Modularity as a dynamic and functional phenomenon
Herbert Sauro, Steve Andrews, Joe Hellerstein: University of Washington, Seattle,
Song Feng, Steve Wiley: PNNL, WA
Terminology
There is some terminology worth mentioning:
Mechanism (or subsystem)
Two or more biochemical processes forming a network where species evolve in time (John J Tyson, Katherine C Chen, Bela Novak, Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell, Current Opinion in Cell Biology, 2006)
Motif
A topological pattern that is found enriched in interaction graphs (Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U: Network motifs: simple building blocks of complex networks, PNAS, 2002)
Module
To be discussed, but there are many interpretations (18+ on Wilipedia’s page)
Terminology
Mofits
Subsystems
Modules
Tyson, Chen, Novak
Mangan & Alon
?
Origins
The modern use of the word module* started in the 1950s with the entry of the word into the dictionary to mean “interchangeable part”.
New post-war electronics companies were building modular systems where faulty “modules” could be pulled out and easily replaced. NASA also picked up the term by to refering to the "lunar module" as a separate self-contained system in 1961.
PDP-8 transistor/diode logic module (triple flip flop, circa 1965/66)
The use of the word module grew in in biology in the late 1990s.
https://www.computerhistory.org/revolution/minicomputers/11/331/1905
*Originates from the Latin modulus, meaning "a small measure".
Trends: Reported in Books
books.google.com/ngrams/
In Biology
In biology the word module came to promince with the publication:
“From molecular to modular cell biology”, Leland H. Hartwell, John J. Hopfield, Stanislas Leibler and Andrew W. Murray, 1999.
Hartwell et al emphasized the functional aspects of a module:
“A functional module is, by definition, a discrete entity whose function is separable from those of other modules.
Since then the use of the word module has dramatically increased. I did a PubMed search for the word ‘module’ and it picked up:
80,402 matches
On the other hand:
In the Encyclopedia of Systems Biology, the chapter on modules defines it thus:
“A biological module is a subnetwork entity composed of nodes that are more closely related among them than to the rest of the components in a network;”
Application of Graph Theory for Identifying Connectivity Patterns in Human Brain Networks: A Systematic Review - Scientific Figure on ResearchGate. Available from: https://www.researchgate.net/figure/of-global-graph-measures-A-Segregation-measures-include-clustering-coefficient-which_fig4_333968671 [accessed 12 Apr 2026]
The notion of function has disappeared
Modularity and community structure in networks
M. E. J. Newman, PNAS, 2006
�The structure and function of complex networks, 2003
https://arxiv.org/abs/cond-mat/0303516
SIAM Review
Other uses of the word module in biology
Some common occurrences of the word module include:
What might be the general consensus?
The word module seems to be attached to anything that is a collection of closely connected parts, be it genes, biochemical neworks, graphs, protein subunits etc. Is that a sufficient definition? Is this the question for ths week?
Copilot generated.
Waddington’s Famous Epigentic Landscape
Genes influence the modular landscape by which organisms develop.
The Strategy of the Genes: A Discussion of Some Aspects of Theoretical Biology,
Waddington, C. H. [ With an Appendix by H. Kacser, Pd. D. ], 1957
Returning to the 1950s. What characteristics would an engineer of the 1950s list as particular to a module?
Returning to the 1950/60s. What characteristics would an engineer of the 1950s list as particular to a module?
Summary Characteristics of a Module
We can summarise the characteristics of a hardware module in the most abstract sense as:
Well-defined interface: ports are explicitly declared and interactions are constrained to those ports
Well-defined function: the input-output behaviour is specified and predictable
Composable: can be connected to other modules without side effects
Biology is going to be a bit more messy that this but these are probably the basic characteristics. There is no encapsulation because we’re in a liquid phase but it makes it easier to change the interface.
The interface defines the boundary.
The function characterises what crosses that boundary.
Composability is the guarantee that when modules are assembled, the functional characteristics are guaranteed.
Summary Characteristics of a Module
Function
Interface
Composability
Modularity can also be hierarchical
Human engineers use this strategy all the time
Taking an Engineering Approach to Biology
This idea was taken up by Domitilla Del Vecchio at MIT. She drew a parallel between what electrical engineers do and what biology might do.
Available Mathematical Approaches
Classical Differential Equation Analysis
Focuses on stability, bifurcation analysis and chaotic dynamics, role of positive and negative feedback in stability.
Both Feinberg and Clarke focus on stability analysis based on topology alone
Mixture of stability, sensitivity (robustness) and the role of feedback , primarily used for design in engineering and reverse engineering in biology.
Copilot generated.
Introduction to Biochemical Control Theory
Control theory is a good choice for understanding biochemical networks and modularity. It directly addresses:
Introduction to Biochemical Control Theory
Later in the week we will be giving an instructory tutorial on biochemical control theory as well as new work we have done on how to define a modularity coefficient given a particular ‘module’ and its context.
You’ll also hear more on this topic from Joe Hellerstein, Steve Wiley and Steve Andrews and ways in which modularity can be defined.
Copilot generated.
Acknowledgements
BIC: Evolving Signal Processing Circuits from Biological Reaction Networks
Award Number: 0432190, 2004
Extension of Metabolic Control Analysis and Biochemical Systems Theory to Stochastic Systems
Award Number: 0827592, 2009
Reinhart Laubenbacher’s monthly modularity meetings��Extensive discussions with Steve Andrews, Song Feng, Joe Hellerstein, Steve Wiley
Resources
A Frequency Domain Approach to Sensitivity Analysis of Biochemical Networks�Brian P. Ingalls�The Journal of Physical Chemistry B 2004 108 (3), 1143-1152�DOI: 10.1021/jp036567u
What do we mean by retroactviity?
To the left is a TTL NAND gate chip, part of the 7400 series. Developed in the mid 1960s, it revolutionized digital electronics for professionals and hobbyists.
It offered two two key benefits: 1) all chips in the series worked off a standard 5v rail. 2) Secondly an output could connect to up to 10 other inputs without signal degradation.
From these may cases what can we distill out?
1) Interchangeability/reusability, �2) Function independence, �3) Defined interface, �4a) Evolability�4b) Modifiability, �5) Standardization�6) Structural separability (different from functional independence, eg a NAND gate is functionally separate but a network graph is structurally separable since it has no intrinsic function);
Generating functional networks using evolution
This network will compute the square root of the input x. The square root will be the concentration at node 3
Here is a range of networks that can compute the square root:
Solve quadratic equation
Cube Root Calculator
Other Evolved networks:
But there are many other definitions of modularity
The word modularity is one of the overused words and to some extend has lost its meaning.