Transcript In silico method for modeling metabolism and gene product expr. at

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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