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Related Concept Videos

Energy Diagrams - II01:10

Energy Diagrams - II

Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the system.
The point in the energy diagram at which the system’s potential energy is the lowest is known as the local minima. The system tends to stay in this position indefinitely unless acted upon by a net force. The slope of the potential energy diagram at the local minima is zero, indicating that zero net force is acting on the system. The slope...
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
Stability01:28

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
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Potential-Energy Criterion for Equilibrium01:16

Potential-Energy Criterion for Equilibrium

Potential energy or potential function plays an essential role in determining the stability of a mechanical system. If a system is subjected to both gravitational and elastic forces, the potential function of the system can be expressed as the algebraic sum of gravitational and elastic potential energy. If the system is in equilibrium and is displaced by a small amount, then the work done on the system equals the negative of the change in the system's potential energy from the initial to the...
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...

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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

Quasi-potential landscape in complex multi-stable systems.

Joseph Xu Zhou1, M D S Aliyu, Erik Aurell

  • 1Institute for Systems Biology, Seattle, WA, USA. joseph.zhou@systemsbiology.org

Journal of the Royal Society, Interface
|August 31, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for understanding cell differentiation by analyzing multi-stable systems. It develops a quasi-potential function to model the relative stabilities of multiple cell types during organism development.

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Area of Science:

  • Developmental biology
  • Systems biology
  • Theoretical biology

Background:

  • Multicellular organism development involves multi-stable systems where cell types are attractors and differentiation paths are transitions.
  • Waddington's quasi-potential landscape metaphor is relevant but existing theories primarily address two-attractor systems.
  • Current methods for computing landscapes in systems biology, like gene regulatory networks, are often ad hoc and limited.

Purpose of the Study:

  • To provide an overview and critique of existing methods for computing quasi-potential landscapes in developmental systems.
  • To propose a novel decomposition of vector fields for calculating a global quasi-potential function.
  • To extend landscape analysis beyond pairwise attractor transitions to systems with multiple attractors (N > 2).

Main Methods:

  • Overview and critical analysis of existing landscape computation methods in systems biology.
  • Development of a new vector field decomposition technique.
  • Computation of a quasi-potential function applicable to multi-attractor systems.

Main Results:

  • Existing methods for landscape computation have limitations, particularly for systems with more than two attractors.
  • The proposed vector field decomposition allows for the computation of a global quasi-potential function.
  • This new function is equivalent to the Freidlin-Wentzell potential but is generalized for N > 2 attractors.

Conclusions:

  • The developed quasi-potential function offers a more comprehensive framework for understanding developmental dynamics in multi-stable systems.
  • This approach overcomes limitations of pairwise transition theories and ad hoc methods.
  • The significance lies in providing a unified mathematical framework for modeling complex cell differentiation pathways.