Computational tools for whole-cell simulation

Cara Haney (Plant Science)

E-CELL: software environment for whole-cell simulation

Tomita et al. 1999. Bioinformatics 15(1): 72-84

Mathematical simulation and analysis of cellular metabolism and regulation

Goryanin et al. 1999. Bioinformatics 15(9): 749-758

Questions addressed in E-CELL

• Can gene expression, signaling and metabolism be simulated in a manner that will allow one to make predications about a cell?

• In simplifying a cell, what functions can be sacrificed?

• What is the minimal gene set?

Overview• Simple cell based on Mycoplasma genitalium

• User can define interactions between proteins, DNA and RNA within the cell,

etc. as sets of (first order) reaction rules

• User can observe changes in proteins, etc.

M. Genitalium www.nature.come/nsu/010222/010222-

17.html

• Lists loaded at runtime:– Substances – Rule list – System List

• Calculates change in concentration of substrates over a user-specified time interval

• User can select either first-order Euler [error is O(Δt2)] or fourth-order Runge-Kutta [O(Δt5)] integration methods for each compartment

Running the Program

Cell Model• Hypothetical minimal cell from M. genitalium

• Only genes essential for metabolism

• Cell can take up glucose from environment and generates ATP by turning glucose into lactate via glycolysis and fermentation. Lactate is exported from the cell

• Transcription and translation modeled by including transcription factors, rRNA, tRNA

• Cell takes up glycerol and fatty acids in order to maintain membrane structure

• Cell does not replicate

Metabolism in the model cell• Includes glycolysis, phospholipid biosynthesis, and transcription and

translation metabolisms

• Does not include machinery for replication (DNA replication, cell cycle), amino acid/nucleotide synthesis

Classes of Objects• Substance

– all molecular species within the cell

• Genes– Modeled as class GenomicElements with coding

sequences, protein binding sites and intergenic spacers

– Gene class includes transcribed GenomicElements – 120 (out of 507) M. genetalium. 7 from other

organisms.– includes enzymes to recycle nucleotides and amino

acids

Genes in the cellGene type M. Gen Other Total

Glycolysis

Lactate fermentation

Phospholipid biosynthesis

Phosophotransferase system

Glycerol uptake

RNA polymerase

Amino Acid metabolism

Ribosomal L. subunit

Ribosomal S. subunit

rRNA

tRNA

tRNA ligase

Initiation factor

Elongation factor

9

1

4

2

1

6

2

30

19

2

20

19

4

1

0

0

4

0

0

2

0

0

0

0

0

1

0

0

9

1

8

2

1

8

2

30

19

2

20

20

4

1

Proteins coding genes

RNA coding genes

Total

98

22

120

7

0

7

105

22

127

Classes of Objects cont.• Reaction Rules

– One substance turned into another via an enzyme

D-fructose 6 phosphate D-fructose 1-6 bisphosphate

– Can also represent formation of complexes and movement of substances within the cell

– No repressors/enhancers (genes are never turned on or off) although user can specify gene regulation

– Each protein and mRNA contain equal proportions of aa’s and nucleotides

C0085 + C00002 C00354 + C00008 + C00080

[EC 2.7.1.11]

ATP ADP + H+

6-phosphofructasokinase

Reaction Kinetics

Reactions are modeled from EcoCyc and KEGG

Non-enzymatic reactions:

v = k • Π [Si]vi

Enzymatic Reactions (Mechaelis-Menton):

Vmax • [S]

[S] + Km

Also works for a number of substrates and products or formation/degredation of molecular complexes

J-1

i

v =

Virtual Experiments

‘Starve’ cell by decreasing glucose

Level of ATP plummets: cell dies

ATP initially increases

Changes in mRNA levels upon drop of ATP due to Glucose Deprivation

Applications

• Optimization of culture systems

• Minimal gene set

• Discover new gene functions

• Model more complex organisms

• Genetic engineering

• Drugs

The good and the bad

• As is, can it tell us anything about the cell?– No repressors/enhancers (genes are not

turned on or off)– Cell cannot replicate– No aa/nucleotide biosynthesis

• Even modified, can it really tell us anything new?

Mathematical simulation and analysis of cellular metabolism and regulation

• Interface for dealing with systems of differential equations.

• Enter a matrix of equations, has ODE (ordinary differential equation) solver

• In order to use this for biological applications:– Assumes genome has been sequenced, have

gene networks and differential equations of how one gene influences another over time.

– Need array of equations specifying how gene A changes with respect to gene B

• Evaluates over long period of time until steady state is reached within the ‘cell’

• Determine relative levels of proteins within a cell

• Explicit solver– If it is known how much energy is being consumed

from these genes undergoing given reactions

• Implicit solver– If gene X doubles expression, how are all other genes

affected? – Can plot change in GeneY as GeneX changes

Features

More Features

• Bifurcation Analysis– Chaos, multiple steady states may exist. – Bifurcation points—points where a slight shift in one

substance may cause drastic change in steady state

• Experimental data– Fit your model to experimental data to try and find the

best steady state.

• “It is now feasible to generate a complete metabolic model where complete genome data are available”

hmm…

• Data available is not there at whole cell level.

• Even if all data is available, can we solve a 6,000 x 6,000 matrix?

• Just using isolated pathways is this useful?

Problems

Comparison between two systems

Similarities

• Both use similar approaches to looking at the dynamics of a cell.

• Both make it possible to ‘knock out’ genes

• Can make plots to observe changes

Differences

• E-CELL starts from the ground up; builds cell as things are discovered. Math. Sim. Assumes information is there

• E-CELL only useful for M. genetalium; Can use Math. Sim for any organism and adjust based on experimental data.