing cells is slightly longer than that in PS1-WT-expressing cells (Fig 7E), frequencies of the blips are almost the same (10.67/sec versus 9.99/sec) (Fig 7F). Thus the higher number of single-channel events caused by higher sensitivity of IP3RPS1M146L to activation by IP3 translates into triggering more frequent and longer puffs.
(A) Distribution of puff peak amplitude, (B) life time (duration from the start of the puff to the end of the puff), and (C) termination time (duration from the time at which maximum number of channels are open to the time when the last active channel becomes inactive). (D) Life time distribution of blips. Frequency of puffs (E) and blips (F). Simulations were performed at 100nM IP3 concentration.
Accumulation of Aβ aggregates and intracellular neurofibrillary tangles of τ protein are the main symptoms of AD . However, most drugs focused on restricting Aβ production and accumulation or enhancing its clearance from the brain have yielded disappointing results . This could be due to the fact that these drugs target the late stage features of the disease, i.e. plaque formation—whereas there is poor correlation between Aβ deposits and the progressive memory loss and cognitive decline observed . Compelling evidence suggests that FAD-causing mutant PS disrupt intracellular Ca2+ signaling before Aβ deposition, pointing towards the up-regulated Ca2+ signaling as a proximal event that could be involved in disease pathogenesis. Previously, we showed that FAD-causing mutant PS interact with ER-localized IP3Rs, leading to their gain-of-function enhanced channel activity [14, 15]. However, further analysis is needed to elucidate the modified gating properties leading to the gain-of-function enhancement of IP3R channel activity and to quantify their sensitization due to FAD-causing PS mutations.
Our modeling results show that there is a significant increase in the H mode prevalence, and a corresponding significant reduction in the L mode prevalence of IP3R channels in the presence of PS1-M146L. This change in the prevalence of L and H modes arises mainly from the shorter mean life-time of the L mode and longer mean-life-time of the H mode. On the other hand, both the life-time and prevalence of I mode remain constant. Our model predicts that the Po of IP3RPS1M146L saturates at significantly lower IP3 concentrations and its peak value is higher compared to that of IP3RPS1WT. Furthermore, our model predicts that the channel’s gain-of-function enhancement is sensitive to both IP3 and Ca2+ (Fig 6A). Interestingly, our model predicts that the higher Po of IP3RPS1M146L as compared to IP3RPS1WT is mainly due to the lower occupancy of state and higher occupancy of the state (with small change in the occupancies of and ). This means that PS1-M146L interacts with IP3R in such a way that the closed configuration of the channel with 3 Ca2+ ions and 2 IP3 bound is less likely and the open configuration in the H mode with 2 Ca2+ ions and 4 IP3 molecules bound more easily attainable. The changes in the occupancies of states and lead to the increase in the prevalence of H mode and the corresponding decrease in the prevalence of L mode, resulting in the gain-of-function enhancement of IP3R gating in the presence of PS1-M146L.
Our goal in this study was to use all the data at our disposal to model the gating kinetics of IP3RPS1WT and IP3RPS1M146L; and use resulting models to simulate the behavior of IP3RPS1WT and IP3RPS1M146L in a wide range of ligand concentrations to gain a better understanding of how the gain-of-function enhancement of IP3RPS1M146L alters the characteristics of local Ca2+ release events at IP3R clusters.
Because of the considerable technical difficulties in obtaining single-channel current records of IP3R channels in their native membrane milieu by nuclear patch clamp electrophysiology, the most comprehensive set of such single-channel data (including steady-state gating records over a broad range of combinations of cytoplasmic IP3 and Ca2+ , long gating records in multiple constant ligand conditions suitable for modal gating analysis , records of response kinetics of IP3R channel to rapid changes in cytoplasmic ligand conditions ) was obtained in the study of the endogenous IP3R from insect Sf9 cells. This set of data was used to develop the twelve-state kinetic model  that provides the basis of the models we develop here to simulate the behavior of the endogenous Sf9 IP3R in the presence of exogenous recombinant human PS1 (WT and mutant). Until a comparable or more comprehensive set of single-channel data for a mammalian IP3R becomes available, our approach is the best that can be achieved to simulate gating behaviors of IP3R interacting with WT and mutant PS1. Although Sf9 IP3R does not interact with human PS1 in its natural environment, the study in  showed that endogenous IP3R in human lymphoblasts in presence of PS1-M146L exhibits very similar changes in its gating characteristics (increase in Po and τo with corresponding reduction in τc) and modal gating behavior (rise in πH with simultaneous drop in πL) when compared to IP3R in the presence of PS1-WT. Therefore, we have reason to be confident that simulation results from our modeling effort do reflect the gating behaviors of IP3R naturally interacting with WT and mutant PS1, and that the insights our effort provides about the effects of mutant PS1 on IP3R single-channel gating and local intracellular Ca2+ release events can improve our understanding of the pathophysiology of FAD.
The higher prevalence and longer life-time of H mode and shorter life-time of L mode for IP3RPS1M146L may have important implications for cell physiology. Since the open time in the H mode is significantly higher than that in the L mode, in which the channel has near-zero mean open time, IP3R gating in the H mode will have higher probability of activating neighboring channels through Ca2+-induced-Ca2+ release (CICR), thus leading to higher frequency of Ca2+ puffs (Fig 7D). The higher sensitivity of IP3RPS1M146L to activation by Ca2+ and IP3 also increases the number of open channels in an IP3R channel cluster during a puff, leading to bigger (Fig 7A) and longer (Fig 7B) puffs, which in turn will cause more frequent global Ca2+ waves and oscillations at the cellular level, in line with observations [35, 12]. The higher prevalence of IP3R channel being in the H mode resulting in the higher probability of inducing global Ca2+ events can account for the higher frequency of Ca2+ oscillations in B lymphoblasts from FAD patients and DT40 cells expressing FAD-causing mutant PS [14, 15].
Our model reveals that even at resting level of 𝓘 (8 nM), IP3RPS1M146L exhibits significant Po of 0.35 (40% of the Po when the channel is in saturating 𝓘) at 𝓒 = 1μM whereas the Po of IP3RPS1WT in the same ligand condition is negligible. This will lead to stronger CICR among channels in the same cluster and between IP3R channel clusters, thereby generating more global spontaneous Ca2+ oscillations in cells expressing FAD-causing mutant PS as observed experimentally [14, 15].
To conclude, our study provides insights into the gating modulation of IP3R that leads to the gain-of-function enhancement due to FAD-causing mutations in PS. Furthermore, significant activity exhibited by IP3R at resting IP3 concentration in cells expressing FAD-causing mutant can explain the spontaneous global Ca2+ signals observed in those cells. The models developed here for single-channel IP3R channel gating and local Ca2+-release events can provide part of the foundation for building whole-cell models to judiciously separate the key pathways leading to the global Ca2+ signaling dysregulation in AD from those that are by-products due to the CICR nature of Ca2+ signaling. For example, what are the relative contributions of gain-of-function enhancement and over-expression of ryanodine receptors [39, 20] to Ca2+ signaling dysregulation in AD? Does the down-regulation of Ca2+ buffers such as calbindin [40, 41] and higher resting Ca2+ concentration  play a role (through CICR mechanism) in the exaggerated Ca2+ signals? What are the conditions or factors that would reverse the exaggerated Ca2+ signaling back to normal state? These and many other interesting questions are the focus of our future research and the models developed here will play a key role in addressing them.
Conceived and designed the experiments: DODM KHC JKF GU. Performed the experiments: DODM KHC PT GU. Analyzed the data: DODM KHC PT GU. Contributed reagents/materials/analysis tools: DODM KHC PT JKF GU. Wrote the paper: DODM KHC PT GU.
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