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dr. Sander Hilleshille@math.leidenuniv.nl
http://pub.math.leidenuniv.nl/~hillesc
Spring semester 2016
MathematicalBiology:
The virtual cell
Lecture series for masterBioinformatics, Mathematics or LST
Snellius, Niels Bohrweg 1, room 220Mathematisch
Instituut
The virtual cell
(2) Sander Hille
‘Virtual Cell’ :
It requires:Mathematical modeling of relevant biological processes-- to enable computatations;
Spring semester 2016 Virtual Cell C-1
commonly used to mean a computational approach to simulate (part of) the functioning of a living cell
-- what type of modeling is appropriate depends on the processes…
A suitable computational environment-- to make the computations
MathematischInstituut
Various ‘virtual cell’ initiatives exist-- check e.g. ‘VCell’: www.vcell.org-- Tyson Lab – mpf.biol.vt.edu-- Virtual Cell environment of the (US) National Resource for Cell Analysis and
Modeling (NRCAM)
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The virtual cell
(3) Sander Hille
Why ‘Virtual Cell’ ?
Virtual Cell C-1
Why simulate a living cell?
Enable theoretic interpretation of experimental data
Validate or falsify biophysical / biochemical hypotheses concerning the functioning of cellular processes
As part of ‘Reverse Engineering ’ of cellular system:-- what subsystems can be identified?-- what is their role?-- how are these (and the whole) controled?
In (far?) future:
Predict outcome of modifications / external challenges
Spring semester 2016
MathematischInstituut
The virtual cell
(4) Sander Hille
So ‘Virtual Cell’ requiresMathematical modeling
Virtual Cell C-1
A computational environment
What may be neglected easily is, that it also requi res:Modeling skills-- what to do when… what to do not… why…-- what are reasonable assumptions / approximations / etc.
Mathematical skills-- to master manipulation and modification of models-- to interpret computational results -- assess validity of results, comparison with experiment, etc.
Spring semester 2016
MathematischInstituut
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Objectives of this course
(5) Sander Hille
Provide basic knowledge of biology , biophysics and biochemistry to enable collaboration in the field
Provide understanding of mathematical modeling of biochemical processes with differential equations
Acquaintance with tools to analyse these models and skills to interpret computational results
Be able to read the current research literature on this topic
e.g. through issues that arrise when applying methods to:Mammelian or plant cells, instead of bacteriaHigher organisms, instead of unicellular ones
Virtual Cell C-1
Start to appreciate the complexity of Life
Spring semester 2016
MathematischInstituut
Literature
Virtual Cell C-1(6) Sander Hille
Christopher P. Fall, Eric S. Marland, John M. Wagner, John J. Tyson:
Computational Cell Biology.
Springer, 2002.(ISBN: 0-387-95369-8)
Auxiliary research and review papersDownload from electronic library, using ULCNlogin name and password
Lecture notes and slidesSome material will become available onpub.math.leidenuniv.nl/~hillesc/
Spring semester 2016
MathematischInstituut
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Book coverage
(7) Sander Hille
Ch 1. Dynamic Phenomena in CellsCh 2. Votage gated Ionic Currents
Part I: Introductory Course
Ch 3. Transporters and PumpsCh 4. Fast and Slow Time ScalesCh 5. Whole Cell Models
Part II: Advanced Material
Ch 6. Intercellular Communication
+ additional literature
Appendices
A. Qualitative Analyses of Differential EquationsB. Solving and Analyzing Dynamical Systems Using XPPAUT
C. Numerical Algorithms
Virtual Cell C-1Spring semester 2016
MathematischInstituut
What to expect?-- outline of lecture series --
(8) Sander Hille
A short introduction to (cell) biologyTo appreciate the complexity and simplification of biological questions
Discussion of relevant biochemistry/-physicsFor understanding building blocks of models
Mathematical analysis and/or simulation:Tools, interpretation of results
Virtual Cell C-1Spring semester 2016
MathematischInstituut
Mathematical modelingWhy/when take particular mathematical approach? Pitfalls…
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(9) Sander Hille
Neurons, pancreatic beta cells (insulin/hormone secretion)
Effective membrane transportBiophysics / thermodynamicsHow to compute/approximate rate expressions?
Virtual Cell C-1Spring semester 2016
MathematischInstituut
What to expect?-- biological and mathematical focus --
Modeling electrical activity of cells
Mathematical modeling:Non-spatial compartment modelsMainly deterministic: systems of ODEsTouch upon stochastic viewpoint sometimes…
(10) Sander Hille
Positioning:
Virtual Cell C-1Spring semester 2016
MathematischInstituut
Mathematical Biology
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(10) Sander Hille
Positioning:
Virtual Cell C-1Spring semester 2016
MathematischInstituut
Mathematical Biology
Quantitative Biology
(11) Sander Hille
Biological introductionThe ‘Tree of Life ’
Virtual Cell C-1Spring semester 2016
MathematischInstituut
(Charles Darwin, 1837);
Concept needs replacement though -- cross breeding
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(11) Sander Hille
The ‘Tree of Life’
Some cell biology(‘the cell’ does not exist…)
A feel for complexity in higher organisms
Fundamentals on biological networks : metabolic, signaling and regulatory networks
Virtual Cell C-1Spring semester 2016
MathematischInstituut
Biological introduction
(12) Sander Hille
Bron: Introduction to the Archaea (http://www.ucmp.berkeley.edu/archaea/archaea.html)
E. coli
‘Tree of life’
Biological introduction-- Nature’s diversity --
Virtual Cell C-1
‘Prokaryotes’
Spring semester 2016
MathematischInstituut
8
A history of life(and the solar system)
(13) Sander Hille
MathematischInstituut
(1 bio = 1 billion = 109; 1 mio = 1 million = 106)
-4.57 bio
(time measured in years before this day…)
-3.5 bio
First bacteria
-2 bio First multicellularorganism
-3
-1.5 bio
First fungi
1
First plants -0.5 bio -230 mio
First dinosaurs
-65 mio
Extinction of dinosaurs
-0.2 mio
Homo sapiens
Formation of the Sun
-3.5 bio
-4.54 bio Formation of the Earth
NOW
-3 -2 -10.5 bio
End of life supportability
First life forms on Earth
Cambrian explosion of life
-0.5 bio
Virtual Cell C-1Spring semester 2016
(14) Sander Hille
There is no ‘generic cell’…
Prokaryotic cell Eukaryotic cells
(no organelles, length ~ 1 µm) (various organelles, diameter ~ 10 µmand much larger in plants)
Biological introduction-- diversity in cells --
Virtual Cell C-1Spring semester 2016
MathematischInstituut
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(14) Sander Hille
There is no ‘generic cell’…
Prokaryotic cell Eukaryotic cells
(no organelles, length ~ 1 µm) (various organelles, diameter ~ 10 µmand much larger in plants)
Biological introduction-- diversity in cells --
Virtual Cell C-1
Chara corallina
Single cell of 3-8 cm!
Spring semester 2016
MathematischInstituut
Diversity in cells
(15) Sander Hille
A ‘typical’ bacterial cell
Virtual Cell C-1
An animal cell
Spring semester 2016
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10
Diversity in cells
(15) Sander Hille
An animal cell A plant cell
Cellulose cell wall
Vacuole
Plastids
A ‘typical’ bacterial cell
Virtual Cell C-1
Eukaryotic cells are highly compartmentised ; in particular they have a nucleus
Spring semester 2016
MathematischInstituut
Amoeba (slime mould)(Dictyostelium discoideum)
Cellular membranes
(16) Sander Hille Virtual Cell C-1
Compartments are created by cellular membranesConsist of phospholipid bilayer with various embedded proteinsIs a viscous, fluid-like structure!
(Borislav Mitev)Membrane lipids
Spring semester 2016
MathematischInstituut
11
water
Cellular membranes
(17) Sander Hille
(Borislav Mitev)Membrane lipid(s)
‘Head’: hydrophilic
‘Tails ’: hydrophobic
Virtual Cell C-1Spring semester 2016
MathematischInstituut
Cellular membranes
(18) Sander Hille
water
Virtual Cell C-1Spring semester 2016
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Diversity in cells (2)-- different membrane structures --
(19) Sander Hille
Cell wallCell membrane
Bacillus subtilis
Listeria …
Bacillus anthraxisExamples:
Virtual Cell C-1
Gram-positive and Gram-negative bacteria
Spring semester 2016
MathematischInstituut
Diversity in cells (2)-- different membrane structures --
(19) Sander Hille
Gram-positive and Gram-negative bacteria
Cell wallCell membranePeriplasmic space
Plasma membrane
Bacillus subtilis
Listeria …
Bacillus anthraxisExamples:Examples:
Escherichia coli
Salmonella …Legionella …
Virtual Cell C-1Spring semester 2016
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Unicellular and higher organisms-- beyond comparison… --
(20) Sander Hille
B. subtilisE. coli
Dictyostelium discoideum
Caenorhabditis elegans
Homo sapiensArabidopsis thaliana
Remote tribal village Metropolis
C. elegans: 959/1031 cells
Human skin only: ~ 1011
Human total: ~ 1014
Virtual Cell C-1Spring semester 2016
MathematischInstituut
environment
Interaction with the environment
(21) Sander Hille Virtual Cell C-1
Observation Behaviour
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environment
Interaction with the environment
(22) Sander Hille Virtual Cell C-1
EnvironmentalObservation
Behaviour
InternalObservation
Memory‘Decision making’
Spring semester 2016
MathematischInstituut
Interaction with the environment
(23) Sander Hille Virtual Cell C-1
Behaviour
Behaviour, e.g.:Cellular movement
-- Metabolism
Organisation of internal processes, e.g. -- Developmental ‘programme’ :
vegetative, sporulation, programmed cell death (apoptosis)
-- collective, with intercellular communication
Dictyostelium amoebae moving towards scource
of cyclic AMP(Gerisch, MPI Biochemie)
Spring semester 2016
MathematischInstituut
Neutrophil (immune cell) chasing a bacterium
(David Rogers, 1950s,Vanderbilt Univ.)
-- individual
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Intracellular dynamics
(24) Sander Hille
Three fundamental chemical reaction networks:
Virtual Cell C-1Spring semester 2016
MathematischInstituut
Metabolic networks – metabolism
Signaling networks – signal reception & transduction
Regulatory networks – gene transcription & translation
Focus of this course
(25) Sander Hille
• membranes• proteins (e.g. enzymes)
• RNA / DNA• organelles• …
• sugars• cellulose• proteins• fats• …
The set of chemical reactions that occur in living organisms in order to sustain life.
Metabolism:
Nut
rient
s
Str
uctu
ral
com
pone
nts
Catabolism Anabolism
Virtual Cell C-1Spring semester 2016
MathematischInstituut
Intracellular dynamics-- Metabolism --
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Intermediary metabolites
(25) Sander Hille
Nut
rient
s
Str
uctu
ral
com
pone
nts
Energy
• membranes• proteins (e.g. enzymes)
• RNA / DNA• organelles• …
• sugars• cellulose• proteins• fats• …
The set of chemical reactions that occur in living organisms in order to sustain life.
Metabolism:
Catabolism Anabolism
Virtual Cell C-1
Breaking down of large compounds into smaller
Spring semester 2016
MathematischInstituut
Intracellular dynamics-- Metabolism --
Metabolites must cross membranes:
(26) Sander Hille Virtual Cell C-1
Almost all metabolic reactions are catalysed by enzymes
Hexokinase Phosphoglucoseisomerase
Enzymes
Some reactions effectively do not occur in their absence
Glucose G6P F6P
ATP ADPE.g.: first steps in glycolysis:
1. Simple diffusion
Passive transport:
2. Carrier mediated3. Selective channels
or pores
Active transport:
a. transporters / ion pumps
Spring semester 2016
MathematischInstituut
Intracellular dynamics-- Metabolism --
17
(27) Sander Hille Virtual Cell C-1
EnvironmentalObservation
InternalObservation
‘Decision making’
Observation and part of decision making realised by the signaling network
Environmental observation e.g. throughreceptor proteins
Spring semester 2016
MathematischInstituut
Intracellular dynamics-- Signaling --
(27) Sander Hille Virtual Cell C-1
EnvironmentalObservation
InternalObservation
‘Decision making’
Observation and part of decision making realised by the signaling network
Environmental observation e.g. throughreceptor proteins
An activated receptor catalysesfurther chemical reactions,‘integrating’ other internal observations
Spring semester 2016
MathematischInstituut
Intracellular dynamics-- Signaling --
18
(27) Sander Hille Virtual Cell C-1
EnvironmentalObservation
InternalObservation
‘Decision making’
Observation and part of decision making realised by the signaling network
Environmental observation e.g. throughreceptor proteins
An activated receptor catalysesfurther chemical reactions,‘integrating’ other internal observationsOften in interaction with regulationof gene expression
Spring semester 2016
MathematischInstituut
Intracellular dynamics-- Signaling --
Signaling network-- E. coli chemotaxis motor control --
(28) Sander Hille
Chemotactic agent(aspartate)
Cytoplasm
Plama membrane
Flagellum
Molecular motor
Receptor(Tar)
W WmR
A Bp
B
Y
Y
ATP
ATP
ADP p
Ap
Yp Y
p
Intra-cellular diffusion
Control of directionof rotation
Z
Outer membrane
Periplasmic space
Flagellum
Virtual Cell C-1Spring semester 2016
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(29) Sander Hille
‘Implements decission-making’ on the basis of a perceived environment as realised by the signaling network(s).
Acts over the cell’s DNA
Single molecule interaction
Stochastic ( = random ) effects may play a role or may need to be controlled / reduced
Involves:TranscriptionTranslation
MathematischInstituut
Intracellular dynamics-- Regulatory network – overall control --
Virtual Cell C-1Spring semester 2016
Gene transcription
(30) Sander Hille
(Basics… for prokaryotes – eukaryotic transcription m uch more involved)
2
RNA strand (mRNA)
3
Bound transcription factor
MathematischInstituut
RNA polymerase
DNA
1
σ- factor
Virtual Cell C-1Spring semester 2016
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mRNA translation
(31) Sander Hille
MathematischInstituut
Virtual Cell C-1Spring semester 2016
Regulatory networks-- sporulation control in B. subtilis --
(32) Sander Hille
ATP ADP
Signal
KinA~P
Spo0FSpo0F~P
KinA
Spo0B~P
Spo0A
Spo0B
Spo0A~P
σH
kinAσH
-
spo0AσA σH
spo0FσA σH
-- +
+ -
abrB
spo0H
--
AbrB
-
σA
σA
MathematischInstituut
Virtual Cell C-1Spring semester 2016
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Regulatory networks-- sporulation control in B. subtilis --
(33) Sander Hille
ATP ADP
Signal
KinA~P
Spo0FSpo0F~P
KinA
Spo0B~P
Spo0A
Spo0B
Spo0A~P
σH
kinAσH
-
spo0AσA σH
spo0FσA σH
-- +
+ -
abrB
spo0H
--
AbrB
-
σA
σA
Part of signaling network
Regulatory feedback
MathematischInstituut
Virtual Cell C-1Spring semester 2016
(34) Sander Hille
Some aspects to remain aware of
Virtual Cell C-1Spring semester 2016
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The crowded cell
(35) Sander Hille
E. coli
David S. Goodsell’s ‘Crowded cell’http://mgl.scripps.edu/people/goodsell/
MathematischInstituut
(Wilhelm e.a., Science 344 (2014), 1023-1028)
Molecular crowding in the synapse of a neuron
Virtual Cell C-1Spring semester 2016
The crowded cell
(36) Sander Hille
E. coli
David S. Goodsell’s ‘Crowded cell’http://mgl.scripps.edu/people/goodsell/
Further reading:Ch.M. Dobson (2004). Chemical space and biology, Nature 432, 824-828
Many different molecules can function independently under extremely crowded conditions
(Oppositely) charged polar groups on the molecular surfaces (self-)organise the packing
Small mutations in genes coding for proteins may result in unwanted aggregation…
Sickle cell anaemia
Virtual Cell C-1
Free diffusion??
Spring semester 2016
MathematischInstituut
23
Dynamics
(37) Sander Hille
Living systems may look static at macroscopic time scale, but they are dynamic at smaller time scales…
Average life span of human cells (days):
(Flindt (2004), Amazing numbers in Biology)
White blood cell 1.0 – 3.0
Skin (epidermis)
Liver 10 – 2014 – 34
Red blood cell 120Nervous system No (hardly any) regeneration
Chicken embryo fibroblasts (motile cells)
Stained cytoskeleton in fybroblasts
The complete cytoskeleton has been recycled several times when cell has moved one cell length…
Turnover of cellular metabolites: ~ minute
Virtual Cell C-1Spring semester 2016
MathematischInstituut
Different notions of ‘ model ’
(38) Sander Hille Virtual Cell C-1
(Biological) ‘ Model system ’
A ‘cartoon ’
A specific organism that is used in experiments,
E. coli B. subtilis Dictyostelium discoideum
Caenorhabditis elegans
Arabidopsis thaliana
… etc. …
e.g.
i.e. a mechanistic view of how the system
could work
-- of various types (as we will see…)
-- a system of equations,‘Mathematical model ’
Spring semester 2016
MathematischInstituut
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