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Related Concept Videos

Definition of Laplace Transform01:22

Definition of Laplace Transform

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The Laplace transform is an indispensable mathematical technique for simplifying the resolution of differential equations by converting them into more manageable algebraic expressions. The Laplace transform of a function is denoted by L[x(t)], where x(t) is the time-domain function. The laplace transform is mathematically expressed as
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Quantitative Aspects of Drug-Receptor Interaction01:30

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The receptor occupancy theory connects a drug's response to the number of occupied receptors. With higher drug concentrations, more receptors are occupied, leading to increased responses. The formation of drug-receptor complexes involves association and dissociation rates, which reach equilibrium when the forward and backward reactions are equal. The equilibrium association constant (Ka) and its inverse, the equilibrium dissociation constant (Kd), indicate drug affinity. Higher Ka and lower...
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Linear Approximation in Frequency Domain01:26

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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Electrical Systems01:21

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In electrical engineering, the analysis of networks composed of passive linear components — resistors (R), capacitors (C), and inductors (L) — is fundamental. These components are organized into circuits where the relationship between input and output can be analyzed using transfer functions. The transfer function of an RLC circuit, which relates the voltage across a capacitor to the input voltage, can be derived using Kirchhoff's laws.
To derive the transfer function, consider an RLC...
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The Integrated Rate Law: The Dependence of Concentration on Time02:39

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While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
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Properties of Laplace Transform-I01:15

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The Laplace transform is a powerful mathematical tool used to convert functions from the time domain into the frequency domain, greatly simplifying the analysis and solution of linear time-invariant systems. This transformation is facilitated by several universal properties: Linearity, Time-Scaling, Time-Shifting, and Frequency Shifting.
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Updated: Feb 24, 2026

Titration ELISA as a Method to Determine the Dissociation Constant of Receptor Ligand Interaction
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Receptor binding kinetics equations: Derivation using the Laplace transform method.

Sam R J Hoare1

  • 1Pharmechanics LLC, 14 Sunnyside Drive South, Owego, New York 13827, USA.

Journal of Pharmacological and Toxicological Methods
|August 19, 2017
PubMed
Summary
This summary is machine-generated.

Pharmacologists can now easily derive kinetic equations for drug-receptor interactions using the Laplace transform, simplifying the measurement of unlabeled ligand binding kinetics. This method avoids complex calculus, making kinetic analysis more accessible for drug optimization.

Keywords:
Data analysisDrug discoveryDrug kineticsLigand bindingMethodsReceptor binding kineticsReceptor theoryResidence time

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Area of Science:

  • Pharmacology
  • Biophysics
  • Mathematical Modeling

Background:

  • Accurate measurement of ligand-receptor binding kinetics is crucial for drug development and understanding drug action.
  • Deriving kinetic equations traditionally involves complex calculus, posing a significant barrier for many researchers.
  • The Laplace transform offers a method to simplify these derivations, transforming differential equations into algebraic ones.

Purpose of the Study:

  • To demonstrate the application of the Laplace transform for deriving kinetic equations in receptor-ligand binding.
  • To provide a simplified method for pharmacologists to obtain kinetic parameters without advanced calculus.
  • To derive new equations for measuring unlabeled ligand binding kinetics, including those with pre-incubation steps.

Main Methods:

  • The Laplace transform was applied to models of receptor-ligand interaction.
  • Equations for association and dissociation of labeled ligand binding were derived.
  • The kinetics of competitive binding for unlabeled ligands were derived, along with new equations incorporating pre-incubation.

Main Results:

  • The Laplace transform successfully simplified the derivation of kinetic equations.
  • Two new equations for unlabeled ligand kinetics were derived and verified against numerical solutions.
  • The derived equations were formatted for curve-fitting software like GraphPad Prism.

Conclusions:

  • The Laplace transform provides a powerful and accessible tool for pharmacologists to derive kinetic equations.
  • This method expands the available toolkit for measuring unlabeled ligand binding kinetics.
  • The approach facilitates a deeper understanding of time-dependent pharmacological activities.