Mathematical Biology: The virtual cellshille/Virtual_cell/VC_C1_Intro... · 2016-01-31 · A short introduction to (cell) biology To appreciate the complexity and simplification of

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dr. Sander [email protected]

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



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.



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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



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/



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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


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



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?



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:



Mathematical Biology

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(10) Sander Hille

Positioning:



Mathematical Biology

Quantitative Biology

(11) Sander Hille

Biological introductionThe ‘Tree of Life ’



(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



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’



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A history of life(and the solar system)

(13) Sander Hille


(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

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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


(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 --



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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!



Diversity in cells

(15) Sander Hille

A ‘typical’ bacterial cell

Virtual Cell C-1

An animal cell



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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



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



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water

Cellular membranes

(17) Sander Hille

(Borislav Mitev)Membrane lipid(s)

‘Head’: hydrophilic

‘Tails ’: hydrophobic



Cellular membranes

(18) Sander Hille

water



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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



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 …



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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



environment

Interaction with the environment


Observation Behaviour



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environment



EnvironmentalObservation

Behaviour

InternalObservation

Memory‘Decision making’





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)



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:



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



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




Metabolites must cross membranes:


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




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InternalObservation

‘Decision making’

Observation and part of decision making realised by the signaling network

Environmental observation e.g. throughreceptor proteins



Intracellular dynamics-- Signaling --



InternalObservation




An activated receptor catalysesfurther chemical reactions,‘integrating’ other internal observations




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InternalObservation




An activated receptor catalysesfurther chemical reactions,‘integrating’ other internal observationsOften in interaction with regulationof gene expression




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



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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


Intracellular dynamics-- Regulatory network – overall control --


Gene transcription

(30) Sander Hille

(Basics… for prokaryotes – eukaryotic transcription m uch more involved)

2

RNA strand (mRNA)

3

Bound transcription factor


RNA polymerase

DNA

1

σ- factor


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mRNA translation

(31) Sander Hille



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



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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



(34) Sander Hille

Some aspects to remain aware of



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The crowded cell

(35) Sander Hille

E. coli

David S. Goodsell’s ‘Crowded cell’http://mgl.scripps.edu/people/goodsell/


(Wilhelm e.a., Science 344 (2014), 1023-1028)

Molecular crowding in the synapse of a neuron


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??



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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



Different notions of ‘ model ’


(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 ’



Documents

Mathematical Biology: The virtual cellshille/Virtual_cell/VC_C1_Intro... · 2016-01-31 · A short introduction to (cell) biology To appreciate the complexity and simplification of