EMBO/SourceData huggingface dataset:
Figure 8 A and B, Efficiency of AAV9-mediated gene delivery. AA9 viruses expressing the reporter GFP gene were stereotaxically injected into the SN of mice, and GFP expression in astrocytes, microglia, and neuronal cells was quantified. Data are represented as mean ± SEM. n=3 mice (>5 randomly selected microscopic fields per animal were counted). Significantly different at p=0.006*, 5.1E-09#, 5.36E-09+ in graph B.  SGK1 knockdown effect in vivo by treatment with shSgk1-AAV9. Total SGK1 mRNA levels were estimated in the midbrain SN of the PD mice injected with shSgk1(shControl as control) AAV9 using real time-PCR (D). Cell type-specific SGK1 knockdown was estimated by counting SGK1-immuonoreactivity in neuron (MAP2+), astrocyte (GFAP+), and microglia (Iba1+) populations (E).  Data are represented as mean ± SEM. n=4 mice in each group. Significantly different at p=0.0004# in graph D and p=0.049*, 0.007**, 0.002*** in graph E. (F-H) Behavior of the PD mice assessed by pole (F), beam (G) at 6-12 weeks, and locomotor activity (H) tests at 12 weeks post- SNCA injection. Significantly different at p=0.0003#, 0.0428*, 7.46E-06##, 0.0012** in graph F and p=8.04E-08#, 0.004*, 1.62E-09##, 3.3E-06** in graph G and p=0.0002#, 0.0194* (total distance), 9.54E-06#, 0.0047* (average speed) in graph H.  Histologic assessment of p129-SNCA immunoreactivity ( I,J), TH+ mDA neuron counts (I,K), neurite lengths (L), and cell body sizes (M) in the SN Significantly different at p=0.0001* in graph J, p=2.35E-25#, 1.09E-16##, 4.36E-08* in graph K and p=1.5E-40#, 1.08E-24##, 2.32E-07* in graph L and p=9.07E-20#, 2.59E-16##, 0.05* in graph M and p=4.62E-22#, 5.11E-12##, 3.49E-06* (TH), n= 7 sh-SGK1-AAV9-treated PD mice, 7 sh-cont-AAV9-treated PD mice, and 8 SNCA-untreated mice. Data are represented as mean ± SEM. One-way ANOVA. Scale bar, 100µm.  Histologic assessment of TH+ and DA transporter (DAT) fiber intensities in the striatum n= 7 sh-SGK1-AAV9-treated PD mice, 7 sh-cont-AAV9-treated PD mice, and 8 SNCA-untreated mice. Data are represented as mean ± SEM. One-way ANOVA. Scale bar, 100µm.
Figure 9 A-C, Quantitative and morphometric analyses of microglia in the SN area of SNCA-PD mice. Shown in A are representative views of Iba1+ microglia neighboring TH+ mDA neurons in the SNs of PD mice treated with GSK-650394 and vehicle. Insets, enlarged views for the boxed areas. Data are represented as mean ± SEM. n=3 mice per group. Significantly different at p=1.49E-11* in graph B and p=0.000003* in graph C.  D and E, The M1 marker CD16/32 expression in Iba1+ microglia. Data are represented as mean ± SEM. n=3 mice per group. Significantly different at p=0.0016* in graph E.  F and G, mRNA expression of NLRP3-inflammasome components and pro-inflammatory cytokines in MPTP (F) and SNCA (G) PD mice injected with the SGK1 inhibitor or vehicle (control). Each bar represents the mean ± SEM of 3 PCR values from each animal, n=3 mice per group. Significantly different at p=0.0372*, 0.0173**, 0.0003*** in graph F and p=0.002#, 0.0113##, 0.0053###, 0.0001#### in graph G.  H-J, ASC expression in the SNs and SN microglia of SNCA-PD mice. n=5 mice per group. Data are represented as mean ± SEM. Significantly different at p=1.91E-09* in graph I and p=0.0079* in graph J.  K and L, β-gal-stained cell senescence in SNCA-PD mouse SN. Data are represented as mean ± SEM. n=5 mice per group. Significantly different at p=0.0001*
f1(a) Mitochondrial tubules in HeLa cells (top, TMRE stained) exceeded the dimensions of that for autophagosomes (labelled by EGFP-LC3B) under either normal (middle, same field as TMRE image) or starvation conditions (right).(c) Illuminating a selective region (white dotted circle, top) within a KR-dMito/EBFP2-parkin-expressing HeLa cell led to the immediate loss of KR fluorescence (top two panels). Third to fifth row: magnified view of the photo-impaired region, EBFP2-parkin translocated onto impaired mitochondrial tubules synchronously (38-60 min after 559 illumination, white arrows). Scale bars (all panels), 10 μm.
f2(a) A HeLa cell expressing KR-dMito, EGFP-LC3B and EBFP2-parkin (cyan) were 559 nm illuminated (white dotted circle region; immediate loss of KR fluorescence). (b-d) Magnified view of the photo-inactivated region in a 34-93 min after 559 nm illumination. (b) Induction of parkin-mediated mitophagy on a single, long mitochondria tubule (white arrows). (c) LC3B-coated structures were recruited onto distinct spots on the photo-impaired mitochondrial tubule (white arrows: the location of the original impaired single mitochondrial tubule). (d) White dotted line region outlined in c, LC3 structures segregated from the main parkin-labelled cluster, carrying away bits of the parkin-labelled mitochondria with them. Two individual events are labelled in the image sequence with white and yellow arrows, respectively. Scale bars (all panels), 5 μm.
f3(a) A HeLa cell expressing KR-dMito (red), EGFP-DFCP1 (green) and EBFP2-parkin (cyan) were illuminated with 559 nm at the white dotted circle region, leading to the generation of a long parkin-labelled mitochondria tubule (right, magnified view of the light-activated region) for autophagic turnover (white arrow). Scale bars, 10 μm.(b) After the generation of parkin-labelled mitochondrial tubules following treatments in a, discrete DFCP1 foci (green, middle panel, ER-associated omegasomes) formed along the parkin-labelled mitochondria (white arrows indicate DFCP1 spots that colocalized with parkin). Bottom panel: merged image of parkin and DFCP1. Scale bar, 10 μm.(c) Time-lapse imaging showing DCFP1 puncta formation on parkin-labelled mitochondria. A HeLa cell expressing KR-dMito, EGFP-DFCP1 (green) and EBFP2-parkin (pseudo-coloured red) were 559 nm illuminated, leading to the generation of parkin-labelled mitochondria tubules. Time-lapse imaging (1 frame per min) revealed that DFCP1 puncta (green) formed transiently at discrete sites on parkin-labelled mitochondrial tubules (red). White arrows mark two DFCP1 puncta (ER-associated omegasomes) formation/disassembly events directly on parkin-labelled tubules. Scale bar, 5 μm.(d) A COS-7 cell expressing EBFP2-parkin (cyan), AcGFP-sec61β (green) and TagRFP-DFCP1 (red) were treated with 10 μM CCCP for 4 h and imaged. Omegasomes (DFCP1) appeared where ER (sec61β) and impaired mitochondria (parkin) overlap. Scale bar, 10 μm.(e) Histogram of the lifetime of individual DFCP1 foci on parkin-labelled mitochondria in CCCP-treated HeLa cells expressing TagRFP-DFCP1, EGFP-LC3B and EBFP2-parkin.(f) Wortmannin treatments delayed the initial LC3 recruitment times onto parkin-labelled mitochondria in HeLa cells expressing KR-dMito, EGFP-LC3B and EBFP2-parkin. Each '+' marks the times measured in individual HeLa cells (the red '□' (square) denotes the average from five cells). P=0.0172 (Student's t-test).
f4(a) A COS-7 cell expressing EBFP2-Ub (red), AcGFP-sec61β (green) and mcherry-parkin (cyan) was treated with 10 μM CCCP for 1 h and imaged. Impaired mitochondria (parkin) displayed preferentially ubiquitinated foci (white arrows) at selected regions that overlap with the ER (sec61β).(b) HeLa cells expressing KR-dMito (red), EGFP-LC3 (green) and EBFP2-parkin (cyan) were illuminated with 559 nm at the white dotted square regions, generating parkin-labelled mitochondria (bottom right, magnified view of the light-activated regions). (c) Magnified view of the photo-inactivated region in b 80 min after illumination (post-stained with anti-ubiquitin antibody). LC3 and ubiquitin colocalized at discrete sites along parkin-labelled mitochondria (white arrows).(d) A MG-132 treated HeLa cell expressing KR-dMito, EBFP2-parkin (green) and EGFP-LC3B (red) was 559 nm illuminated, leading to the appearance of parkin-labelled mitochondria (white arrows one to three indicated structures, top panels). The parkin-labelled structures did not fragment nor became engulfed by LC3 structures (bottom panels) in the presence MG-132. Scale bars (all panels), 5 μm.
Figure 1A. Confocal images of mitochondrial morphology in wild-type (WT) and Drp1-/- 293T cells transfected with empty vector (left panel) and Myc-hFis1 (right panel), stained with MitoTracker (red) followed by immunostaining with anti-Myc antibody (green).B. Quantitative analyses of fragmented mitochondria size (mean area (μm2) per mitochondrion) after Myc-hFis1 overexpression in WT and Drp1-/- 293T cells using Image J software (Particle analysis) in three independent experiments. In each cell, only dispersed individual mitochondria were analyzed. The total number of mitochondria (mito) analyzed is indicated for each condition.C. Quantitative analysis of mean mitochondria number per cell in WT and Drp1-/- 293T cells overexpressing Myc-hFis1 using Image J software (Particle analysis) in three independent experiments.E. Percentages of cells with indicated mitochondrial morphologies in WT and Drp1-/- 293T cells transfected with empty vector (control), Myc-hFis1 and either Myc- or GFP-tagged mutants as indicated in three independent experiments.
Figure 2A. Confocal images of mitochondrial morphology in WT 293T cells treated with scrambled siRNA (control) and Dyn2 siRNA as indicated, followed by transfection with empty vector (left panel) and Myc-hFis1 (right three panels) as indicated. Cells were stained with MitoTracker (red) followed by immunostaining with anti-Myc antibody (green).B. Western blot of Dyn2, Myc-hFis1, Drp1 and GAPDH in WT 293T cells collected from the experiments in (A).C. Percentages of cells with indicated mitochondrial morphologies in WT 293T cells treated with scrambled siRNA and Dyn2 siRNA as indicated, followed by transfection with empty vector or Myc-hFis1 in three independent experiments.D. Confocal images of mitochondrial morphology in Drp1-/- 293T cells treated with scrambled siRNA and Dyn2 siRNA as indicated, followed by transfection with empty vector (left panel) and Myc-hFis1 (right three panels). Cells were stained with MitoTracker (red) followed by immunostaining with anti-Myc antibody (green). Representative examples of tubular, fragmented and tubular cluster phenotypes are indicated.E. Western blot of Dyn2, Myc-hFis1 and GAPDH in Drp1-/- 293T cells collected from the experiments in (D).F. Percentages of cells with indicated mitochondrial morphologies in Drp1-/- 293T cells treated with scrambled siRNA or Dyn2 siRNA, followed by transfection with empty vector or Myc-hFis1 as indicated in three independent experiments.
Figure 3A. Confocal images of mitochondrial morphology in Drp1-/- 293T cells transfected with scrambled siRNA (control) or with hFis1-siRNA and then stained with MitoTracker (red).B. Confocal images of mitochondrial morphology in Drp1-/- 293T cells transfected with either Mfn1-Myc, Mfn2-Myc or OPA1-Myc, stained with MitoTracker (red) followed by immunostaining with anti-Myc antibody (green).C. Percentages (mean ± s.e.m.) of cells with indicated mitochondrial morphologies in Drp1-/- 293T cells transfected with either scrambled siRNA (Ctr), hFis1 siRNA, Mfn1-Myc, Mfn2-Myc or OPA1-Myc in three independent experiments for each condition (n represents the number of cells analyzed).D. hFis1 interacts with Mfn1, Mfn2 and OPA1 as well as Drp1, but not with Dyn2 at endogenous levels following chemical crosslinking. Wild-type (WT) and Drp1-/- 293T cells were in vivo crosslinked with 1% formaldehyde (FA) and cell lysates were used for co-immunoprecipitation (IP) with Protein G beads bound to rabbit normal IgG (negative control) or rabbit anti-hFis1 antibody as indicated, followed by immunoblotting with indicated antibodies.hFis1 binds to Mfn1, Mfn2 and OPA1 at endogenous levels also in the absence of chemical crosslinking. Cell lysates prepared from WT 293T (E) cells without chemical crosslinking were used for co-immunoprecipitation (IP) with Protein G beads bound to rabbit normal IgG (negative control) or rabbit anti-hFis1 antibody as indicated, followed by Western blotting with indicated antibodies.F. hFis1 binds to Mfn1, Mfn2 and OPA1 at endogenous levels also in the absence of chemical crosslinking. Cell lysates prepared from HeLa (F) cells without chemical crosslinking were used for co-immunoprecipitation (IP) with Protein G beads bound to rabbit normal IgG (negative control) or rabbit anti-hFis1 antibody as indicated, followed by Western blotting with indicated antibodies.G, H. Interaction of hFis1 with Mfn1/2 and with OPA1 are independent events. WT 293T cells were treated with control, OPA1 (G) or Mfn1 plus Mfn2 (H) siRNA, followed by in vivo crosslinking with 1% FA. Cell lysates were used for co-IP with Protein G beads bound to rabbit normal IgG (negative control) or rabbit anti-hFis1 antibody as indicated, followed by immunoblotting with indicated antibodies.I. Interactions between Mfn1/2 and OPA1 occur independent of hFis1. WT 293T cells were treated with control or hFis1 siRNA, followed by in vivo crosslinking with 1% FA. Cell lysates were used for co-IP with Protein G beads bound to mouse normal IgG (negative control) or mouse anti-OPA1 antibody as indicated, followed by immunoblotting with indicated antibodies.J. Interaction between Mfn1 and Mfn2 is not affected by hFis1 overexpression. 293T cells were transfected with empty vector or Myc-hFis1, followed by in vivo crosslinking with 1% FA. Cell lysates were used for co-IP with Protein G beads bound to mouse normal IgG or mouse anti-Mfn1 antibody, followed by immunoblotting with indicated antibodies.
Figure 4B. Interaction of different hFis1 mutants with Mfns and OPA1. hFis1-/- 293T cells were transfected with the full-length and the truncated hFis1 mutants as indicated, followed by in vivo crosslinking with 1% FA. Cell lysates were used for co-IP with anti-Myc or anti-GFP agarose beads and the immunoprecipitates were analyzed by Western blotting with indicated antibodies.
Figure 5A, B. Representative confocal images of mitochondrial fusion in WT 293T polykaryons in cultures subjected to the PEG-based fusion assay in the presence or absence of exogenous hFis1. WT 293T cells stably expressing mitoGFP or mitoRFP were co-cultured, subsequently transfected with empty vector (control) or with Myc-hFis1 as indicated and then treated with PEG for cell fusion. Mitochondrial fusion is indicated by co-localization of mitoGFP and mitoRFP (i.e. yellow mitochondria). Left panel: empty vector transfected; right panel: Myc-hFis1transfected. Insets represent magnification of the boxed areas in upper panel (A). Quantitative analysis of the extent of mitochondrial fusion in individual hybrid cells was performed by the Pearson's correlation coefficient (PCC) in three independent experiments for each condition and data summarized in (B).C, D. Representative confocal images of mitochondrial fusion in WT 293T cells assessed by the mito-PAGFP-based fusion assay in the presence or absence of exogenous hFis1. WT 293T cells co-transfected with mito-PAGFP (0.5 µg), mito-DsRed (0.2 µg), and either empty vector (0.5 µg, the upper panel) or hFis1 (0.5 µg, the lower panel) were photoactivated in a small region of interest (ROI) (white circle, 3 µm diameter) in preactivation images of mitochondria seen by mito-DsRed (red). After photoactivation, sequential Z-stack images with photoactivated GFP (green) and mitochondrial marker (mito-DsRed) were collected at indicated time points using series of Z-sections from the top to the cell bottom with intervals between sections set to 0.5-0.75 μm (C). Mitochondrial fusion was quantified by analyzing changes in fluorescence intensity of photoactivated mito-PAGFP in ROIs at 40 sec, 15, 30, 45 min after photoactivation. The dilution rates (percentage) of the GFP fluorescence intensity at different time points were normalized by the fluorescence intensity at 40 sec after photoactivation (D).E, F. Representative confocal images of mitochondrial fusion in WT 293T polykaryons in cultures subjected to the PEG-based fusion assay in the presence or absence of endogenous hFis1. Both WT 293T cells stably expressing mitoGFP or mitoRFP were transfected with scrambled siRNA (control siRNA) or hFis1-siRNA as indicated and then co-cultured and fused using PEG treatment. Left panel: control siRNA transfected; right panel: hFis1-siRNA transfected (E). Quantitative analysis of the mitochondrial fusion in individual hybrid cells was performed by the Pearson's correlation coefficient in three independent experiments and data summarized in (F).G, H. Representative confocal images of mitochondrial fusion in WT 293T cells assessed by the mito-PAGFP-based fusion assay in the presence or absence of endogenous hFis1. Scrambled siRNA or hFis1 siRNA treated cells were co-transfected with mito-PAGFP and mito-DsRed and were subsequently photoactivated (G) as described in (C). Mitochondrial fusion was quantified (H) as described in (D).
Figure 6A, B. Representative confocal images of mitochondrial fusion in Drp1-/- 293T polykaryons in cultures subjected to the PEG-based fusion assay in the presence or absence of exogenous hFis1. Drp1-/- cells stably expressing mitoGFP or mitoRFP were co-cultured, subsequently transfected with empty vector (control) or Myc-hFis1 as indicated and then stimulated with PEG treatment for cell fusion, followed by immunostaining with anti-Myc antibody (green). Mitochondrial fusion was indicated by co-localization of mitoGFP and mitoRFP (i.e. yellow mitochondria). Left panel: empty vector transfected; right panel: Myc-hFis1 transfected. Insets represent magnification of the boxed areas in upper panel (A). Quantitative analyses for measuring the extent of mitochondrial fusion in individual hybrid cells were performed by the Pearson's correlation coefficient (PCC) in three independent experiments and summarized in (B).C, D. Representative confocal images of mitochondrial fusion in Drp1-/- 293T cells assessed by the mito-PAGFP-based fusion assay in the presence or absence of exogenous hFis1. Drp1-/- cells co-transfected with mito-PAGFP, mito-DsRed, and either empty vector (the upper panel) or hFis1 (the lower panel) were photoactivated in a small region of interest (ROI) (white circle, 3 µm diameter) as indicated in preactivation images of mitochondria seen by mito-DsRed (red). After photoactivation, Z-stack images with photoactivated GFP (green) and mitochondrial marker (mito-DsRed) were collected at times 40 sec, 15, 30, 45 min as indicated (C). Mitochondrial fusion was quantified by analysis of changes in the fluorescence intensity of photoactivated mito-PAGFP in ROIs at 40 sec, 15, 30, 45 min after photoactivation. The dilution rates (percentage) of the GFP fluorescence intensity at different time points were normalized by the fluorescence intensity at 40 sec after photoactivation (D).E, F. Representative confocal images of mitochondrial fusion in Drp1-/- 293T polykaryons in cultures subjected to the PEG-based fusion assay in the presence or absence of endogenous hFis1. Drp1-/- cells stably expressing mitoGFP or mitoRFP were transfected with scrambled siRNA (control siRNA) or with hFis1-siRNA as indicated and then co-cultured and fused by PEG treatment. Left panel: control siRNA transfected; right panel: hFis1-siRNA transfected (E). Quantitative analysis of extent of mitochondrial fusion in individual hybrid cells was performed by the Pearson's correlation coefficient (PCC) in three independent experiments and summarized in (F).G, H. Representative confocal images of mitochondrial fusion in Drp1-/- 293T cells monitored by the mito-PAGFP-based fusion assay in the presence or absence of endogenous hFis1. Scrambled siRNA or hFis1 siRNA treated cells were co-transfected with mito-PAGFP and mito-DsRed and were subsequently photoactivated (G) as described in (C). Mitochondrial fusion was quantified by analysis of changes in the fluorescence intensity of photoactivated mito-PAGFP (H) as described in (D).
Figure 7A, B. GTP hydrolysis activities of Mfn1, Mfn2, Mfn2K109A and OPA1 in the presence or absence of recombinant GST-hFis1 or GST (negative control) were determined by measuring the concentration of free phosphate (Pi) released from GTP. Myc-tagged Mfn1, Mfn2, Mfn2K109A and OPA1 were transiently expressed separately in 293T cells and immunopurified by anti-Myc agarose beads. GTPase activities of immunopurified Myc-tagged Mfn1, Mfn2, Mfn2K109A and OPA1 were determined after treatment with or without recombinant GST-hFis1 or GST protein (A). The input levels of immunopurified Mfn1-Myc, Mfn2-Myc and OPA1-Myc (left panel) as well as recombinant GST-hFis1 (~42 kDa) and GST (~26 kDa) (right panel) were assessed by immunoblotting with indicated antibodies (B).C, D. GTP hydrolysis activities of Drp1 in the presence or absence of recombinant GST-hFis1 or GST (negative control) were determined as described in (A). Untagged WT Drp1 and Drp1Q34A were transiently expressed in Drp1-/- 293T cells and immunopurified by protein G beads pre-incubated with Drp1 antibody. GTPase activities of immunopurified Drp1 and Drp1Q34A were determined after treatment with or without recombinant hFis1 or GST protein (C). The input levels of immunopurified Drp1 and Drp1Q34A were assessed by immunoblotting with anti-Drp1 antibody (D).E, F. GTP hydrolysis activities of Dyn2 in the presence or absence of recombinant GST-hFis1 or GST (negative control) were determined as described in (A). Endogenous Dyn2 in Drp1-/- 293T cells was immunopurified by protein G beads pre-incubated with anti-Dyn2 antibody. GTPase activity of immunopurified Dyn2 was determined after treatment with or without recombinant GST-hFis1 or GST protein (E). The input levels of immunopurified Dyn2 were assessed by immunoblotting with anti-Dyn2 antibody (F).G. Summary of the effects of pro-fusion GTPases (Mfns and OPA1) on hFis1-induced mitochondrial fragmentation in Drp1-/- cells. Percentages (mean ± s.e.m.) of cells with indicated mitochondrial morphologies in Drp1-/- 293T cells co-expressing Myc-hFis1 and either empty vector, Mfn1-Myc, Mfn2-Myc or OPA1-Myc in three independent experiments. n represents the number of cells analyzed. Corresponding confocal images shown in Fig EV4.
Figure 8A. Ablation of OPA1 using CRISPR-Cas9 gene editing in Drp1-/- 293T cells was confirmed by Western blotting analysis.B. Confocal images of mitochondrial morphology in Drp1-/- (left panel) and Drp1/OPA1DKO 293T (right panel) cells. (Aggr/frag: aggregation/fragmentation of mitochondria; Bulb/tubular: bulb-like/tubular mitochondria).C. Confocal images of mitochondrial morphology in Drp1/OPA1DKO 293T cells treated with the indicated siRNAs, combinations of siRNAs or with Myc-hFis1 plasmid (lower three panels) compared to mitochondrial morphology in Drp1-/- 293T cells overexpressing Myc-hFis1 or not (upper panel).D. Percentages (mean ± s.e.m.) of cells with indicated mitochondrial morphologies in Drp1-/- 293T cells transfected with empty vector or Myc-hFis1 plasmid, and in Drp1/OPA1DKO 293T cells treated with the indicated siRNA, combinations of siRNA or Myc-hFis1 plasmid. The data were collected from three independent experiments. Total cell numbers (n) used for statistical analysis are indicated for each condition.E. Knockdown of the indicated proteins by siRNA in Drp1/OPA1DKO 293T cells was confirmed by Western blotting analysis.
Figure 1Expression of Mpc proteins in mitochondria assessed by SDS-PAGE and immunoblot analysis of crude mitochondrial preparations. The individual untagged Mpc1 (Mpc1), histidine-tagged Mpc1 (Mpc1his), histidine-tagged Mpc3 (Mpc3his) or the Mpc1/Mpc3 hetero-complex (Mpc1/Mpc3his) were detected with antibodies raised against Mpc1 (left panel) or Mpc3 (right panel) and are shown with dashed arrows.Five micrograms of each affinity-purified Mpc protein were analysed by SDS-PAGE and the bands were visualised by Coomassie Blue stain. Peptide mass finger printing was used to identify the major protein bandsThe stability of the purified proteins was assessed via thermal denaturation by fluorescent CPM-adduct formation. The thermal denaturation profiles (left) were used to calculate the first derivative (right), which provides the apparent melting temperature, indicated with the same colour coding.The stability of the same samples, as in panel (D), was assessed by NanoDSF. The changes in the 330 nm/350 nm ratio with temperature (left) were used to calculate the first derivative (right).