Random movements help color-detecting cells form the proper pattern

October 02, 2017

In fish and other animals, the color detecting cone cells in the retina are arranged in specific patterns, and this is believed to be important for allowing animals to properly sense their surroundings. Now, in research published in Physical Review E, an interdisciplinary group of physicists and biologists have used a mathematical model to determine how the cone cells in zebrafish--a common experimental fish model--are arranged in a specific pattern in all individuals. It turns out that small defects in the patterns lead the cells to arrange themselves into only one of two possible patterns that might otherwise emerge.

The eyes of these fish have four different types of cone cells, which sense blue, ultraviolet, and a combination of red and green. The "double cone" cells that sense red and green can be arranged in different orientations, so the cells can end up in a pattern of ultraviolet, blue, and red/green cells in different patterns. As the fish eyes develop, these cells originate from an area called the ciliary marginal zone, differentiate into the different cone cells, and arrange themselves into a random pattern. However, they eventually rearrange themselves into a certain pattern. One hypothesis is that the patterns emerge from the different adhesion force between the cells in various orientations. Essentially, they end up in a pattern that has the lowest energy level.

"While this is well known," explains Noriaki Ogawa, the first author of the paper, "there is an unexplained problem. It turns out there are two patterns with the same lowest energy level, one parallel to the growth of the retina and the other perpendicular to it, so that they are simply the same pattern but rotated 90 degrees. In real fish, however, only one of the two patterns is actually found."

The authors realized there must be some mechanism leading to that pattern. They found that though the two patterns are equivalent if looked at using a static model, they were not so in a dynamic setting. Using a mathematical model, dynamic pattern selection, they discovered that small flaws that appear in the pattern can disrupt it and drive it to rearrange itself in a way that always leads to the pattern found in real fish.

"This is an important finding," explains Ogawa, "because this could have implications for the development of other structures in many organisms." "There is much work to be done to fully explain the situation," he continues. "We do know that there are other mechanisms, namely concentration gradients of chemicals, known as morphogens, that direct the development process, and the polarities of cells. In order to fully understand how these patterns emerge in real organisms, we also need to understand the relationship between these mechanisms, and also to experimentally determine the actual adhesion strength between cells and other parameters."
-end-
The work was conducted by scientists from the RIKEN Interdisciplinary Theoretical Science Research Group (iTHES) and interdisciplinary Theoretical & Mathematical Sciences group (iTHEMS).

RIKEN

Related Mathematical Model Articles from Brightsurf:

A mathematical model facilitates inventory management in the food supply chain
A research study in the Diverfarming project integrates transport resources and inventory management in a model that seeks economic efficiency and to avoid shortages

Mathematical modelling to prevent fistulas
It is better to invest in measures that make it easier for women to visit a doctor during pregnancy than measures to repair birth injuries.

Predicting heat death in species more reliable with new mathematical model
An international research with the involvement of the Universitat Autònoma de Barcelona (UAB), published in Science, has developed a new dynamic mathematical model which represents a change in paradigm in predicting the probability of heat-related mortality in small species.

Using a Gaussian mathematical model to define eruptive stages of young volcanic rocks
Precise dating of young samples since the Quaternary has been a difficult problem in the study of volcanoes and surface environment.

Moffitt mathematical model predicts patient outcomes to adaptive therapy
In an article published in Nature Communications, Moffitt Cancer Center researchers provide a closer look at a mathematical model and data showing that individual patient alterations in the prostate-specific antigen (PSA) biomarker early in cancer treatment can predict outcomes to later treatment cycles of adaptive therapy.

New mathematical model can more effectively track epidemics
As COVID-19 spreads worldwide, leaders are relying on mathematical models to make public health and economic decisions.

Mathematical model could lead to better treatment for diabetes
MIT researchers have developed a mathematical model that can predict the behavior of glucose-responsive insulin in humans and in rodents.

New mathematical model reveals how major groups arise in evolution
Researchers at Uppsala University and the University of Leeds presents a new mathematical model of patterns of diversity in the fossil record, which offers a solution to Darwin's ''abominable mystery'' and strengthens our understanding of how modern groups originate.

Mathematical model reveals behavior of cellular enzymes
Mathematical modeling helps researchers to understand how enzymes in the body work to ensure normal functioning.

New mathematical model for amyloid formation
Scientists report on a mathematical model for the formation of amyloid fibrils.

Read More: Mathematical Model News and Mathematical Model Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.