1. Computational and Systems Biology
  2. Neuroscience

New insights on the modeling of the molecular mechanisms underlying neural maps alignment in the midbrain

  1. Elise Laura Savier  Is a corresponding author
  2. James Dunbar
  3. Kyle Cheung
  4. Michael Reber  Is a corresponding author
  1. Department of Biology and Psychology, University of Virginia, United States
  2. Donald K. Johnson Eye Institute, Krembil Research Institute, University Health Network, Canada
  3. Laboratory of Medicine and Pathobiology, University of Toronto, Canada
  4. Ophthalmology and Vision Sciences, University of Toronto, Canada
  5. Cell and System Biology, University of Toronto, Canada
  6. CNRS UPR 3212, University of Strasbourg, France
https://doi.org/10.7554/eLife.59754
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Cite this article
  1. Elise Laura Savier
  2. James Dunbar
  3. Kyle Cheung
  4. Michael Reber
(2020)
New insights on the modeling of the molecular mechanisms underlying neural maps alignment in the midbrain
eLife 9:e59754.
https://doi.org/10.7554/eLife.59754
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6 figures, 2 tables and 1 additional file

Figures

Figure 1
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Dot plots representing Ephas/Efnas expression in Isl2Epha3/Epha3retinas, V1 cortex and SC.

(A) Median Efna2/a3/a5 expression levels (relative to wild-type nasal expression) in P1/2 wild-type (WT - white) and Isl2Epha3/Epha3 (gray) acutely isolated RGCs from nasal (N), central (C) and temporal (T) retinas (WT, Isl2Epha3/Epha3, n = 6 animals, 12 retinas), Two-way ANOVA without replication: Efna2 x genotype: F(1,2) = 3.72 < Fcrit.=18.5, p=0.19; Efna3 x genotype : F(1, 2)=11.13 < Fcrit.=18.5, p=0.07; Efna5 x genotype: F(1, 2)=3.58 < Fcrit.=18.5, p=0.20. (B) Median Efna2/a3/a5 ligands and Epha4/a7 receptors expression levels (relative to WT expression levels) in Isl2Epha3/Epha3 V1 (WT n = 5 animals, Isl2Epha3/Epha3n = 8 animals; variables are normally distributed, one sample t-test: Efna2: p=0.29; Efna3: p=0.43; Efna5: p=0.42; Epha4: p=0.07; Epha7: p=0.54) and SC (WT n = 5 animals, Isl2Epha3/Epha3n = 6 animals; variables are normally distributed, one sample t-test: Efna2: p=0.20; Efna3: p=0.65; Efna5: p=0.71; Epha4: p=0.11; Epha7: p=0.17). qPCRs were repeated three times with duplicates for each sample.

Figure 1—source data 1

Data for Figure 1A: Expression levels, relative to wild-type, of retinal Efna in Isl2Epha3/Epha3 animals.

Data for Figure 1B: Expression levels, relative to wild-type, of collicular and cortical V1 Ephas and Efnas in Isl2Epha3/Epha3 animals.

https://cdn.elifesciences.org/articles/59754/elife-59754-fig1-data1-v1.xlsx
Figure 2
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Simulations of retino- and cortico-collicular mapping in Isl2-Epha3KI animals.

(A, G, M) Representation of measured retinal Epha gradients along the nasal-temporal (NT) axis in WT (A), Isl2Epha3/+ (G) and Isl2Epha3/Epha3 (M) animals (see Materials and methods and Table 1 for equations). (B, H, N) Representation of the estimated collicular Efna gradients along the rostral-caudal (RC) axis in WT (B), Isl2Epha3/+ (H) and Isl2Epha3/Epha3 (N) animals (see Materials and methods and Table 1 for equations). (C, I, O) Representation of the transposed retinal Efna gradients into the SC along the RC axis in WT (C), Isl2Epha3/+ (I) and Isl2Epha3/Epha3 (O) animals (see Materials and methods and Table 1 for equations). (D, J, P) Representation of the estimated cortical Epha gradients along the medial-lateral (ML) axis in V1 in WT (D), Isl2Epha3/+ (J) and Isl2Epha3/Epha3 (P) animals (see Materials and methods and Table 1 for equations). (E, K, Q) Simulated RC map in in WT (E), Isl2Epha3/+ (K) and Isl2Epha3/Epha3 (Q) animals generated by the 3-step map alignment algorithm (representative of n = 20 runs). (F, L, R) Simulated cortico-collicular map in WT (F), Isl2Epha3/+ (L) and Isl2Epha3/Epha3 (R) animals generated by the 3-step map alignment algorithm (representative of n = 20 runs). Abbreviations: N, nasal; T, temporal; R, rostral; C, caudal; M, medial; L, lateral.

Figure 3
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Experimental validation of retino- and cortico-collicular mapping in Isl2-Epha3KI animals.

(A) Images of two experimental injections showing the collicular terminations zones (triangles and square, top-view, upper panels) after focal retinal injections (arrows, flat-mount, lower panel) in Isl2Epha3/+ animals. (B) Cartesian representation of the injections (triangles and square) in (A) superimposed with the simulated RC map (black dots, n = 100) in Isl2Epha3/+. Map profile is calculated by LOESS smoothing (black and gray lines). (C) Images of two experimental injections showing the collicular termination zones (sagittal view, upper panels) after focal cortical V1 injection (top-view, lower panels). Arrows and arrowheads indicate the site of the termination zones. Lower left panel shows CO staining (dark gray) delineating V1. (D) Cartesian representation of the experimental (red dots/lines, n = 15 animals) and simulated (black dots, n = 100) CC maps calculated by LOESS smoothing (black, red and gray lines). Arrows and arrowhead represent the two injections shown in (C). Two-samples Kolmogorov-Smirnov test, D-stat = 0.273 < D-crit.=0.282, p=0.06, simulated and experimentally measured CC maps are not significantly different. (E) Images of two experimental injections showing the collicular terminations zones (triangles and squares, top-view, upper panels) after focal retinal injection (arrows, flat-mount, lower panel) in Isl2Epha3/Epha3 animals. (F) Cartesian representation of the injections (triangles and squares) in (E) superimposed with the simulated RC map (black dots, n = 100) in Isl2Epha3/Epha3. Map profile is calculated by LOESS smoothing (black and gray lines). (G) Images of two experimental injections showing the collicular duplicated termination zones (arrows and arrowheads, sagittal view, upper panels) after focal cortical V1 injection (top-view, lower panels). (H) Cartesian representation of the experimental (red dots/lines, n = 7 animals) and simulated (black dots, n = 100) CC maps calculated by LOESS smoothing (black, red and gray lines). Arrows and arrowheads represent the two examples in (G). Two-samples Kolmogorov-Smirnov test, D-stat = 0.190 < D-crit.=0.371, p=0.72, simulated and experimentally measured CC maps are not significantly different. Scale bars: 400 μm (A upper, C, E upper, G), 1 mm (A, E lower). Abbreviations: N, nasal; T, temporal; R, rostral; C, caudal; M, medial; L, lateral.

Figure 3—source data 1

Data for Figure 3B: Cartesian values of experimentally measured collicular termination zones and corresponding retinal injections in Isl2Epha3/+ animals.

Data for Figure 3D: Cartesian values of experimentally measured collicular termination zones and corresponding cortical V1 injections in Isl2Epha3/+ animals. Data for Figure 3F: Cartesian values of experimentally measured collicular termination zones and corresponding retinal injections in Isl2Epha3/Epha3 animals. Data for Figure 3B: Cartesian values of experimentally measured collicular termination zones and corresponding cortical V1 injections in Isl2Epha3/Epha3 animals.

https://cdn.elifesciences.org/articles/59754/elife-59754-fig3-data1-v1.xlsx
Figure 4
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Intrinsic dispersion index (IDI) and alignment index (AI) in Isl2-Epha3KI and Isl2-Efna3KI animal models.

(A) Violin plot representation of the median IDIs (from n = 10 simulated maps, each composed of 100 projections) in WT, Isl2-Epha3KI and Isl2-Efna3KI animal models. Mann-Whitney test: WT IDIretino vs. Isl2Epha3/+ IDIretino, z-score = 12.08, effect r = 0.85, p=6E-55; WT IDIcortico vs. Isl2Epha3/+ IDIcortico, z-score = 12.04, effect r = 0.85, p=8E-52; Isl2Epha3/+ IDIretino vs Isl2Epha3/Epha3 IDIretino, z-score = 11.25, effect r = 0.80, p=2E-39; Isl2Epha3/+ IDIcortico vs Isl2Epha3/Epha3 IDIcortico, z-score = 10.53, effect r = 0.74, p=1E-32; WT IDIcortico vs Isl2Efna3/+ IDIcortico, z-score = 8.30, effect r = 0.59, p=1E-18; WT IDIcortico vs Isl2Efna3/Efna3 IDIcortico, z-score = 10.37, effect r = 0.73, p=3E-31; Isl2Efna3/+ IDIcortico vs Isl2Efna3/Efna3 IDIcortico, z-score = 6.93, effect r = 0.49, p=6E-13; ***p<0.001. (B, C, D, E, F) Representation and superimposition of simulated RC (retino-collicular) (white dots) and CC (cortico-collicular) (black dots) maps in WT (B), Isl2Epha3/+ (C), Isl2Epha3/Epha3 (D), Isl2Efna3/+ (E) and Isl2Efna3/Efna3 (F) animals (representative of n = 10 runs). (G) Box plot representation of median AI (from n = 20 simulated RC/CC maps) in WT, Isl2Epha3/+, Isl2Epha3/Epha3, Isl2Efna3/+ and Isl2Efna3/Efna3 animals. Mann-Whitney test: AI WT vs. AI Isl2Epha3/+, z-score = 1.62, effect r = 0.26 p=0.10; AI WT vs. AI Isl2Epha3/Epha3, z-score = 0.11, effect r = 0.02, p=0.90; AI WT vs AI Isl2Efna3/+, z-score = 5.40, effect r = 0.85, p=1.45E-11; AI WT vs AI Isl2Efna3/Efna3, z-score = 5.40, effect r = 0.85, p=1.45E-11. ***p<0.001. Abbreviations: IDI, intrinsic dispersion index; AI, alignment index; WT, wild-type; N, nasal; T, temporal; R, rostral; C, caudal; M, medial; L, lateral.

Figure 4—source data 1

Data for Figure 4A: Intrinsic Dispersion Index values for retino-collicular (RC) and cortical-collicular (CC) mapping in wild-type (WT), Isl2-Epha3KI and Isl2-Efna3KI animals.

Data for Figure 4G: Total RC and CC map alignment index (AI) values in wild-type (WT), Isl2-Epha3KI and Isl2-Efna3KI animals.

https://cdn.elifesciences.org/articles/59754/elife-59754-fig4-data1-v1.xlsx
Figure 5
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Local intrinsic dispersion variation (local IDV) in WT, Isl2-Epha3KI and Isl2-Efna3KI animal models.

(A, B, C, D, E) Representation of the local IDV values for both retinal (light colors) and cortical (dark colors) projections along the rostral R (0%) – caudal C (100%) axis of the SC in WT (A), Isl2Epha3/+ Isl2Epha3/+ (B), Isl2Epha3/Epha3 (C), Isl2Efna3/+ (D) and Isl2Efna3/Efna3 (E) animals (representative of n = 10 runs). Dashed line represents the threshold above which maps are duplicated. Abbreviations: IDV, intrinsic dispersion variation; WT, wild-type; R, rostral; C, caudal.

Figure 5—source data 1

Local intrinsic dispersion variation (local IDV) values for retino-collicular (RC) and cortical-collicular (CC) mapping in wild-type (WT), Isl2-Epha3KI and Isl2-Efna3KI animals.

https://cdn.elifesciences.org/articles/59754/elife-59754-fig5-data1-v1.xlsx
Figure 6
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Proposed mechanism of visual map duplication and alignment in Isl2-Epha3KI animals based on the 3-step map alignment model.

Step 1: Isl2(+) RGCs expressing WT levels Ephas + ectopic Epha3 (dark red) and Isl2(-) RGCs expressing WT levels of Ephas (light red to red) send their axons into the SC during the first postnatal week. These retino-collicular (RC) projections form a duplicated map due to the oscillatory gradient of Ephas receptors in the RGCs reading the WT collicular Efna gradients (blue R-C gradient in SC) through forward signaling. Step 2: Retinal Efna gradients (high Efnas-nasal-dark green, low Efnas-temporal-light green) are carried to the SC during the formation of the RC projections. This transposition of retinal Efnas generates two exponential gradients of Efna in the SC, due to the duplication of the RC map and replaces the WT collicular Efna gradients previously used by the RGCs axons (Janes et al., 2005). Step 3: V1 axons, expressing smooth gradients of Ephas receptors (light red – red), are facing two exponential gradients of Efnas, of retinal origin, in SC. Through forward signaling, this two exponential Efna gradients generate a duplication of the CC projections, which aligns with the RC map. Abbreviations: N, nasal; T, temporal; M, medial; L, lateral; R, rostral; C, caudal; SC, superior colliculus; RGCs, retinal ganglion cells.

Tables

Key resources table
Reagent type
(species) or resource		DesignationSource or referenceIdentifiersAdditional
information
Genetic reagent (Mus. musculus)Isl2tm1(Epha3)GrlLemke Lab (Salk Institute)MGI:3056440 RRID:MGI:3057124
Commercial assay, kitNeural tissue dissociation Kit – Postnatal neuronsMiltenyiCat # 130-094-802
Commercial assay, kitRNeasy Mini kitQiagenCat # 74104
Commercial assay, kitQuantiTect SYBR Green RT-PCR KitQiagenCat # 204243
AntibodyGoat anti-rabbit IgG (H+L), polyclonalJackson ImmunoresearchCat # 111-005-003 RRID:AB_23379131:3000
AntibodyGoat anti-mouse IgM (H+L)BiotrendCat # 610–11071:3000
AntibodyMouse anti-CD90, monoclonalBioradCat # MCA02R F7D5 IgM RRID:AB_3234811:3000
AntibodyRabbit anti-rat macrophage, polyclonalLife ScienceCat # AIA512401:3000
Chemical compound, drugNeurobasal mediumGibco/ThermofisherCat # 21103049
Chemical compound, drugB27ThermofisherCat # 17504044
Chemical compound, drugBDNFPeproTechCat # 450–0225 ng/ml
Chemical compound, drugCNTFPeproTechCat # 450–1310 ng/ml
Chemical compound, drugForskolinSigmaCat # F391710 mM
Chemical compound, drugGlutamineThermofisherCat # 250301492 mM
Chemical compound, drugN-acetyl-l-cysteineSigmaCat # A0916560 mg/ml
Chemical compound, drugPenicilin/streptomycinGibcoCat # 15070–022100 units/ml
Chemical compound, drugSodium pyruvateThermofisherCat # 113600701 mM
Chemical compound, drugDiI (1,1-dioctadecyl-3,3,3,3-tetramethylindocarbocyanine perchlorate)ThermofisherCat # D282
Chemical compound, drugDiD (1,1’–dioctadecyl-3,3,3’,3’- tetramethylindodicarbocyanine, 4-chlorobenzenesulfonate)ThermofisherCat # D7757
Software, algorithmR Project for Statistical Computingwww.r-project.orgRRID:SCR_001905
Software, algorithmImageJhttps://imagej.nih.gov/ijRRID:SCR_003070
Software, algorithmMATLABRRID:SCR_001622
Software, algorithm3-step map alignmentReber Lab (Krembil)https://github.com/michaelreber/3-step-Map-Aligment-Model/blob/master/threestepsMapAlignment.m
Software, algorithmLOESS smoothingReber Lab (Krembil)https://github.com/michaelreber/Leave-one-out-LOESS/blob/master/wtloess.R
Table 1
summary of the parameters of the 3-step map alignment algorithm.
ReceptorEpha3Epha4Epha5Epha6Source
RetinaWT = 0
Epha3KI/KI = 1.86
Epha3KI/+ = 0.93		1.050.14e0.018x0.09e0.029xMeasured (Brown et al., 2000; Reber et al., 2004)
V1e(-x/100) – e((x – 200/100) + 1)Estimated (Tsigankov and Koulakov, 2010; Tsigankov and Koulakov, 2006)
LigandEfna2Efna3Efna5
Retina1.85 e-0.008x0.441.79 e-0.014xMeasured (Savier et al., 2017)
SCe((x – 100)100) – e((-x-100)/100)Estimated (Cang et al., 2005; Savier et al., 2017; Tsigankov and Koulakov, 2010; Tsigankov and Koulakov, 2006)
Parameters
γ1Strength of activity interaction
α200Chemical strength
d3SC interaction distance
b0.11Retinal correlation distance

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  1. Elise Laura Savier
  2. James Dunbar
  3. Kyle Cheung
  4. Michael Reber
(2020)
New insights on the modeling of the molecular mechanisms underlying neural maps alignment in the midbrain
eLife 9:e59754.
https://doi.org/10.7554/eLife.59754