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Introduction to Developmental
Mathematical Biology Lecture 3
James A. Glazier
(All Uncredited Figures From Wolpert et al.
Principles of Development)
Development in Ninety Minutes
What is Development?
Biological Process by Which a
Fertilized Egg  Organism
[Lauren Palumbi]
Physical Process Which Translates
Genetic Information (Genotype)
Structure and Behavior (Phenotype)
Development as Self-Organization
• Interesting to Physicists and Mathematicians
because largely self-organized not prespecified.
• About 5×104 genes and 109 cells. Genome does
not contain enough information to specify each
• Even if it did, development would be fragile if
completely specified.
• Instead, highly robust at all levels.
Main Processes
Cell Differentiation
Cell Movement
Cell Proliferation and Death
Cellular Secretion and Absorption
of Extracellular Scaffolding
One Cell Type Initially, Many in Adult
All Cells Have the Same Genes (modulo
immune cells…)
Cell Type Determined by Epigenetic
– Pattern of Gene Expression
– Internal Structure
– Metabolic Factors
Gene Switching
• Promoters Turn On Repressors Turn Off Translation of
Genes into Messenger RNA (mRNA)
• Can Also Regulate the Lifetime of mRNA and the
Translation of mRNA into Proteins
• More Exotic Regulation as Well
• Regulation has Complex Feedback and Interactions in
the Gene Regulatory Network
• Enzymes can Methylate Stretches of DNA Turning
Genes off “Permanently”
• Hence Differentiation is Usually a One-Way process:
Less DifferentiatedMore Differentiated
• Opposite Ends of Spectrum: Stem Cells, Terminally
Differentiated Cells (e.g. Neurons)
Homeotic Regulatory Genes
Cell Lines
Fundamental Distinction:
Germ Cells (immortal)
vs. Somatic Cells (disposable)
Germ Layers:
Cartilage, Bone, Germ Cells,
Internal Organs (Heart, Blood,
Kidneys, ….)
Endoderm—Gut, Lungs,
Nervous System
How Does a Cell Know What to
Differentiate Into?
•Cell Does Not Carry a Road Map!
Only Knows its Own Composition
and Local Environment.
•Positional Information:
•Part of the Cytoplasm in the
Egg from Which Cell Derived.
•Contact With Other Cells or
•Reception of Extracellular
•Previous Differentiation
History of Cell.
Reaction Diffusion Equation
after Cook & Murray
Two diffusing Species:Activator A; Inhibitor B
 f ( A, B)  d A 2 A
 g ( A, B)  d B  2 B
 0,
 0,0  d A  d B
Activator-Inhibitor Interactions in Cartilage
Pattern Formation
Philip Maini
Consequences of Differentiation
• Cells—
Change Shape
Polarize (Become Asymmetric)
Send and Respond to Chemical and Electrical Signals
Secrete and Absorb Extracellular Material
Cell Shape Changes
• Determined by Cytoskeleton
– Microfilaments (Actin)—Cell Movement, Force
Generation, Cell Division.
– Microtubules (Tubulin)—Compressive Strength,
Cell Shape and Polarization, Chromosome
Separation, Long-range Transport inside Cell.
– Intermediate Filaments—Tensile Strength
– Molecular Motors—Myosin, Kinesin, Dynein,…
Cell Polarization
• Localization of Receptors and Junctions on
Surface of Cell.
• Asymmetry of Cytoskeleton.
• E.g. of Egg (Animal and Vegetal Poles), Neuron
(Axon, Dendrite and Soma).
• Most Cells form Monolayer Sheets (Epithelia).
• Epithelial Cells have Different Properties on their
Apical, Basal and Lateral Surfaces. They Bind
Tightly to their Neighbors and Variably on their
Tops and Bottoms.
• Mesenchymal Cells are More Symmetrical and
Form Connective Tissue.
Cell Movement
Cells Move Long Distances During Development.
Move by Protruding and Retracting Filopodia or
Lamellipodia (Leading Edge)
Shape Changes During Movement May be
Random or Directed.
Move By Sticking Selectively to Other
Cells (Differential Adhesion)
Move By Sticking to Extracellular Material
Move By Following External Chemical
Gradients (Chemotaxis)
Can also have Bulk Movement:
Secretion of ECM
Differential Cell Division
Oriented Cell Division
Play Movies
Mechanical Changes in
Feedback Loops
• Not Simply:
SignalDifferentiationPattern (Known
as Prepatterning).
• Cells Create Their Own Environment, by
Moving and Secreting New Signals, so
Signaling Feeds Back on Itself.
• Hence Self-Organization and Robustness.
Development of Body Plan
• Specification of Body
• Cleavage
• Gastrulation (Formation
of Primitive Streak—
• Somitogenesis
(Formation of AP
• Organogenesis
Initial Axis Determination
Cleavage Basics
• Period of rapid cell division (up to once every ten
• No cell growth (no interphase).
• Karyokinesis (Chromosome replication) and
Cytokinesis (Cell division) may occur separately.
• Cytokinesis may be missing or partial.
• Karyokinesis and Cytokinesis are usually
synchronous throughout the embryo.
• Little or no relative cell movement.
• Many types in different species.
Types of Cleavage
• Holoblastic (entire egg cleaves): usually little yolk in egg.
– Isolecithal (symmetric yolk)
Bilateral—Ascidians/Tunicates (sea squirts, jellyfish)
– Mesolecithal (yolk mostly at one end)
• Radial—Amphibians
• Bilateral—Cephalopods
• Meroblastic (partial cleavage): lots of yolk
– Telolecithal (yolk at one end)
• Bilateral Discoidal—Reptiles, Fish, Birds
– Centrolecithal (yolk in middle)
• Superficial—Arthropods
Query: How can closely related families differ so radically at the very earliest
stages of development? How could they have changed their developmental
programs in a non-lethal way?
Gastrulation (Formation of Germ Layers)
Organogenesis/Limb Development
Dictyostelium discoideum
Plant Development
Lung Development
Kidney Development
Other Possibilities
Vascular Development
Bone Development
Tumor Growth
Ear (Otic) Development
Liver (Hepatic) Development