Mathematical and computational modeling in biology at multiple scales
Jack A Tuszynski1, Philip Winter, Diana White
1Department of Physics and Department of Oncology, University of Alberta, Edmonton, Canada. jackt@ualberta.ca.
Theoretical Biology & Medical Modelling
|December 28, 2014
Summary
This review explores mathematical and computational modeling in biology, from population dynamics to quantum mechanics. It highlights applications in drug discovery, epidemiology, and understanding complex biological systems.
Area of Science:
- Integrative biology
- Computational science
- Biophysics
Background:
- Mathematical and computational modeling are crucial for understanding biological systems across diverse scales.
- Advancements in computational power enable complex simulations and data analysis in biology.
- Interdisciplinary approaches are increasingly important in biological research.
Purpose of the Study:
- To provide a comprehensive overview of mathematical and computational modeling techniques in biology.
- To discuss the application of these methods in various biological subfields.
- To highlight emerging trends and tools in computational biology.
Main Methods:
- Review of established and novel mathematical and computational modeling approaches.
- Discussion of inference tools such as maximum entropy.
- Survey of methods including molecular dynamics and quantum mechanical calculations.
Main Results:
- Mathematical and computational modeling are applicable from atomic to population scales.
- Key areas of application include drug discovery, epidemiology, cell physiology, and cancer research.
- Techniques like molecular dynamics and quantum mechanics offer powerful insights into biomolecular behavior.
Conclusions:
- Computational modeling is indispensable for modern biological research.
- The integration of diverse computational methods enhances our understanding of life.
- Future research will likely see further advancements in predictive biological modeling.
More Related Videos
12:32Combining Fluidic Devices with Microscopy and Flow Cytometry to Study Microbial Transport in Porous Media Across Spatial Scales
Published on: November 25, 2020
7.2K
07:31Author Spotlight: Advancing Cell Membrane Biophysics - Exploring Interactions and Challenges Through Experimental and Computational Approaches
Published on: September 1, 2023
3.5K
Related Concept Videos
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
415
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
415
01:25Modeling with Differential Equations
289
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...
289
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
342
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
342
01:27Growth Models with Integration: Problem Solving
157
In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
157
01:29Mathematical Modeling: Problem Solving
544
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,...
544
01:21Mechanistic Models: Overview of Compartment Models
550
Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...
550