Naoki H et al. (2016), Multi-phasic bi-directional chemotactic respons...

XB-ART-54876

Sci Rep 2016 Nov 03;6:36256. doi: 10.1038/srep36256.

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Multi-phasic bi-directional chemotactic responses of the growth cone.

Naoki H , Nishiyama M , Togashi K , Igarashi Y , Hong K , Ishii S .

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The nerve growth cone is bi-directionally attracted and repelled by the same cue molecules depending on the situations, while other non-neural chemotactic cells usually show uni-directional attraction or repulsion toward their specific cue molecules. However, how the growth cone differs from other non-neural cells remains unclear. Toward this question, we developed a theory for describing chemotactic response based on a mathematical model of intracellular signaling of activator and inhibitor. Our theory was first able to clarify the conditions of attraction and repulsion, which are determined by balance between activator and inhibitor, and the conditions of uni- and bi-directional responses, which are determined by dose-response profiles of activator and inhibitor to the guidance cue. With biologically realistic sigmoidal dose-responses, our model predicted tri-phasic turning response depending on intracellular Ca2+ level, which was then experimentally confirmed by growth cone turning assays and Ca2+ imaging. Furthermore, we took a reverse-engineering analysis to identify balanced regulation between CaMKII (activator) and PP1 (inhibitor) and then the model performance was validated by reproducing turning assays with inhibitions of CaMKII and PP1. Thus, our study implies that the balance between activator and inhibitor underlies the multi-phasic bi-directional turning response of the growth cone.

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Species referenced: Xenopus
Genes referenced: camk2g cdc42 npy4r prkg1 rac1

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	Figure 1. The mathematical growth cone model encompasses an activator and inhibitor system.(A) The schematic drawing depicting the one-dimensional model growth cone encountering an extracellular gradient of guidance cues. (B) In the growth cone, guidance cues, e.g., Netrin-1, lead to the production of cAMP and cGMP, which activate PKA and PKG, respectively, in turn inducing a Ca2+ increase. The intracellular Ca2+ up-regulates CaMKII and PP1, which function as an activator and inhibitor, respectively, of their effector to regulate growth cone motility (referred to as ‘X’ in the text and (D)), e.g., Rac1 and Cdc42. (C) Extracellular gradients of cues are transduced to intracellular gradients of Ca2+ (middle panel) in the same direction as the extracellular gradients, and the increase in the intracellular Ca2+ level that depends on the ratio of cAMP to cGMP regulates the turning direction of the growth cone, i.e., attraction or repulsion. The biased direction of the effector distribution is thought to be reversed between attraction and repulsion (lower panel). High and low levels of intracellular Ca2+ induce attraction and repulsion, respectively, as indicated by the dotted arrows. (D) An activator-inhibitor system of intracellular signaling in chemotaxis: Guidance signal (G) regulates activator (A) and inhibitor (I) in turn up- and down-regulating the effector X. G, A, I and X correspond to Ca2+, CaMKII, PP1 and Rac1/Cdc42, respectively, in the growth cone. (E) Following exposure to a gradient of the guidance cue G, the gradients of A and I are formed across the growth cone, thereby the gradient of X is also formed. A, I and X* represent the levels of A, I and X, respectively, at the center of the growth cone. ΔA, ΔI and ΔX represent the spatial differences of A, I and X, respectively, across the growth cone. (F) The turning angle of the growth cone is formulated as ΔX/X* based on the Weber-Fechner law. The balance between ΔA/Aand ΔI/I governs the turning direction, which is illustrated by scales: attraction when ΔA/A> ΔI / I and repulsion when ΔA/A* < ΔI/I*.
	Figure 2. The theoretical model is capable of producing both uni-directional and multi-phasic bi-directional turning responses.(A,C,E,G) Examples of activator and inhibitor activities in response to increasing guidance signal (intracellular Ca2+ in the case of the growth cone). Red and blue lines indicate the dose-responses of activator A and inhibitor I, respectively, to the guidance signal. The dose-response curves are given by Hill equations (Equations (8 and 9)). Parameter values are listed in Methods. (B,D,F,H) Turning responses (black lines) are calculated based on the dose-responses of activator and inhibitor, shown in (A,C,E,G) (see Methods). When the intracellular Ca2+ level is in the red and blue shaded regions, the growth cone exhibits attraction and repulsion, respectively. The turning response is given by the sum of the attractive factor (red dashed line: the first term in Equation (1)) and the repulsive factor (blue dashed line: the second term in Equation (1)). Each dashed line represents the ratio between the slope and amplitude of the dose-response curve in (B), (C), (E) or (G); e.g., the red dashed line in (B) was obtained from the slope (ΔA) and amplitude (A*) of the red solid line in (A). Thus, the theoretical model is able to produce a simple uni-directional attraction (A,B) or repulsion (C,D), bi-phasic bi-directional turning response (E,F), and tri-phasic bi-directional turning response (G,H). These complex responses are primarily due to the nonlinear responses of the activator and inhibitor to the guidance signal, typically observed in (G).
	Figure 3. The growth cone exhibits multi-phasic bi-directional turning responses when the total concentration of [cAMP + cGMP] is changed at the fixed ratio of cAMP/cGMP.(A) Representative images of growth cones at the onset (0 hr) and after (1 hr) exposure to a gradient solution containing a mixture of the membrane permeable cyclic nucleotide analogues, [Sp-8-Br-cAMPS] and [8-Br-cGMP], at a fixed ratio of 9:1 at different concentrations (5 mM [4.5 cAMP + 0.5 cGMP]; 50 mM [45 cAMP + 5 cGMP]; and 100 mM [90 cAMP + 10 cGMP]) in the application micropipette. Superimposed traces on the right depict the total neurite trajectories examined over the 1 hr period, where the initial position of the growth cone is at the origin, and the original direction of growth is vertical. The arrows in both the representative images and trajectories mark the direction of the gradient. (B) The average growth cone turning angles in response to gradient of a mixture solution of [Sp-8-Br-cAMPS] and [8-Br-cGMP] with different concentrations (0, 1, 5, 10, 20, 50, and 100 mM) at the fixed ratio of 9:1 in the micropipette, which are indicated as “cNMP”. (C) The average growth cone turning angles in response to gradient of a solution of [Sp-8-Br-cAMPS] at different concentrations (5, 10, 20, 50, and 100 mM) in the micropipette. Positive and negative turning angles indicate attraction and repulsion, respectively. Error bars = s.e.m. (n) = number of growth cones examined. Significant differences compared to the control are indicated (p < 0.05; *p < 0.01; Mann-Whitney U test).
	Figure 4. Multi-phasic bi-directional turning depending on the concentration of cAMP/cGMP gradients is accompanied by a monotonic Ca2+ increase.(A) Representative images of Oregon Green 488 BAPTA-1 (OGB)-dextran fluorescent growth cones obtained at various times during exposure to either culture medium (control) or gradients of different concentrations of a 9:1 ratio of cAMP/cGMP (arrows). The fluorescence intensity is expressed as pseudo-colors (top; blue = low, red = high). (B) Sample traces (top) and summary (bottom) of the percentage changes in OGB-dextran fluorescence (ΔF/F) in the growth cones exposed to culture medium (control) or to different concentration gradients of cAMP/cGMP. OGB-dextran fluorescence was normalized to the fluorescent intensity of co-injected Texas Red–dextran in the growth cones before and after exposure to the cyclic nucleotide gradients (arrows in (A)). Cyclic nucleotide (cNMP) gradients: grey horizontal bars. Error bars = s.e.m. (n) = number of growth cones examined. Significant differences compared to the control are indicated (p < 0.05; *p < 0.01; Mann-Whitney U test). (C) Left panel: Cumulative distribution of the average ΔF/F (%) at 10–20 min after exposure to cyclic nucleotide gradients as in (B). Right panel: Monotonic increase in the averages ΔF/F at 15–20 min that resulted from growth cone exposure to cyclic nucleotide gradients as in (B). The red curve is a regression function.
	Figure 5. System identification of CaMKII and PP1 activities in the bi-directional turning response.(A) The schematic drawing depicting the regulation of CaMKII and PP1, which up- and down-regulate the effector X, respectively, in the growth cone model. (B) Simulation of the multi-phasic bi-directional turning response by a mathematical model where the parameters were identified by the reverse engineering approach (solid red line). Points and error bars represent the experimental results (the same as in Fig. 3B). Goodness of fitting was evaluated by the Pearson’s chi-square test (p = 0.78), indicating no significant difference. (C) Reverse-engineered dose-responses of CaMKII (Red line) and PP1 (blue line) to the total cAMP:cGMP concentration (cNMP). The dose-responses were normalized. The blue line is the sum of CaN- and Calpain-dependent PP1 (blue dashed and dotted lines). The estimated parameter values are listed in Methods. (D) Contributions of the activator (A; CaMKII) and the inhibitor (I; PP1) to growth cone turning (black line in (B)) depending on the cNMP level. Attractive and repulsive influences of the activator and inhibitor are represented by red and blue solid lines, respectively, which correspond to the first and second terms in Equation (1). The PP1-induced repulsion (blue solid line) is given by the sum of the CaN- and Calpain- dependent factors (dashed and dotted blue lines, respectively).
	Figure 6. Bi-directional turning depends on the molecular switching between CaMKII and PP1.(A) Model simulation of growth cone turning responses during the inhibition of either the activator, CaMKII (red line) or the inhibitor, PP1 (blue line). Inhibition of CaMKII or PP1 activity was simulated by a 90% reduction of the estimated parameter for each concentration. (B) Growth cone turning responses were experimentally observed in response to a gradient solution that contained [Sp-8-Br-cAMPS] and [8-Br-cGMP] at a fixed ratio (9:1) at different concentrations in the presence of KN-93 (0.5 μM; CaMKII inhibitor, red line) or tautomycin (4 nM; PP1 inhibitor, blue line) in the assay medium. Significant differences compared to the control are indicated (p < 0.05; *p < 0.01; Mann-Whitney U test). Goodness of fitting of model simulation to experiment was evaluated by p-value of the Pearson’s chi-square test (p < 0.01 with KN-93; p = 0.38 with tautomycin).

References [+] :

Adler, Logarithmic and power law input-output relations in sensory systems with fold-change detection. 2014, Pubmed

	Figure 1. The mathematical growth cone model encompasses an activator and inhibitor system.(A) The schematic drawing depicting the one-dimensional model growth cone encountering an extracellular gradient of guidance cues. (B) In the growth cone, guidance cues, e.g., Netrin-1, lead to the production of cAMP and cGMP, which activate PKA and PKG, respectively, in turn inducing a Ca2+ increase. The intracellular Ca2+ up-regulates CaMKII and PP1, which function as an activator and inhibitor, respectively, of their effector to regulate growth cone motility (referred to as ‘X’ in the text and (D)), e.g., Rac1 and Cdc42. (C) Extracellular gradients of cues are transduced to intracellular gradients of Ca2+ (middle panel) in the same direction as the extracellular gradients, and the increase in the intracellular Ca2+ level that depends on the ratio of cAMP to cGMP regulates the turning direction of the growth cone, i.e., attraction or repulsion. The biased direction of the effector distribution is thought to be reversed between attraction and repulsion (lower panel). High and low levels of intracellular Ca2+ induce attraction and repulsion, respectively, as indicated by the dotted arrows. (D) An activator-inhibitor system of intracellular signaling in chemotaxis: Guidance signal (G) regulates activator (A) and inhibitor (I) in turn up- and down-regulating the effector X. G, A, I and X correspond to Ca2+, CaMKII, PP1 and Rac1/Cdc42, respectively, in the growth cone. (E) Following exposure to a gradient of the guidance cue G, the gradients of A and I are formed across the growth cone, thereby the gradient of X is also formed. A, I and X* represent the levels of A, I and X, respectively, at the center of the growth cone. ΔA, ΔI and ΔX represent the spatial differences of A, I and X, respectively, across the growth cone. (F) The turning angle of the growth cone is formulated as ΔX/X* based on the Weber-Fechner law. The balance between ΔA/Aand ΔI/I governs the turning direction, which is illustrated by scales: attraction when ΔA/A> ΔI / I and repulsion when ΔA/A* < ΔI/I*.
	Figure 2. The theoretical model is capable of producing both uni-directional and multi-phasic bi-directional turning responses.(A,C,E,G) Examples of activator and inhibitor activities in response to increasing guidance signal (intracellular Ca2+ in the case of the growth cone). Red and blue lines indicate the dose-responses of activator A and inhibitor I, respectively, to the guidance signal. The dose-response curves are given by Hill equations (Equations (8 and 9)). Parameter values are listed in Methods. (B,D,F,H) Turning responses (black lines) are calculated based on the dose-responses of activator and inhibitor, shown in (A,C,E,G) (see Methods). When the intracellular Ca2+ level is in the red and blue shaded regions, the growth cone exhibits attraction and repulsion, respectively. The turning response is given by the sum of the attractive factor (red dashed line: the first term in Equation (1)) and the repulsive factor (blue dashed line: the second term in Equation (1)). Each dashed line represents the ratio between the slope and amplitude of the dose-response curve in (B), (C), (E) or (G); e.g., the red dashed line in (B) was obtained from the slope (ΔA) and amplitude (A*) of the red solid line in (A). Thus, the theoretical model is able to produce a simple uni-directional attraction (A,B) or repulsion (C,D), bi-phasic bi-directional turning response (E,F), and tri-phasic bi-directional turning response (G,H). These complex responses are primarily due to the nonlinear responses of the activator and inhibitor to the guidance signal, typically observed in (G).
	Figure 3. The growth cone exhibits multi-phasic bi-directional turning responses when the total concentration of [cAMP + cGMP] is changed at the fixed ratio of cAMP/cGMP.(A) Representative images of growth cones at the onset (0 hr) and after (1 hr) exposure to a gradient solution containing a mixture of the membrane permeable cyclic nucleotide analogues, [Sp-8-Br-cAMPS] and [8-Br-cGMP], at a fixed ratio of 9:1 at different concentrations (5 mM [4.5 cAMP + 0.5 cGMP]; 50 mM [45 cAMP + 5 cGMP]; and 100 mM [90 cAMP + 10 cGMP]) in the application micropipette. Superimposed traces on the right depict the total neurite trajectories examined over the 1 hr period, where the initial position of the growth cone is at the origin, and the original direction of growth is vertical. The arrows in both the representative images and trajectories mark the direction of the gradient. (B) The average growth cone turning angles in response to gradient of a mixture solution of [Sp-8-Br-cAMPS] and [8-Br-cGMP] with different concentrations (0, 1, 5, 10, 20, 50, and 100 mM) at the fixed ratio of 9:1 in the micropipette, which are indicated as “cNMP”. (C) The average growth cone turning angles in response to gradient of a solution of [Sp-8-Br-cAMPS] at different concentrations (5, 10, 20, 50, and 100 mM) in the micropipette. Positive and negative turning angles indicate attraction and repulsion, respectively. Error bars = s.e.m. (n) = number of growth cones examined. Significant differences compared to the control are indicated (p < 0.05; *p < 0.01; Mann-Whitney U test).
	Figure 4. Multi-phasic bi-directional turning depending on the concentration of cAMP/cGMP gradients is accompanied by a monotonic Ca2+ increase.(A) Representative images of Oregon Green 488 BAPTA-1 (OGB)-dextran fluorescent growth cones obtained at various times during exposure to either culture medium (control) or gradients of different concentrations of a 9:1 ratio of cAMP/cGMP (arrows). The fluorescence intensity is expressed as pseudo-colors (top; blue = low, red = high). (B) Sample traces (top) and summary (bottom) of the percentage changes in OGB-dextran fluorescence (ΔF/F) in the growth cones exposed to culture medium (control) or to different concentration gradients of cAMP/cGMP. OGB-dextran fluorescence was normalized to the fluorescent intensity of co-injected Texas Red–dextran in the growth cones before and after exposure to the cyclic nucleotide gradients (arrows in (A)). Cyclic nucleotide (cNMP) gradients: grey horizontal bars. Error bars = s.e.m. (n) = number of growth cones examined. Significant differences compared to the control are indicated (p < 0.05; *p < 0.01; Mann-Whitney U test). (C) Left panel: Cumulative distribution of the average ΔF/F (%) at 10–20 min after exposure to cyclic nucleotide gradients as in (B). Right panel: Monotonic increase in the averages ΔF/F at 15–20 min that resulted from growth cone exposure to cyclic nucleotide gradients as in (B). The red curve is a regression function.
	Figure 5. System identification of CaMKII and PP1 activities in the bi-directional turning response.(A) The schematic drawing depicting the regulation of CaMKII and PP1, which up- and down-regulate the effector X, respectively, in the growth cone model. (B) Simulation of the multi-phasic bi-directional turning response by a mathematical model where the parameters were identified by the reverse engineering approach (solid red line). Points and error bars represent the experimental results (the same as in Fig. 3B). Goodness of fitting was evaluated by the Pearson’s chi-square test (p = 0.78), indicating no significant difference. (C) Reverse-engineered dose-responses of CaMKII (Red line) and PP1 (blue line) to the total cAMP:cGMP concentration (cNMP). The dose-responses were normalized. The blue line is the sum of CaN- and Calpain-dependent PP1 (blue dashed and dotted lines). The estimated parameter values are listed in Methods. (D) Contributions of the activator (A; CaMKII) and the inhibitor (I; PP1) to growth cone turning (black line in (B)) depending on the cNMP level. Attractive and repulsive influences of the activator and inhibitor are represented by red and blue solid lines, respectively, which correspond to the first and second terms in Equation (1). The PP1-induced repulsion (blue solid line) is given by the sum of the CaN- and Calpain- dependent factors (dashed and dotted blue lines, respectively).
	Figure 6. Bi-directional turning depends on the molecular switching between CaMKII and PP1.(A) Model simulation of growth cone turning responses during the inhibition of either the activator, CaMKII (red line) or the inhibitor, PP1 (blue line). Inhibition of CaMKII or PP1 activity was simulated by a 90% reduction of the estimated parameter for each concentration. (B) Growth cone turning responses were experimentally observed in response to a gradient solution that contained [Sp-8-Br-cAMPS] and [8-Br-cGMP] at a fixed ratio (9:1) at different concentrations in the presence of KN-93 (0.5 μM; CaMKII inhibitor, red line) or tautomycin (4 nM; PP1 inhibitor, blue line) in the assay medium. Significant differences compared to the control are indicated (p < 0.05; *p < 0.01; Mann-Whitney U test). Goodness of fitting of model simulation to experiment was evaluated by p-value of the Pearson’s chi-square test (p < 0.01 with KN-93; p = 0.38 with tautomycin).