Related Experiment Video
Updated: Jul 2, 2026
08:06
A Microfluidics Approach for the Functional Investigation of Signaling Oscillations Governing Somitogenesis
Published on: March 19, 2021
Oscillations in multi-stable monotone systems with slowly varying feedback
Tomáš Gedeon1, Eduardo D Sontag
1Department of Mathematical Sciences Montana State University, Bozeman, MT gedeon@math.montana.edu.
Journal of Differential Equations
|August 16, 2008
Summary
This study enhances systems biology by analyzing gene regulatory networks using feedback loop decomposition. It proves oscillation existence in systems with state-dependent feedback strength.
Area of Science:
- Systems Biology
- Computational Biology
- Molecular Systems
Background:
- Gene regulatory networks (GRNs) are crucial in cellular functions.
- Analyzing GRN dynamics is complex, requiring advanced modeling techniques.
- Decomposition into feedback loops around monotone systems offers a powerful analytical framework.
Purpose of the Study:
- To extend existing input-output system frameworks for GRN analysis.
- To demonstrate the existence of oscillations in GRNs with specific feedback characteristics.
- To provide a method for deducing system dynamics from feedback loop properties.
Main Methods:
- Utilizing input-output system characteristics to analyze feedback loops.
- Applying mathematical frameworks to model gene regulatory network dynamics.
- Investigating the impact of state-dependent feedback strength on system oscillations.
Main Results:
- Successfully extended the input-output system framework for GRN analysis.
- Proved the existence of oscillations under conditions of slowly varying, state-dependent feedback.
- Established a link between feedback loop properties and emergent system dynamics.
Conclusions:
- The input-output system framework is effective for analyzing complex GRN dynamics.
- State-dependent feedback strength is a key factor in generating oscillations.
- This approach offers novel insights into the behavior of biological regulatory systems.
Related Concept Videos
01:04Oscillations 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...
01:28Stability
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.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
01:24BIBO stability of continuous and discrete -time systems
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
01:18Second Order systems II
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If ζ...
If ζ...
01:26Feedback control systems
Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
01:23Root Loci for Positive-Feedback Systems
The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
The construction rules for the root locus in positive feedback systems are similar to those in...