Fig 1.
The phase regulation of Ca2+-cAMP oscillation and corresponding mathematical modeling.
(A) Schematic showing out-of-phase Ca2+-cAMP oscillation outside the nanodomain and in-phase behavior when localized to AKAP/AC nanodomains. This schematic is designed based on experiments in [32] (created with BioRender.com). (B) In this work, we aim to explore the biochemical mechanism of the phase difference (or time delay) between Ca2+ and cAMP oscillation and study the possible contributing factors. (C) Mathematical modeling of the AKAP-Ca2+-cAMP circuit. On the left-hand side, the diagram of the signaling pathway is shown; the solid arrow indicates production, degradation, or binding events, and the dashed arrow indicates the regulation effect that usually does not consume the reactants. The voltage module (highlighted in gray) includes a capacitor with the membrane capacitance Cm and four ion channels: Ca2+ channel, K+ channel, Ca2+ gated K+ channel, and leak channel. Currents for ion channels are represented by ICa, IK, IKCa, and IL, where the subscript indicates the specific ion channel. On the right-hand side, the simulation domain is a hexagonal prism, which is only a small compartment of one cell (created with BioRender.com). In this compartment, the top surface (yellow area) denotes the cell membrane; the AKAP/AC nanodomain (the large patch in red) is located on the cell membrane; the volume under the top surface is cytosol. Molecules (dots in gray and orange) can diffuse in the cytosol or on the membrane depending on the location of the molecule. (D) A single AKAP/AC nanodomain was modeled using a Gaussian distribution. (E) Interactions between AC and AKAP that can generate a Turing pattern.
Fig 2.
Phase oscillations of Ca2+ and cAMP are driven by active AC and PDE.
(A) The simulation domain and initial condition of AC and AKAP. The compartment and the assumption of one AKAP/AC nanodomain are the same as those in [32]. (B) The time delay between Ca2+ and cAMP as a function of the distance x to the AKAP/AC nanodomain. The time delay is defined as the difference of peak time between Ca2+ and cAMP. (C) The non-normalized dynamics of Ca2+ and cAMP at x = 0, 40, 49, 60, 200 nm. The vertical dashed lines label the time when cAMP achieves the peak. The blue color indicates the value of x: the lighter the blue is, the larger the x is. (D) The normalized dynamics of Ca2+ (in red) and cAMP (in blue) at x = 0 nm (upper panel), x = 49 nm (middle panel), and x = 200 nm (lower panel). (E) Kymographs depicting the dynamics for Ca2+, active AC (AC*), and active PDE (PDE*) at different locations at the cell membrane. The x coordinate is the time, and the y coordinate is the distance x present in (B). Trough time and peak are indicated by a plus sign and triangle, respectively. Here, the peak time is the time when the concentration of species reaches the maximal value, and the trough time the minimal value. (F) Comparisons between Ca2+ trough time and AC* trough time (left; plus sign), between Ca2+ peak time and AC* peak time (left; triangle), between Ca2+ trough time and PDE* trough time (right; plus sign), and between Ca2+ peak time and PDE* peak time (right; triangle). The diagonal line indicates the equality of the x-axis and y-axis. (G) Kymograph depicting cAMP dynamics. The color intensity indicates the normalized cAMP level. The plus sign and triangle denote the cAMP peak time when x is large and small, respectively. (H) Comparisons between AC* peak time and cAMP peak time on the AKAP/AC nanodomain (left), and between PDE* trough time and cAMP peak time outside the AKAP/AC nanodomain (right).
Fig 3.
Experimental data supports model predictions of in- and inversely out-of-phase Ca2+-cAMP oscillations.
(A) Schematic of the dependence of time delay between Ca2+ and cAMP on the interplay between active AC and PDE. The arrow thickness indicates the regulation strength: the thicker the arrow is, the stronger the regulation is. On the AKAP/AC nanodomain, the active AC dominates, driving the in-phase Ca2+-cAMP oscillation. However, the active PDE dominates outside the AKAP/AC nanodomain, leading to inversely out-of-phase Ca2+-cAMP oscillation. (B) The experimentally observed in-phase Ca2+-cAMP oscillation on the AKAP/AC nanodomain and inversely out-of-phase Ca2+-cAMP oscillation outside the AKAP/AC nanodomain. The in-phase Ca2+-cAMP oscillation is illustrated by the same cAMP peak time and Ca2+ peak time; the inversely out-of-phase Ca2+-cAMP oscillation is indicated by the same cAMP peak time and Ca2+ trough time. These peak or trough time data (circular makers) are from Tenner et al., eLife, 2020 [32], and the black line denotes the diagonal line.
Fig 4.
A simple incoherent feedforward loop explains in-phase oscillation and inversely out-of-phase oscillation.
(A) The signal used in the simple ODE model. We used a sine wave sin(t) + 1.1 as the signal S(t) to mimic the dynamics of Ca2+, where 1.1 is to ensure the positive sign of the signal. (B) Schematic of the ODE model. We constructed a simple circuit with only two regulatory links: one is the activation from the signal S(t) to the output x(t); the other is the inhibition from the signal S(t) to the output x(t). This circuit captures the positive role of Ca2+ not only in the cAMP production through active AC but also in the cAMP degradation through active PDE. The equation describing the dynamics of x(t) is shown in the right panel. (C) The dynamics of S(t) (red) and x(t) (blue) under different values of k1 and k2, and v. Values of k1 and k2 are labeled over the plots. Values of v are indicated by the intensity of blue color (the darker the blue is, the higher the v is): v = [0, 2, 3.1, 4, 6] (i), v = [0, 0.5, 1, 2, 3] (ii), and v = [0, 0.5, 1, 2, 3] (iii). The trough and peak of x(t) are marked by the dashed and solid lines, respectively. (D) The time delay between S(t) and x(t) as a function of the signal strength v for different values of k1 and k2. Three values of k2 are considered: 0.1 (i), 1 (ii), and 10 (iii). In each panel, k1 is changed from 10−1 to 100.5, shown in different colors and markers. The stars in each panel indicate the parameters used in (C). The time delay has been proven to have only two values when the activation strength v is increased while keeping other kinetic parameters fixed (see Simple ODE model subsection in Methods for details), and thus the fluctuations in the plot of time delay versus v come from numerical errors.
Fig 5.
Simulation results predict the role of AC in driving the in-phase behavior and decreasing time delay for inversely out-of-phase behavior.
(A-C) The dynamics of Ca2+ and cAMP at different locations when the AC level is varied. The AC concentration is 75% (A), 50% (B), and 25% (C) of the original value. (D) The in-phase and inversely out-of-phase cAMP behavior in (A-C). (E) The time delay of peaks between Ca2+ and cAMP as a function of the distance x in (A-B). The x has the same definition as that in Fig 2B.
Fig 6.
Cellular compartment size determines the time delay for the inversely out-of-phase Ca2+-cAMP oscillation.
(A) The Ca2+ and cAMP dynamics for a double-width compartment. Dynamics on the AKAP/AC nanodomain (i) and at the edge of the compartment (ii) are shown. (B-C) Same plots as (A) except the compartment size. The compartment is doubled in height in (B) and doubled in both height and width in (C). (D) The in-phase and inversely out-of-phase oscillations in (A-C). (E) The time delay in (A-C) as a function of the distance x to the nanodomain. The lower panel shows the magnified view of the Ca2+ and cAMP dynamics when x is close to the critical value, which is defined as the time when the transition of time delay occurs.
Fig 7.
AKAP/AC nanodomain formation can be explained by Turing patterns.
(A) The phase diagram of Turing pattern for parameters vr and vs (upper left panel), β and b (upper middle panel), and m2 and μ (upper right panel). Three patterns occur in the parameter space: the first is that the AC (denoted by r) and AKAP (denoted by s) are uniformly distributed; the second is the Turing pattern where the AKAP and AC are co-localized, which is denoted as Turing pattern 1; the third is also a Turing pattern but the AC level is high outside the AKAP cluster, which is referred to as Turing pattern 2. Typical distributions of AC and AKAP for these three types of pattern are shown in lower panels. The marker over the plot indicates the value of Dr, Ds, β, b, m2 and μ. (B) The dynamics of Ca2+ and cAMP on (i) or outside AKAP/AC nanodomains (ii) when initial conditions of AC and AKAP are re-scaled from the lower middle panel in (A). When the maximal concentration of AC is same as that in Fig 6, the cAMP oscillates in phase with Ca2+ on and outside AKAP/AC nanodomains (upper right panel); when the AC level is one eighth of that in Fig 6, the cAMP oscillates in phase with Ca2+ on AKAP/AC nanodomains but out of phase with Ca2+ outside AKAP/AC nanodomains (lower right panel). (C) The in-phase and inversely out-of-phase oscillations in (B). (D) The time delay in (B) as a function of the distance x to the center of AKAP/AC nanodomains.
Fig 8.
Prediction of the time delay from a realistic distribution of AKAP/AC nanodomains.
(A) Extraction of AC8 data from STORM image. The AC8 STORM data (left panel) is from [32], where the red dashed line indicates the boundary of a single cell. We selected an area with 1000 nm length and 10000 nm width (middle panel), then smoothed the STORM data in this small area by a Gaussian function with FWHM (full width at half maximum) of 60 nm, and finally obtained a smooth distribution of AC8 on the small area (right panel). We chose a hexagon indicated by the white dashed line as the distribution of AC in the following simulations. (B) The dynamics of Ca2+ and cAMP on the AKAP/AC nanodomain (i) and outside the AKAP/AC nanodomain (ii) when the initial distribution of AC is from (A). The initial distribution of AKAP is set to be the same as that of AC. Two cases are studied: the AC has the same maximal values as before (i.e., 9600 copies/μm2) (upper right panel); the AC level is halved (lower right panel). (C) The in-phase and inversely out-of-phase oscillations in the lower right panel in (B). (D) The time delay as a function of the distance to the AKAP/AC nanodomain. (E) Summary of Ca2+-cAMP oscillation, underlying biochemical mechanisms, and the effect of the biophysical properties of the cell. (F) The core motif of the Ca2+/cAMP circuit—incoherent feedforward loop from Ca2+ to cAMP and the feedback from cAMP to Ca2+.