Spatio-temporal characterization of S- and M/L-cone degeneration in the Rd1 mouse model of retinitis pigmentosa

Background The Pde6brd1 (Rd1) mouse is widely used as a murine model for human retinitis pigmentosa. Understanding the spatio-temporal patterns of cone degeneration is important for evaluating potential treatments. In the present study we performed a systematic characterization of the spatio-temporal patterns of S- and M/L-opsin + cone outer segment and cell body degeneration in Rd1 mice, described the distribution and proportion of dual cones in Rd1 retinas, and examined the kinetics of microglial activation during the period of cone degeneration. Results Outer segments of S- and M/L-cones degenerated far more rapidly than their somas. Loss of both S- and M/L-opsin + outer segments was fundamentally complete by P21 in the central retina, and 90% complete by P45 in the peripheral retina. In comparison, degeneration of S- and M/L-opsin + cell bodies proceeded at a slower rate. There was a marked hemispheric asymmetry in the rate of S-opsin + and M/L-opsin + cell body degeneration. M/L-opsin + cones were more resilient to degeneration in the superior retina, whilst S-opsin + cones were relatively preserved in the inferior retina. In addition, cone outer segment and cell body degeneration occurred far more rapidly in the central than the peripheral retina. At P14, the superior retina comprised a minority of genuine S-cones with a much greater complement of genuine M/L-opsin cones and dual cones, whilst the other three retinal quadrants had broadly similar numbers of genuine S-cones, genuine M/L-cones and dual cones. At P60, approximately 50% of surviving cones in the superior, nasal and temporal quadrants were dual cones. In contrast, the inferior peripheral retina at P60 contained almost exclusively genuine S-cones with a tiny minority of dual cones. Microglial number and activity were stimulated during rod breakdown, remained relatively high during cone outer segment degeneration and loss of cone somas in the central retina, and decreased thereafter in the period coincident with slow degeneration of cone cell bodies in the peripheral retina. Conclusion The results of the present study provide valuable insights into cone degeneration in the Rd1 mouse, substantiating and extending conclusions drawn from earlier studies.

Spatio-temporal characterization of S- and M/L-cone degeneration in the Rd1 mouse model of retinitis pigmentosa

Background The Pde6brd1 (Rd1) mouse is widely used as a murine model for human retinitis pigmentosa. Understanding the spatio-temporal patterns of cone degeneration is important for evaluating potential treatments. In the present study we performed a systematic characterization of the spatio-temporal patterns of S- and M/L-opsin + cone outer segment and cell body degeneration in Rd1 mice, described the distribution and proportion of dual cones in Rd1 retinas, and examined the kinetics of microglial activation during the period of cone degeneration. Results Outer segments of S- and M/L-cones degenerated far more rapidly than their somas. Loss of both S- and M/L-opsin + outer segments was fundamentally complete by P21 in the central retina, and 90% complete by P45 in the peripheral retina. In comparison, degeneration of S- and M/L-opsin + cell bodies proceeded at a slower rate. There was a marked hemispheric asymmetry in the rate of S-opsin + and M/L-opsin + cell body degeneration. M/L-opsin + cones were more resilient to degeneration in the superior retina, whilst S-opsin + cones were relatively preserved in the inferior retina. In addition, cone outer segment and cell body degeneration occurred far more rapidly in the central than the peripheral retina. At P14, the superior retina comprised a minority of genuine S-cones with a much greater complement of genuine M/L-opsin cones and dual cones, whilst the other three retinal quadrants had broadly similar numbers of genuine S-cones, genuine M/L-cones and dual cones. At P60, approximately 50% of surviving cones in the superior, nasal and temporal quadrants were dual cones. In contrast, the inferior peripheral retina at P60 contained almost exclusively genuine S-cones with a tiny minority of dual cones. Microglial number and activity were stimulated during rod breakdown, remained relatively high during cone outer segment degeneration and loss of cone somas in the central retina, and decreased thereafter in the period coincident with slow degeneration of cone cell bodies in the peripheral retina. Conclusion The results of the present study provide valuable insights into cone degeneration in the Rd1 mouse, substantiating and extending conclusions drawn from earlier studies.

Spatio-temporal characterization of S- and M/L-cone degeneration in the Rd1 mouse model of retinitis pigmentosa

Background The Pde6brd1 (Rd1) mouse is widely used as a murine model for human retinitis pigmentosa. Understanding the spatio-temporal patterns of cone degeneration is important for evaluating potential treatments. In the present study we performed a systematic characterization of the spatio-temporal patterns of S- and M/L-opsin + cone outer segment and cell body degeneration in Rd1 mice, described the distribution and proportion of dual cones in Rd1 retinas, and examined the kinetics of microglial activation during the period of cone degeneration. Results Outer segments of S- and M/L-cones degenerated far more rapidly than their somas. Loss of both S- and M/L-opsin + outer segments was fundamentally complete by P21 in the central retina, and 90% complete by P45 in the peripheral retina. In comparison, degeneration of S- and M/L-opsin + cell bodies proceeded at a slower rate. There was a marked hemispheric asymmetry in the rate of S-opsin + and M/L-opsin + cell body degeneration. M/L-opsin + cones were more resilient to degeneration in the superior retina, whilst S-opsin + cones were relatively preserved in the inferior retina. In addition, cone outer segment and cell body degeneration occurred far more rapidly in the central than the peripheral retina. At P14, the superior retina comprised a minority of genuine S-cones with a much greater complement of genuine M/L-opsin cones and dual cones, whilst the other three retinal quadrants had broadly similar numbers of genuine S-cones, genuine M/L-cones and dual cones. At P60, approximately 50% of surviving cones in the superior, nasal and temporal quadrants were dual cones. In contrast, the inferior peripheral retina at P60 contained almost exclusively genuine S-cones with a tiny minority of dual cones. Microglial number and activity were stimulated during rod breakdown, remained relatively high during cone outer segment degeneration and loss of cone somas in the central retina, and decreased thereafter in the period coincident with slow degeneration of cone cell bodies in the peripheral retina. Conclusion The results of the present study provide valuable insights into cone degeneration in the Rd1 mouse, substantiating and extending conclusions drawn from earlier studies.

Inf–sup conditions on convex cones and applications to limit load analysis

The paper is devoted to a family of specific inf–sup conditions generated by tensor-valued functions on convex cones. First, we discuss the validity of such conditions and estimate the value of the respective constant. Then, the results are used to derive estimates of the distance to dual cones, which are required in the analysis of limit loads of perfectly plastic structures. The equivalence between the static and kinematic approaches to limit analysis is proven and computable majorants of the limit load are derived. Particular interest is paid to the Drucker–Prager yield criterion. The last section exposes a collection of numerical examples including basic geotechnical stability problems. The majorants of the limit load are computed and expected failure mechanisms of structures are visualized using local mesh adaptivity.

APPLICATIONS OF AN INTERSECTION FORMULA TO DUAL CONES

We give a succinct proof of a duality theorem obtained by Révész [‘Some trigonometric extremal problems and duality’, J. Aust. Math. Soc. Ser. A 50 (1991), 384–390] which concerns extremal quantities related to trigonometric polynomials. The key tool of our new proof is an intersection formula on dual cones in real Banach spaces. We show another application of this intersection formula which is related to integral estimates of nonnegative positive-definite functions.

Discrete automorphism groups of convex cones of finite type

We investigate subgroups of $\text{SL}(n,\mathbb{Z})$ which preserve an open nondegenerate convex cone in $\mathbb{R}^{n}$ and admit in that cone as fundamental domain a polyhedral cone of which some faces are allowed to lie on the boundary. Examples are arithmetic groups acting on self-dual cones, Weyl groups of certain Kac–Moody algebras, and they do occur in algebraic geometry as the automorphism groups of projective manifolds acting on their ample cones.