Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Modeling with Differential Equations01:25

Modeling with Differential Equations

152
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
152
Scaling01:26

Scaling

631
In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
631
Population Growth00:57

Population Growth

29.4K
Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
29.4K
Cells Coordinate Growth and Proliferation02:36

Cells Coordinate Growth and Proliferation

5.3K
Cell size is a significant factor impacting cellular design, function, and fitness. There exists some internal coordination by which cells double their masses before division, thus, achieving homeostasis. Coordination between cell growth and proliferation depends on the checkpoints in between cell cycle phases. Loss of coordination or failure in the checkpoint mechanism can drive the cell to uncontrolled growth and loss of cellular function. Like dividing cells that coordinate cellular growth,...
5.3K
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

409
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
409
Reaction Mechanisms: Rate-limiting Step Approximation01:29

Reaction Mechanisms: Rate-limiting Step Approximation

50
The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
50

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Stationary periodic patterns in a model of growing population of motile bacteria.

Bio Systems·2025
Same author

Modelling ethnogenesis.

Bio Systems·2022
Same author

Scaling of Morphogenetic Patterns.

Methods in molecular biology (Clifton, N.J.)·2018
Same author

On the heterogeneity of human populations as reflected by mortality dynamics.

Aging·2016
Same author

Modelling Chemotactic Motion of Cells in Biological Tissues.

PloS one·2016
Same author

Time-evolution of age-dependent mortality patterns in mathematical model of heterogeneous human population.

Experimental gerontology·2014

Related Experiment Video

Updated: Mar 20, 2026

Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila
06:00

Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila

Published on: October 1, 2011

14.5K

Scaling of morphogenetic patterns in reaction-diffusion systems.

Manan'Iarivo Rasolonjanahary1, Bakhtier Vasiev1

  • 1Department of Mathematical Sciences, University of Liverpool, Liverpool, UK.

Journal of Theoretical Biology
|June 4, 2016
PubMed
Summary

This study analyzes how biological patterns scale with organism size. Researchers developed a new method to quantify system sensitivity, revealing mechanisms for robust morphogen gradient scaling in developing organisms.

Keywords:
Developmental biologyMathematical modellingPattern formationRobustness and scaling

More Related Videos

Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix
09:26

Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix

Published on: June 12, 2015

9.0K
Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

6.7K

Related Experiment Videos

Last Updated: Mar 20, 2026

Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila
06:00

Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila

Published on: October 1, 2011

14.5K
Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix
09:26

Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix

Published on: June 12, 2015

9.0K
Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

6.7K

Area of Science:

  • Developmental biology
  • Systems biology
  • Biophysics

Background:

  • Multicellular organism development relies on cellular responses to morphogen concentration gradients.
  • Morphogen gradients establish biological patterns and enable scaling with organism size.
  • Mechanisms for morphogen gradient formation are known, but scaling processes remain poorly understood.

Purpose of the Study:

  • To formally analyze the scaling properties of chemical patterns in continuous systems.
  • To investigate how morphogen gradient scaling is affected by system size and boundary conditions.
  • To identify mechanisms that improve or enable robust scaling of morphogenetic patterns.

Main Methods:

  • Formal mathematical analysis of scaling in continuous chemical systems.
  • Introduction of a "sensitivity" quantity to assess system size dependence.
  • Analysis of diffusion-decay models, modulated morphogen transport, and activator-inhibitor systems.

Main Results:

  • Scaling properties of diffusion-decay morphogen gradients are sensitive to boundary conditions.
  • Passive modulation and active transport can enhance morphogen gradient scaling.
  • Analysis of opposing gradients and activator-inhibitor systems reveals further scaling insights.

Conclusions:

  • Identified key factors influencing morphogen gradient scaling in biological systems.
  • Proposed potential mechanisms enabling robust scaling of developmental patterns.
  • Highlighted the importance of system sensitivity analysis for understanding biological pattern formation.