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Mathematical Modeling: Problem Solving01:29

Mathematical Modeling: Problem Solving

Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
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The circadian—or biological—clock is an intrinsic, timekeeping, molecular mechanism that allows plants to coordinate physiological activities over 24-hour cycles called circadian rhythms. Photoperiodism is a collective term for the biological responses of plants to variations in the relative lengths of dark and light periods. The period of light-exposure is called the photoperiod.
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The biological clock is involved in many aspects of regulating complex physiology in all animals. It was in 1935 when German zoologists, Hans Kalmus and Erwin Bünning, discovered the existence of circadian rhythm in Drosophila melanogaster. However, the internal molecular mechanisms behind the circadian clock remained a mystery until 1984, when Jeffrey C. Hall, Michael Rosbash, and Michael W. Young discovered the expression of the Per gene oscillating over a 24-hour cycle. In subsequent years,...
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Pharmacokinetic Models: Overview01:20

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Pharmacokinetic models utilize mathematical analysis to achieve a detailed quantitative understanding of a drug's life cycle within the body. They are instrumental in simulating a drug's pharmacokinetic parameters, predicting drug concentrations over time, optimizing dosage regimens, linking concentrations with pharmacologic activity, and estimating potential toxicity.
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Circadian rhythms are cyclic changes that are crucial in plasma drug concentrations. Various standard circadian parameters, including core body temperature, heart rate, and other cardiovascular factors, directly impact disease states and the therapeutic response to drug therapy.
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Updated: May 12, 2026

A Computational Method to Quantify Fly Circadian Activity
13:05

A Computational Method to Quantify Fly Circadian Activity

Published on: October 28, 2017

Mathematical modeling in chronobiology.

G Bordyugov1, P O Westermark, A Korenčič

  • 1Institute for Theoretical Biology, Humboldt University, Invalidenstr. 43, 10115, Berlin, Germany. Grigory.Bordyugov@hu-berlin.de

Handbook of Experimental Pharmacology
|April 23, 2013
PubMed
Summary
This summary is machine-generated.

Mammalian circadian clocks, regulated by the suprachiasmatic nucleus (SCN), generate rhythms through cellular feedback loops. Mathematical models help understand these complex biological rhythms and optimize chronotherapy.

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Area of Science:

  • Chronobiology
  • Systems Biology
  • Computational Neuroscience

Background:

  • Circadian clocks are endogenous biological oscillators synchronized by environmental cues.
  • In mammals, the suprachiasmatic nucleus (SCN) acts as the master circadian pacemaker.
  • Cellular rhythms are driven by transcriptional feedback loops, and neuronal coupling synchronizes peripheral clocks.

Purpose of the Study:

  • To explore mathematical modeling approaches for understanding circadian rhythms.
  • To discuss modeling at different levels: single-cell rhythm generation, cell synchronization, and chronotherapy optimization.
  • To highlight the role of modeling in deciphering the dynamic complexity of circadian systems.

Main Methods:

  • Discussion of modeling principles for delayed negative feedback loops in single cells.
  • Exploration of models for cell synchronization through external stimuli and cell-cell coupling.
  • Overview of modeling strategies for optimizing chronotherapy.

Main Results:

  • Mathematical models provide insights into rhythm generation via feedback loops.
  • Models elucidate mechanisms of synchronization within the circadian system.
  • Modeling aids in understanding and optimizing therapeutic timing (chronotherapy).

Conclusions:

  • Mathematical modeling is a powerful tool for dissecting the complexity of circadian clocks.
  • Understanding coupled oscillator networks is crucial for circadian biology.
  • Modeling approaches can advance personalized medicine through optimized chronotherapy.