Espinal J et al. (2011), Discrete dynamics model for the speract-activat...

ECB-ART-42150

PLoS One 2011 Jan 01;68:e22619. doi: 10.1371/journal.pone.0022619.

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Discrete dynamics model for the speract-activated Ca2+ signaling network relevant to sperm motility.

Espinal J , Aldana M , Guerrero A , Wood C , Darszon A , Martínez-Mekler G .

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Understanding how spermatozoa approach the egg is a central biological issue. Recently a considerable amount of experimental evidence has accumulated on the relation between oscillations in intracellular calcium ion concentration ([Ca2+]i) in the sea urchin sperm flagellum, triggered by peptides secreted from the egg, and sperm motility. Determination of the structure and dynamics of the signaling pathway leading to these oscillations is a fundamental problem. However, a biochemically based formulation for the comprehension of the molecular mechanisms operating in the axoneme as a response to external stimulus is still lacking. Based on experiments on the S. purpuratus sea urchin spermatozoa, we propose a signaling network model where nodes are discrete variables corresponding to the pathway elements and the signal transmission takes place at discrete time intervals according to logical rules. The validity of this model is corroborated by reproducing previous empirically determined signaling features. Prompted by the model predictions we performed experiments which identified novel characteristics of the signaling pathway. We uncovered the role of a high voltage-activated Ca2+ channel as a regulator of the delay in the onset of fluctuations after activation of the signaling cascade. This delay time has recently been shown to be an important regulatory factor for sea urchin sperm reorientation. Another finding is the participation of a voltage-dependent calcium-activated K+ channel in the determination of the period of the [Ca2+]i fluctuations. Furthermore, by analyzing the spread of network perturbations we find that it operates in a dynamically critical regime. Our work demonstrates that a coarse-grained approach to the dynamics of the signaling pathway is capable of revealing regulatory sperm navigation elements and provides insight, in terms of criticality, on the concurrence of the high robustness and adaptability that the reproduction processes are predicted to have developed throughout evolution.

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Genes referenced: LOC100887844 LOC100893907 LOC576642 LOC583082

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	Figure 1. Signaling pathway triggered by speract in sea urchin sperm.A) Main components involved in the speract signaling pathway. The binding of speract with its receptor in the flagellar membrane triggers the cascade that produces changes in in two different forms: a sustained (tonic) increment and superimposed (supratonic) fluctuations. B) Events produced by the signaling pathway.
	Figure 2. Speract-activated signaling logical network.Yellow and green boxes indicate binary and ternary nodes, respectively. Black arrows indicate activation, red lines inhibition and the yellow arrows can represent activation or inhibition depending on the value of the voltage node (v). Numbers over the arrows show references for the corresponding interaction. As an example, the regulatory function (or truth table) of the cAMP node is shown at the bottom left. The first 3 columns in this table contain all the possible activation states of the cAMP regulators (AC, PDE, cAMP); the fourth column shows the values for the function that correspond to each combination of the regulators.
	Figure 3. Derrida maps for random Boolean networks.This figure illustrates the Derrida map for networks operating in the three different regimes: Ordered (, black), critical (, red), and chaotic (, green and , blue). Note that the Derrida map corresponding to the critical network (red curve) becomes tangent to the identity close to the origin.
	Figure 4. Dynamics of the signaling network.Activation pattern time-courses of the signaling network under different conditions. In each case, the nodes have been lined up horizontally, and are represented by rectangles colored according to their activation state: For the binary nodes black is “off” and green is “on”. For HVA and LVA Ca channels (nodes 10 and 14) black squares indicate inactive states, yellow are for closed states and red for open ones. For the membrane potential V (node 5), black squares indicate a resting potential, blue is hyperpolarization and red depolarization. For the Ca node (dCa) (node 15) we use yellow to indicate tonic elevation, red for a supratonic increment and black for the basal state. Starting out from an initial condition in which only the speract node is active, the dynamics unfold downwards, with each successive row representing the new dynamical state of the network at the next time step. A) Dynamics of the signaling network without deletions (all nodes present). The attractor has period 4 (for clarity, we indicated the period with a white frame for the calcium node, however, all nodes have the same periodicity). B) Agreement with experiment. Elimination of the K permeability node (dK) destroys the oscillations in practically all the nodes, particularly in the Ca node. C) Agreement with experiment. Elimination of the LVA node suppresses the calcium supratonic states (red squares) without altering the periodicity of the attractor. D) Effect of the elimination of PDE node in the signalling network. When PDE node is eliminated, if we divide the number of supratonic states of calcium (red boxes) by the size of attractor (in this case is 11), the total of calcium (2/11) is less than the total of calcium in the entire network when the attractor is reached (1/4). This is according to the experiment when sperms are treated with IBMX, a blocker of phosphodiesterases. The correspondence between the numerical and alphabetical labels of the nodes is indicated at the right of the figure.
	Figure 5. Snapshot of the Java applet that generates the dynamics of the sea urchin sperm signaling network.This applet can be found at http://www.fis.unam.mx/research/seaurchin/discrete/. The pattern is explained in the caption of Fig. 4. Be means of the applet buttons, it is possible to assign specific initial conditions or changes them randomly. It is also possible to explicitly visualize the regulatory functions of the network and modify them at will. Additionally, by unticking the boxes in the column to the right, it is possible to observe the effect in the pattern formation of deleting elements in the network. Further operational details can be found in the web page mentioned above.
	Figure 6. Graphical representation of the attractor landscape.The top right insert shows the fan-like structure where each dot represents a dynamical state of the network, and the lines represent discrete time steps. Two dots are connected if one is the successor of the other under the dynamics. The fan-like structures represent a set of different states that converge to a single state in one time-step. All the fan-like structures eventually converge towards the attractor, which is represented by the black dots connected by solid black lines. Only two active attractors with their attraction basins are shown: one of period 8 and the other one with period 4. The entire attractor landscape is shown in fig S1.
	Figure 7. Effect of eliminating the CaKC node from the network.A) Typical realization of the network dynamics when the CaKC node is eliminated. In this case the periodicity of the attractor duplicates, and there is an increment in the supratonic states per period of the dCa node. B) This is again verified by experiments, showing that iberiotoxin, a specific blocker of the CaKC, reduces the number of speract-induced Ca fluctuations that occur during the 5 sec immediately after stimulation. (movies S1, S2).
	Figure 8. Effect of eliminating the HVA node.A) Temporal evolution of the average calcium level taken at each time step over initial conditions with HVA (black curve) and without HVA (red curve) in arbitrary units. Note in the inset that when HVA is present the increase of the calcium level starts more rapidly than when HVA is deleted, i.e, in the initial time stages, the black curve preceds the behavior of the red curve. B) Experiments show that verapamil, an HVA inhibitor, prolongs the time between speract stimulation and the onset of the first Ca fluctuation (movie S2).
	Figure 9. Critical dynamics in the calcium signaling network.Plot of the Derrida map that relates the size of the perturbation avalanche at two consecutive time steps. The convergence of this map to a stationary value under successive iterations, determines the dynamical regime in which the network operates. The map shown here was computed numerically for the signaling network by relating an initial separation against separation obtained after one step, averaged over all states initially separated by . Notice that the slope of the curve near the origin is practically 1 in a sizeable neighborhood of the origin. This indicates that the signaling network operates in the critical regime.

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