Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Molecular Models

Molecular Models

Physical models representing molecular architectures of chemical compounds play essential roles in understanding chemistry. The use of molecular models makes it easier to visualize the structures and shapes of atoms and molecules.

Constraints and Statical Determinacy

Constraints and Statical Determinacy

In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...

Random Variables

Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...

Multicompartment Models: Overview

Multicompartment Models: Overview

Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Emergent frequency-dependent selection predicts mutation outcomes in complex ecological communities.

bioRxiv : the preprint server for biology·2026

Same author

Ecology of metagenomes: incorporating genotype-to-phenotype maps into ecological models.

bioRxiv : the preprint server for biology·2026

Same author

From genes to collective modes: biological constraints shape metabolic evolution.

bioRxiv : the preprint server for biology·2026

Same author

Inferring genotype-phenotype maps using attention models.

PNAS nexus·2026

Same author

Parameter-free representations outperform single-cell foundation models on downstream benchmarks.

bioRxiv : the preprint server for biology·2026

Same author

Bidirectional fibrogenic cross-talk revealed in a human iPSC-derived epithelial-mesenchymal co-culture model of pulmonary fibrosis.

bioRxiv : the preprint server for biology·2026

Same journal

In This Issue.

Proceedings of the National Academy of Sciences of the United States of America·2026

Same journal

Correction for Otsuki et al., Extracellular sulfatases support cartilage homeostasis by regulating BMP and FGF signaling pathways.

Proceedings of the National Academy of Sciences of the United States of America·2026

Same journal

Hive mind: Microbial communities and the making of memory.

Proceedings of the National Academy of Sciences of the United States of America·2026

Same journal

Targets for disease modification in schizophrenia: New findings add to evidence for the involvement of the immune complement system.

Proceedings of the National Academy of Sciences of the United States of America·2026

Same journal

Correction for Wang et al., The role of reduced aerosol masking from air pollutant emission reductions in recent global warming acceleration (2013-2023).

Proceedings of the National Academy of Sciences of the United States of America·2026

Same journal

Correction for Mishra, Ecology is not yet ready for AI-and why that matters.

Proceedings of the National Academy of Sciences of the United States of America·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 17, 2026

Protein WISDOM: A Workbench for In silico De novo Design of BioMolecules

Protein WISDOM: A Workbench for In silico De novo Design of BioMolecules

Published on: July 25, 2013

Random-with-constraints: Constructing minimal models for high-dimensional biology.

Ilya Nemenman^1,2,3, Pankaj Mehta^4,5

¹Department of Physics, Emory University, Atlanta, GA 30322.

Proceedings of the National Academy of Sciences of the United States of America

|June 15, 2026

Summary

This summary is machine-generated.

This study introduces a "random-with-constraints" modeling approach for complex biological systems. This strategy effectively captures experimental data across diverse fields like neuroscience and ecology.

Keywords:

constrained random networks dynamics high-dimensional biology modeling in biology

More Related Videos

Generating the Transcriptional Regulation View of Transcriptomic Features for Prediction Task and Dark Biomarker Detection on Small Datasets

Generating the Transcriptional Regulation View of Transcriptomic Features for Prediction Task and Dark Biomarker Detection on Small Datasets

Published on: March 1, 2024

Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues

Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues

Published on: July 14, 2015

Related Experiment Videos

Last Updated: Jun 17, 2026

Protein WISDOM: A Workbench for In silico De novo Design of BioMolecules

Protein WISDOM: A Workbench for In silico De novo Design of BioMolecules

Published on: July 25, 2013

Generating the Transcriptional Regulation View of Transcriptomic Features for Prediction Task and Dark Biomarker Detection on Small Datasets

Generating the Transcriptional Regulation View of Transcriptomic Features for Prediction Task and Dark Biomarker Detection on Small Datasets

Published on: March 1, 2024

Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues

Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues

Published on: July 14, 2015

Area of Science:

Complex Systems Biology
Computational Biology
Theoretical Ecology

Background:

Traditional modeling in biology uses simple, finely tuned systems.
Studying complex biological systems with numerous interacting components remains challenging.
A new paradigm is needed to bridge the gap between simple models and complex biological reality.

Purpose of the Study:

To review the application of the "random-with-constraints" modeling approach in biology.
To demonstrate its utility in connecting theoretical models with experimental observations.
To highlight its potential for analyzing high-dimensional biological data.

Main Methods:

Reviewing recent research employing "random-with-constraints" models.
Analyzing biological systems from neuroscience, ecology, and evolution.
Focusing on models that incorporate biologically motivated constraints.

Main Results:

The "random-with-constraints" paradigm shows promise in diverse biological fields.
This approach effectively captures experimentally observed dynamical and statistical features.
It offers a powerful minimal modeling philosophy for biology.

Conclusions:

The "random-with-constraints" approach is a viable strategy for taming biological complexity.
It provides a framework for understanding typical behaviors in complex biological systems.
This paradigm facilitates the analysis of high-dimensional biological data and experimental validation.