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IN SILICO METHOD FOR MODELING
METABOLISM AND GENE PRODUCT
EXPRESSION AT GENOME SCALE
Lerman, Joshua A., Palsson, Bernhard O.
Nat Commun 2012/07/03
SO FAR – METABOLIC MODELS
(M-MODELS)
Predict reaction flux
 Genes are either ON or OFF
 Special ‘tricks’ to incorporate GE (iMAT)
 ‘tricks’ are imprecise, more tricks needed (MTA)
 Objective function debatable
 Usually very large solution space
 Flux loops are possible leading to unrealistic
solutions.
 No regulation incorporated

NEW – METABOLISM AND EXPRESSION
(ME-MODELS)
Add transcription and translation
 Account for RNA generation and degradation
 Account for peptide creation and degradation
 Gene expression and gene products explicitly
modeled and predicted
 All M-model features included
 GE and proteomic data easily incorporated
 No regulation incorporated.

ME-MODEL: THE DETAILS
THE CREATURE
Model of the hyperthermophilic Thermotoga
maritime (55-90 °C)
 Compact 1.8-Mb genome
 Lots of proteome data
 Few transcription factors
 Few regulatory states…

ADDING TRANSCRIPTION
AND TRANSLATION TO
MODEL
MODELING TRANSCRIPTION
(DECAY AND DILUTION OF M/T/R-RNA)

Flux creating mRNA: 𝑉𝑡𝑟𝑎𝑛𝑠𝑐𝑟𝑖𝑝𝑡𝑖𝑜𝑛

Fluxes deleting mRNA:
𝑚𝑅𝑁𝐴
𝑆𝑒𝑐
(GE)
𝑉𝑚𝑅𝑁𝐴𝑑𝑖𝑙𝑢𝑡𝑖𝑜𝑛 (mRNA transferred to daughter cell)
 𝑉𝑚𝑅𝑁𝐴𝑑𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛 (NTPNMP)



Controlled by two coupling constants:

𝜏𝑚𝑅𝑁𝐴 (mRNA half life, from lab measurements)

𝑇𝑑𝑜𝑢𝑏𝑙𝑖𝑛𝑔 =
ln 2
growth rate
(lab measured or sampling)
𝜏𝑚𝑅𝑁𝐴
𝑉𝑑𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛
𝑇𝑑
𝑇𝑑
removed for every
𝜏𝑚𝑅𝑁𝐴
Fluxes are coupled: 𝑉𝑑𝑖𝑙𝑢𝑡𝑖𝑜𝑛 ≥
Means 1 mRNA must be
times it is degraded
 Cell spends energy in rebuilding NMPNTP

MODELING TRANSLATION:
MRNAENZYMES

Flux creating peptides: 𝑉𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛

Translation limited by 𝑘𝑡𝑟𝑎𝑛𝑠
𝑃𝑟𝑜𝑡
𝑆𝑒𝑐
𝑚𝑅𝑁𝐴
𝑃𝑟𝑜𝑡∙𝑆𝑒𝑐
, upper bound
on rate of single mRNA translation, estimated
from protein length, ribosome translation-frame
and tRNA linking rate (global)

Fluxes are coupled:
𝑉𝑑𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛

𝑉𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛
≥
𝐾𝑡𝑟𝑎𝑛𝑠 ∙ 𝜏𝑚𝑅𝑁𝐴
Means 1 mRNA must be degraded every 𝐾𝑡𝑟𝑎𝑛𝑠 ∙
𝜏𝑚𝑅𝑁𝐴 times it is translated
MODELING REACTION CATALYSIS

𝑉𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑖𝑠 =

𝑘𝑐𝑎𝑡
𝑘𝑐𝑎𝑡 𝐸 𝑆
Κ𝑀 + 𝑆
(Michaelis-Menten kinetics)
𝑆𝑢𝑏𝑠𝑡𝑟𝑀𝑜𝑙𝑒𝑐𝑢𝑙𝑒
𝑃𝑟𝑜𝑑𝑀𝑜𝑙𝑒𝑐𝑢𝑙𝑒∙𝐶𝑜𝑚𝑝𝑒𝑥∙𝑆𝑒𝑐
is turnover number
𝐸 is complex concentration
 [𝑆] is substrate concentration
 Κ 𝑀 is substrate-catalyst affinity

Assume 𝑉𝐶𝑜𝑚𝑝𝑙𝑒𝑥𝐷𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛 ≪ 𝑉𝑐𝑜𝑚𝑝𝑙𝑒𝑥𝐷𝑖𝑙𝑢𝑡𝑖𝑜𝑛
𝑉𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑖𝑠
𝑉𝐷𝑖𝑙𝑢𝑡𝑖𝑜𝑛 ≥
𝑘𝑐𝑎𝑡 ∙ 𝑇𝑑
 Means one complex must be removed for every
𝑘𝑐𝑎𝑡 ∙ 𝑇𝑑 times it catalyzes
 Whole proteome synthesized for doubling
 Fast catalysis faster doubling (dilution)

BUILDING THE
OPTIMIZATION
FRAMEWORK
M-MODEL - REMINDER
Total Biomass Reaction:
Experimentally measure lipid, nucleotide, AA,
growth and maintenance ATP
 Integrate with organism 𝑇𝑑 to define reaction
approximating dilution during cell formation
 Cellular composition known to vary with 𝑇𝑑
 Cellular composition known to vary with media
 LP used to find max growth subject to
(measured) uptake rates

ME-MODEL
Structural Biomass Reaction:

Account only for “constant” cell structure




Cofactors like Coenzyme A
DNA like dCTP, dGTP
Cell wall lipids
Energy necessary to create and maintain them
Model approximates a cell whose composition is a
function of environment and growth rate
 Cellular composition (mRNA, tRNA, ribosomes)
taken into account as dynamic reactions
 LP used to identify the minimum ribosome
production rate required to support an
experimentally determined growth rate

VALIDATION
RNA-TO-PROTEIN MASS RATIO
RNA-to-protein mass ratio (r) observed to
increase as a function of growth rate (μ)
 Emulate range of growths in minimal medium
 Use FBA with LP to identify minimum ribosome
production rate required to support a given μ



Assumption: expect a successful organism to
produce the minimal amount of ribosomes
required to support expression of the proteome
Consistent with experimental observations, MEModel simulated increase in r with increasing μ
COMPARISON TO M-MODEL
max biomass on minimal media, many solutions
−5 chance of
 Sample and approx. Gaussian, 10
finding solution as efficient as ME-model.
 Can be found by minimizing total flux (many
solutions stem from internal flux loops).

OPTIMAL PATHWAYS IN ME-MODEL
Produces small metabolites as by-products of GE
 Accounts for material and energy turnover costs
 Includes recycling S-adenosylhomocysteine,
(by-product of rRNA and tRNA methylation)
and guanine, (by-product of tRNA modification)
 Frugal with central metabolic reactions, proposes
glycolytic pathway during efficient growth


M-Model indicates that alternate pathways are
as efficient
Blue – ME-model paths, Gray – M-model alternate paths
SYSTEM LEVEL MOLECULAR PHENOTYPES
Constrain model to μ during log-phase growth in
maltose minimal medium at 80 °C
 Compare model predictions to substrate
consumption, product secretion, AA composition,
transcriptome and proteome measurements.



Model accurately predicted maltose consumption
and acetate and H2 secretion
Predicted AA incorporation was linearly
correlated (significantly) with measured AA
composition
DRIVING DISCOVERY
Compute GE profiles for growth on medium:
L-Arabinose/cellobiose as sole carbon source
 Identify conditionally expressed (CE) genes essential for growth with each carbon source
 In-vivo measurements corroborate genes found in
simulation – evidence of tanscript. regulation
 CE genes may be regulated by the same TF
 Scan promoter and upstream regions of CE genes
to identify potential TF-binding motifs
 Found high-scoring motif for L-Arab CE genes
and a high-scoring motif for cellobiose CE genes
 L-Arab motif similar to Bacillus subtilis AraR
motif

SUMMARY
ADVANTAGES
Because ME-Models explicitly represent GE,
directly investigating omics data in the context of
the whole is now feasible
 For example, a set of genes highly expressed in
silico but not expressed in vivo may indicate the
presence of transcriptional regulation
 Discovery of new TF highlights how ME-Model
simulations can guide discovery of new regulons

DOWNSIDES
ME-model is more intricate then M-model, more
room for unknown/incomplete knowledge
 May keep ME-model simulations far from reality
on most organisms

Lack of specific translation efficacy for each protein
 Lack of specific degradation rates for each mRNA
 lack of signaling
 Lack of regulatory circuitry

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