Discontinuity of a degenerating escape rate

We look at degenerating meromorphic families of rational maps on $\mathbb{P}^1$ -- holomorphically parameterized by a punctured disk -- and we provide examples where the bifurcation current fails to have a bounded potential in a neighborhood of the puncture. This is in contrast to the recent result of Favre-Gauthier that we always have continuity across the puncture for families of polynomials; and it provides a counterexample to a conjecture posed by Favre in 2016. We explain why our construction fails for polynomial families and for families of rational maps defined over finite extensions of the rationals $\mathbb{Q}$.Comment: 13 page

Humoral responses elicited in mice after immunization.

<p>(<b>A</b>) Kinetics of anti-PbCS IgG responses in mice immunized with N-PbCS yeasts. OD_{450 nm} are expressed in log₁₀ scale. Black arrows indicate immunization schedule. (<b>B</b>) Isotyping of humoral IgG responses at day 42 in mice immunized with N-PbCS. The bars correspond to median values per group. Asterisks (*) indicate significant median differences (p<0.05; Mann-Whitney nonparametric test). (<b>C</b>) Anti-N IgG titers in mice serums collected at day 42 after immunization with WT yeast or yeasts expressing N, PbCS or N-PbCS. Median values were compared by the Wicoxon Two Sample Test (p = 0.4558). (<b>D</b>) Antibody titers of N-PbCS mice are compared (see panels B and C). The lines associate titers from the same mouse. (<b>E</b>) Anti-<i>P. pastoris</i> IgG responses towards whole yeast. (<b>F</b>) Anti-<i>P. pastoris</i> IgG responses towards lysed yeast. The bars in (E) and (F) correspond to mean values per group. Hash sign (#) indicates anti-N antibody-negative mice from the N-PbCS group (see panel C).</p

Expression of N protein in GS115, KM71 and SMD1168 <i>P. pastoris</i> strains.

<p>Concentrations of Geneticin in selection plates for the specific clones, and clone numbers, are indicated. Yeast lysates were diluted 1/600 before loading on western blot.</p

Experimental challenge of immunized mice.

<p>(<b>A</b>) Mean and standard deviations log₁₀ values of parasitemia in mice immunized by N-PbCS, PbCS, N or WT yeast, and in non-immunized mice following infection with 6,000 GFP⁺<i>Pb</i> sporozoites. Blood parasitemia is expressed in log₁₀ scale as the percentage of infected red blood cells (iRBCs) out of total RBCs along the first 7 days follow up. Asterisks (*) indicate the significance level of the Mann-Whitney nonparametric test: two symbols correspond to p<0.005 and three to p<0.0005. (<b>B</b>) Parasitemia at day 5 post-challenge. Bars correspond to medians. Asterisks (*) indicate significant median differences (one symbol for p<0.05 and two for p<0.005; Mann-Whitney nonparametric test). (<b>C</b>) Inverse correlation between the day of death (x axis) and the percentage of iRBCs per total RBCs (y axis; arithmetic scale) per mouse. The cause of death is given in the upper part of the graph. (<b>D</b>) Survival curves of immunized mice after challenge with 6,000 GFP⁺<i>Pb</i> sporozoites.</p

Expression of N-PbCS in <i>P. pastoris</i>.

<p>(A) Schematic representation of N-PbCS fusion protein. MV-N (dark grey) is composed of a core domain in N-terminal and a unstructured tail domain in C-terminal <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086658#pone.0086658-Longhi1" target="_blank">[69]</a>. The GAAGAGA linker is in black. PbCS (light grey) corresponds the central repeat region flanked by major portions of the N-terminal and C-terminal domains of the protein <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086658#pone.0086658-Plassmeyer1" target="_blank">[39]</a>. Amino acids numbering are given according to N from the MV Schwarz vaccine strain and PbCS from the <i>Pb</i> ANKA strain. For sequence details, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086658#pone.0086658.s001" target="_blank">Figure S1</a>. (B) Quantitative western blot analysis of SMD1168 expressing N-PbCS or (C) N. In (B) and (C), yeast lysates were diluted as indicated, the MV-N protein was used as a standard with increasing concentrations and western blots were probed with an anti-N antibody.</p

ELISA quantification of N or PbCS proteins in ultracentrifugation (U) fractions and pellets of SMD1168 lysates expressing N alone at 871 ng/YU (A) or N-PbCS at 12 ng/YU (B).

<p>Yeast cultures, lysates and ultracentrifugations were performed in duplicate (3 U and 4 U for N expressing yeast, and 5 U and 6 U for N-PbCS yeast). Values correspond to optical densities at OD_{450 nm} (taking OD_{620 nm} as reference) multiplied by sample dilutions. SB: suspension buffer.</p

Immunofluorescence analysis of N or N-PbCS expression in yeasts (N staining in green, PbCS staining in red and nuclei in blue).

<p>Each image is the maximal intensity projection of three consecutive focal planes spaced 0.5 µm apart.</p

Schematic representation of the immunization protocol.

<p>Immunization and challenge schedule is given in days (d) and bleeding time points in weeks.</p