scholarly journals Mathematical Models of Retinitis Pigmentosa: The Trophic Factor Hypothesis

2021 ◽  
Author(s):  
Paul A. Roberts
Keyword(s):  
Retinitis Pigmentosa ◽  
Mathematical Models ◽  
Retinal Degeneration ◽  
Reaction Diffusion ◽  
Temporal Patterns ◽  
Photoreceptor Cells ◽  
Trophic Factor ◽  
Cone Dystrophy ◽  
Treatment Rate ◽  
Spatio Temporal

AbstractRetinitis pigmentosa (RP) is the term used to denote a group of inherited retinal-degenerative conditions that cause progressive sight loss. Individuals with this condition lose their light-sensitive photoreceptor cells, known as rods and cones, over a period of years to decades; degeneration starting in the retinal periphery, and spreading peripherally and centrally over time. RP is a rod-cone dystrophy, meaning that rod health and function are affected earlier and more severely than that of cones. Rods degenerate due to an underlying mutation, whereas the reasons for cone degeneration are unknown. A number of mechanisms have been proposed to explain secondary cone loss and the spatio-temporal patterns of retinal degeneration in RP. One of the most promising is the trophic factor hypothesis, which suggests that rods produce a factor necessary for cone survival, such that, when rods degenerate, cone degeneration follows. In this paper we formulate and analyse mathematical models of RP under the trophic factor hypothesis. These models are constructed as systems of reaction-diffusion partial differential equations in one spatial dimension, and are solved and analysed using a combination of numerical and analytical methods. We predict the conditions under which cones will degenerate following the loss of a patch of rods from the retina, the critical trophic factor treatment rate required to prevent cone degeneration following rod loss and the spatio-temporal patterns of cone loss that would result if the trophic factor mechanism alone were responsible for retinal degeneration.

scholarly journals Inverse Problem Reveals Conditions for Characteristic Retinal Degeneration Patterns in Retinitis Pigmentosa under the Trophic Factor Hypothesis

2021 ◽  
Author(s):  
Paul A Roberts
Keyword(s):  
Inverse Problem ◽  
Retinitis Pigmentosa ◽  
Retinal Degeneration ◽  
Retinal Dystrophy ◽  
Visual Field Loss ◽  
Temporal Patterns ◽  
Photoreceptor Cells ◽  
Spatial Dimension ◽  
Trophic Factor ◽  
Spatio Temporal

Retinitis pigmentosa (RP) is the most common inherited retinal dystrophy with a prevalence of about 1 in 4000, affecting approximately 1.5 million people worldwide. Patients with RP experience progressive visual field loss as the retina degenerates, destroying light-sensitive photoreceptor cells (rods and cones), with rods affected earlier and more severely than cones. Spatio-temporal patterns of retinal degeneration in human RP have been well characterised; however, the mechanism(s) giving rise to these patterns have not been conclusively determined. One such mechanism, which has received a wealth of experimental support, is described by the trophic factor hypothesis. This hypothesis suggests that rods produce a trophic factor necessary for cone survival; the loss of rods depletes this factor, leading to cone degeneration. In this paper we formulate a partial differential equation mathematical model of RP in one spatial dimension, spanning the region between the retinal centre (fovea) and the retinal edge (ora serrata). Using this model we derive and solve an inverse problem, revealing for the first time experimentally testable conditions under which the trophic factor mechanism will qualitatively recapitulate the spatio-temporal patterns or retinal regeneration observed in human RP.

Spatio-temporal patterns in a reaction–diffusion system with wave instability

2000 ◽  
Vol 55 (2) ◽  
pp. 223-231 ◽  
Author(s):  
Milos Dolnik ◽  
Anatol M Zhabotinsky ◽  
Arkady B Rovinsky ◽  
Irving R Epstein
Keyword(s):  
Reaction Diffusion ◽  
Temporal Patterns ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Wave Instability ◽  
Spatio Temporal

THECO-OXIDATION REACTION ONIr(111) SURFACES: BISTABILITY, NOISE AND SPATIO-TEMPORAL PATTERNS IN EXPERIMENT AND MODELING

2009 ◽  
Vol 19 (08) ◽  
pp. 2637-2675 ◽  
Author(s):  
STEFAN WEHNER
Keyword(s):  
Steady State ◽  
Reaction Diffusion ◽  
Temporal Patterns ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Gas Composition ◽  
Noise Strength ◽  
Photoelectron Emission ◽  
Spatio Temporal ◽  
Rate Limiting

This review summarizes recent studies on the catalytic CO oxidation on Iridium(111) surfaces. This was investigated experimentally under ultrahigh vacuum (UHV) conditions using mass spectroscopy to detect gaseous products and photoelectron emission microscopy (PEEM) to visualize surface species. The underlying reaction–diffusion system based on the Langmuir–Hinshelwood mechanism was analyzed numerically.The existence of bistability for this surface reaction was shown in experiment. For the first time the effect of noise on a bistable surface reaction was examined. In a surface science experiment the effects on product formation and the development of spatio-temporal patterns on the surface were explored.Steady state CO2rates were measured under constant flux of the CO + O mixture as a function of sample temperature (360 K < T < 700 K) and gas composition, characterized by the molar fraction of CO in the feed gas (0 ≤ Y ≤ 1). The reaction reveals bistability in a limited region of Y and T. A rate hysteresis with two steady state rates was observed for cycling Y up and down, one of high reactivity (upper rate, oxygen covered surface) and one of low reactivity (lower rate, CO covered surface). The position of the hysteresis loop shifts to higher Y values and decreases in width with increasing temperature. For small CO content in the feed gas the CO2rate is proportional to Y3/2. At 500 K extremely slow Y cycling measurements (about 100 hours per direction) were done and showed that bistability still exists and no slowly changing transients were observed. The requirements for the speed with which experiments can be executed without producing experimental artifacts were explored. Since over-sampling alters the measured hysteresis loop, a maximum rate for changing the gas composition in Y cycling experiments was determined.The influence of noise on the reaction rates and the formation of spatio-temporal patterns on the surface was explored by superposing noise of Gaussian white type on Y and on T. Noisy Y (deviation Δ Y) represents multiplicative and additive noise, noisy T (deviation Δ T) multiplicative noise only. Noisy T enters the reaction via the rate-determining step, the observed CO2rates become noisy for low temperatures (around 420 K) when the surface is dominantly oxygen covered ( CO + O reaction step is rate-limiting) and for higher temperatures (around 500 K) when the surface is dominantly CO covered ( CO desorption step is rate-limiting).The effect of noisy Y was examined for a sample temperature of 500 K and is dependent on the selected average gas composition. In the regions with one steady state CO2rate (outside the hysteresis) the recorded rates were noisy. The probability distribution of the rates is Gaussian shaped for the upper rate (below hysteresis) and asymmetric for the lower rate (above hysteresis). For large noise strength bursts, short-time excursions to and above the upper rate, were observed.Inside the hysteresis small noise made the steady state rates noisy, but above a Y-dependent Δ Y transients from the locally stable to the globally stable rate branch were observed. These transients take up to several ten thousand seconds and become faster with increasing noise. For larger Y noise strength bursts and switching between both steady state rates were detected.Photoelectron emission microscopy (PEEM) was done to visualize spatio-temporal adsorbate patterns on the surface as expected from the observations in the CO2rate measurements. CO - and oxygen-covered regions on the Ir (111) surface are visible in PEEM images as gray and black areas as a consequence of their work function contrast. Islands of the adsorbate, corresponding to the globally stable branch, are formed in a background of the other one. The long transient times are the result of the extremely slow domain wall motion of these islands (around 0.05 μm s-1). In the hysteresis region CO oxidation on Iridium(111) surfaces is dominated by domain formation and wall motion for small to moderate noise strength. The island density increases with noise, but the wall velocity is independent of applied Δ Y. For larger noise amplitudes, fast switching between oxygen- and CO -dominated surfaces is observed as well as nucleation and growth of the minority phase in the majority phase.In the numerically analyzed reaction–diffusion system all parameters were taken from the experiment. Modeling the reaction–diffusion system shows qualitative up to quantitative agreement with the experimental observations. The length scale for the modeling grid is determined from wall velocity seen in the experiments.

Instabilities in a Simple Enzyme Reaction Caused by pH-Dependence

1995 ◽  
Vol 50 (12) ◽  
pp. 1147-1150 ◽  
Author(s):  
Gerold Baier ◽  
Peter Strasser ◽  
Ursula Kummer
Keyword(s):  
Reaction Rate ◽  
Ph Dependence ◽  
Enzymatic Reaction ◽  
Enzyme Reaction ◽  
Reaction Diffusion ◽  
Temporal Patterns ◽  
Homogeneous Reactor ◽  
Spatio Temporal

Abstract We investigate the model of an enzymatic reaction with Michaelis-Menten kinetics and bell-shaped pH-dependence of the reaction rate. In the case of proton consumption the reaction can generate oscillations in a homogeneous reactor and turbulent spatio-temporal patterns in a reaction-diffusion environment. I n s t a b il it i e s in a S im p le E n z y m e R e a c tio n C a u s e d b y p H -D e p e n d e n c e *

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

2019 ◽  
Author(s):  
Daniel S. Narayan ◽  
Jack Ao ◽  
John P. M. Wood ◽  
Robert J. Casson ◽  
Glyn Chidlow
Keyword(s):  
Retinitis Pigmentosa ◽  
Cell Body ◽  
Outer Segment ◽  
Temporal Patterns ◽  
Peripheral Retina ◽  
Outer Segments ◽  
Dual Cones ◽  
Spatio Temporal ◽  
Rd1 Mouse

Abstract 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.

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

2019 ◽  
Author(s):  
Daniel S. Narayan ◽  
Jack Ao ◽  
John P. M. Wood ◽  
Robert J. Casson ◽  
Glyn Chidlow
Keyword(s):  
Retinitis Pigmentosa ◽  
Cell Body ◽  
Outer Segment ◽  
Temporal Patterns ◽  
Peripheral Retina ◽  
Outer Segments ◽  
Dual Cones ◽  
Spatio Temporal ◽  
Rd1 Mouse

Abstract 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.

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

2019 ◽  
Author(s):  
Daniel S. Narayan ◽  
Jack Ao ◽  
John P. M. Wood ◽  
Robert J. Casson ◽  
Glyn Chidlow
Keyword(s):  
Retinitis Pigmentosa ◽  
Cell Body ◽  
Outer Segment ◽  
Temporal Patterns ◽  
Peripheral Retina ◽  
Outer Segments ◽  
Dual Cones ◽  
Spatio Temporal ◽  
Rd1 Mouse

Abstract 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.

Sign in / Sign up

Export Citation Format

Share Document