|
Figure 1. Speract-activated [Ca 2+] signaling pathway network model.A) Upper part: Schematic representation of the components of the signaling pathway triggered by speract in the sperm flagellum. Arrows traversing the membrane show ion fluxes. Arrows within the cell are indicative of causal relations. B) Bottom part: Signaling pathway operation diagram, black arrows correspond to activation, red lines to deactivation and yellow arrows can be activating or inhibitory depending on the relative state of the pathway elements being interconnected. Once speract binds to its receptor the several feedback loops are triggered according to the nature of the links involved. The concatenation of these loops leads to oscillatory stages of the whole pathway. The color code identifies corresponding upper and lower part components. Current models propose that the binding of speract to its receptor promotes the synthesis of cGMP that activates K+ selective and cyclic nucleotide-gated channels (KCNG) leading to membrane potential (V) hyperpolarization [3], [4], [7]–[11], [18]. This V change first induces an intracellular pH increase via a Na+/H+ exchanger (NHE) activation, [18], [51], [52], stimulates hyperpolarization-activated and cyclic nucleotide-gated channels (HCN) [53]–[55], removes the inactivation of voltage-gated channels HVA and LVA [18], [56] (CaV), and facilitates extrusion by Na+/Ca2+ exchangers (NCE) [51], [52]. The opening of HCN and the influx of Na+ contribute to V depolarization, and concomitant increases in and further depolarize V. It has been proposed that the increases could lead to the opening of -regulated Cl channels (CaCC) and/or -regulated K+ channels (CaKC), which would then contribute to hyperpolarize the V again, removing inactivation from CaV channels and opening HCN channels, [3], [4], [18]. It is thought that this series of events is then cyclically repeated generating a sequence of V-dependent turns. B) Network model of the signaling pathway. The network can be envisaged as a circuit where each node represents an element of the pathway and links, either in the form of arrows or lines, correspond to connections determined in the bottom part of (A). The activating or inhibitory nature of the yellow lines depends on the value of voltage (V). Yellow nodes represent binary nodes (0,1), and the four brown nodes are ternary nodes that can take values 0, 1 and 2. Changes in the node states are determined by the connected nodes by means of a regulatory function (or truth table). As an illustration we present the case of the cGMP shown at the bottom left of (B). The first 3 columns in this table contain all the possible activation states of the cGMP regulators: GC, which is an activator; PDE, an inhibitor and cGMP (cGMP is a self-regulator); the fourth column shows the values for the function that correspond to each combination of the regulators. Additional nomenclature note: Speract receptor (SR); guanylate cyclase (GC); unknown channels sensitive to cAMP (cAMPCC); pump (CaP); dCa, dCl, dNa, dK are abbreviations for permeability changes in [Ca2+], [Cl−], [Na+] and [K+], respectively.
|
|
Figure 2. Niflumic acid increases the []i mean, maximum peak, amplitude and interval between successive [Ca2+] fluctuations.Experimental determination of the -sensitive colorant Fluo-4 fluorescence in the flagellum, averaged along its length, of sperm exposed to 100 nM caged speract, in the absence of NFA (black trace) and the presence of 10 M of NFA (red trace). Concentration is measured in florescence intensity (F.I) units and time in seconds according to the scale shown in the inset on the upper right part of the figure. The figure is a modified version of the equivalent shown in [4].
|
|
Figure 3. [Ca2+] dynamics comparison between WT network and blocking an individual NFA-sensitive channel.The [Ca] steady state fluctuations calculated form averaging over 100,000 initial conditions. For each initial condition, will take value 0 if it is in the basal state, 1 if it corresponds to a tonic state and 2 if it is supratonic. After averaging it will take values within the range [0–2] with a resolution of 105. Concentration units are arbitrary, they comply with the above restrictions and are set for comparative purposes, time is measured by simulation steps and frequency refers to the fraction of a cycle covered by a simulation step, i.e cycles per simulation step. The values of determined by the logical signaling network model, in the above mentioned A.U. (Arbitrary Units), are shown in black for the wild type case and in colors for the network with deletion of the node indicated in the figure: In the first column note A) for HCN, the loss of regularity; D) For CaCC, the increase in amplitude, and G) for CaKC on scenario 1, a higher average and peak values. J) CaKC on scenario 2 (activating CaKC), the decrease in peak, average and amplitude values. The central column (B, E, H and K) is the comparison between amplitude and mean of the dynamics between the WT curve and those with altered channels. The colors are the same as in the first column. Right column (C, F, I and L): Fourier Power spectra obtained by the curves on the left.
|
|
Figure 4. Effect on the Calcium dynamics of altering the different NFA-sensitive channels taken by pairs.Average over 100,000 initial conditions of the steady-state dynamics for the WT network is shown in black as in Figure 2. The columns are also distributed as in figure 2. A), B) and C) Blocking HCN and CaCC channels case (green line); D), E) and F) Blocking HCN and CaKC (dark green); G), H) and I) Blocking CaCC-CaKC (turquoise); J), K) and L) HCN blocked and CaKC activated; M), N) and O) CaCC blocked and CaKC activated. Notice that cases with HCN blocked produce non-regular [Ca2+] dynamics, opposite to the regularity generated by the CaCC blockage. Elimination of CaKC (scenario 1 in text) generates an elevation in [Ca2+] concentration compared with blockage of CaCC or HCN. Activation of CaKC (scenario 2) generates a decrease in and peak, but the temporal behavior is more elaborate.
|
|
Figure 5. Effect of deletion of the three NFA-sensitive channels corresponding to scenario 1.A) Steady state time evolution of time series calculated as described in Fig 2. Average oscillations for the wild type are in black while oscillations under deletion of the CaCC-CaKC- HCN nodes are in red (the NFA-blocked network). For the wild type, two contiguous 4 element modules can be identified that together constitute a recurrent 8-step module. For the treated network different 4-step and 8-step modules are indicated in the figure. B) Fourier spectra calculated from 1000 steady-state steps of the time series shown in (A). Period 4 and 8 Fourier modes and their harmonics are shown in black. For the NFA-blocked network the spectrum shown in red, determined from 1000 points of the steady-state [Ca2+] time series, is richer due to the appearance of a period 9 Fourier mode with its harmonics, besides the period 8 contribution. C) A four element running average of the series corresponding to (A) including the initial transient time manifests an underlying repeated 8 module for the wild type and 72 module for the NFA-blocked network case. This last module is the minimum common multiple (MCM) of the period 8 and 9 Fourier modes shown in (B). For the wild type case, a period-8 module surfaces which is the MCM of the period 4 and 8 Fourier modes shown in (B). D) Result of performing a running average as in C) using an 8 element window instead. Here the wild type oscillations are wiped out (black graph) while a 9 module envelop (in red) is evidenced for the triply blocked NFA treated case. The insert is an amplification that shows this behavior in detail.
|
|
Figure 6. Effect of deletion of HCN and CaCC channels and activation of CaKC: scenario 2.A) Steady state time evolution of time series calculated as described in Fig 2. Average oscillations for the wild type are in black while oscillations under deletion of the CaCC- HCN as well as CaKC activation nodes are in red. Notice for the treated network, a 3-step module is indicated in the figure. B) Fourier spectra calculated from 1000 steady-state steps of the time series shown in A). Period 4 and 8 Fourier modes and their harmonics are shown in black. For the NFA-treated network the spectrum shown in red, determined from 1000 points of the steady-state [Ca2+] time series, presents a period-3 Fourier mode. C) A four element running average of the series corresponding to (A), manifests an underlying repeated 8 module for the wild type while the NFA-treated network preserves its period 3 oscillation. D) Result of performing a running average as in (C) using an 8 element window instead. Here the wild type oscillations are wiped out (black graph) while the 3 module envelop (in red) is evidenced for the triply blocked NFA treated case. E) Running average of size 3 produces the complete flattening of the NFA-treated network while period 8 persists in the WT.
|
|
Figure 7. Schematic representation of the effect of deletion or activation of CaKC channels in the speract activated signaling pathway.A) the membrane potential dynamics. B), the [Ca2+] dynamics. For (A) the membrane potential is depicted in black for the WT network after speract activation. Hyperpolarization (lower than −40 mV) due to a efflux via the KCNG channel, and the consequent opening of the voltage-dependent HCN channel which in turn depolarizes the sperm flagellum are shown. Depolarization (higher than −40 mV) opens LVA and HVA [Ca2+] channels. The increase in enhances depolarization. This last entrance of [Ca2+] opens the CaCC and CaKC channels with the corresponding influx of and efflux of that hyperpolarize the membrane potential. All these steps are cyclically repeated causing the [Ca2+] oscillation pattern depicted in (B). If the effect of the drug is an inhibition of CaKC channels, this would cause a bigger depolarization, because a decrease in the efflux. This is shown in the purple curve, notice that the amplitude is bigger than in the WT case. If the effect on CaKC is an activation instead, a bigger hyperpolarization is produced, due to the increase in the efflux of . Depolarization takes less time and is smalles than in the WT case for the same reason (blue curve). For (B), the WT [Ca2+] dynamics is again depicted in black. Inhibition CaKC channels (purple curve), reduces the extrusion of diminishing hyperpolarization hence delayning the closure of CaV channels. This will cause the elevation of as well as the time between [Ca2+] peaks (the period). Overall, the activation of CaKC channels (blue curve), produces a shorter [Ca2+] oscillations due to the faster hyperpolarization, which in turn closes the CaV channels avoiding a big elevation of .
|
