Virtual Photobioreactor: Cyanobacterium in Silico
Mikulov, CZ / Nov.11-13, 2010
MINUTES
t.b.d
December 2, 2010
CONFIDENTIAL
Contents
1 What to Model
1.1 Strategy: Top-down & Bottom-up Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
2
2 Bioreactor
2.1 Gas Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Open Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Proposed Experiments & Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
3
3
3
3 Cells I - Top-down Approach
3.1 Carbon & Oxygen . . . . . . . . . . . . . . .
3.2 Nitrogen & Sulphur . . . . . . . . . . . . . .
3.3 Open Problems . . . . . . . . . . . . . . . . .
3.4 Proposed Experiments & Model Development
3.5 Conclusion . . . . . . . . . . . . . . . . . . .
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4
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4 Cells II - Bottom-up Approach
4.1 Kinetic Models . . . . . . . . . . . . . . . . .
4.2 Metabolic Models . . . . . . . . . . . . . . . .
4.3 Open Problems . . . . . . . . . . . . . . . . .
4.4 Proposed Experiments & Model Development
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8
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5 Cells III - Dynamics & Regulation
5.1 Circadian Cycles . . . . . . . . . . . . . . . . . . . . .
5.2 Yeast Respiratory Oscillations as a Benchmark System
5.3 Open Problems . . . . . . . . . . . . . . . . . . . . . .
5.4 Proposed Experiments & Model Development . . . . .
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9
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6 How to Model: Concepts & Methodology
11
7 Conclusion: Proposed Models
7.1 Modelling Teams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
11
1
PROCESS
pH homeostasis
light adaptation
cell division cycle
diurnal cycle
photosynthesis
calvin cycle
respiration
CCM
nitrogen fixation
photorespiration
Mehler reaction
aerob vs. anaerob
limitations: C, N, P, light
1
1.1
PCC 6803
PCC 7942
ATCC 51142
Layer 1
Layer 2
What to Model
Strategy: Top-down & Bottom-up Approach
The emerging picture from the meeting was that we will follow both top-down and bottom-up approaches to reach an integrated and coherent set of models at two to three time-scales, encompassing faster metabolic processes - such as Carbon Concentrating Mechanisms (CCM), or detailed models
of electron transport chain (ETC) & Calvin-Benson Cycle (CBC) - but also gene regulation, cell growth and
circadian processes. The top-down approach is outlined in chapter 3. It starts with a black-box view of
the biology just accounting for the conversion of input gases and substrates to biomass as seen in outside
measurements, i. e. Monod-type growth models [1]. It then step-by-step extends the model to account for
features seen in the measurement, making use of the vast body of existing knowledge on what is actually
happening in the cell to make the model more accurate, and focusing on the (mostly Adenosine-based)
cellular currency metabolites as couplers between lumped overall mass flow processes.
The top-down approach serves to quantiatively map from the possible measurements in continuous culture
in a bioreactor to the major mass fluxes of photosynthetic growth. This basic model is itself supposed to be
a real quantitative model, but will also serve as a scaffold to assemble more detailed models - or modules
(but see below) - from the parallel bottom-up approach (chapter 4). Here we start from existing detailed
c
models of “uptake, assimilation and distribution” (Silke
Thoms), e. g. carbon concentrating mechanism [2]
photosynthesis [3,4,5] and nitrogen fixation [6], and integrate them with bioreactor models, which map cellular
processes to measurements. However, many more processes will have to be accounted to understand the total
bioreactor output and one can think about adding genome-scale reconstructions of the metabolic network, as
e. g. recently published by one of the Mikulov partners [7], using generic rate law expressions [8], as recently
approached for genome-scale baker’s yeast metabolic models [9], and finally add gene-regulatory functions
for each single gene, for example based on promotor and RNA structure analysis.
Note, that this is similar to the approach of predefining modules with certain fixed input/output functions,
which later shall be replaced by more detailed models. As discussed in Mikulov this latter approach was
used for a similar project for yeast, lead by the Westerhoff group and apparently had failed. However, here
we are more flexible, because the modular structure is not fixed, but instead is supposed to grow and change
itself, with ongoing development in the parallel bottom-up approach. The “modular” framework model is
both quantitatively tied to and defined by the measured variables, and grows from a Monod-type model only
where discrepancies with data are observed. The two modelling approaches may then later converge to one
model, or co-exist as a set of coherent and thus hopefully plug-and-playable models, each describing different
levels of detail and time-scales.
First, however, we need to define the outer framework, the photobioreactor, and this is outlined in the
following first chapter 2.
2
2
Bioreactor
Bioreactors and the continuous culture technique were invented by Jacques Monod as tool for theoretical
analysis of cell growth [1]. They provide a controllable environment, with very stable conditions and full
control over the total mass exchanged with with the environment by cellular growth. Off-gas measurement
allow the exact(?) measurement of gases exchanged [10], while media outflow allow to establish exactly
how much biomass has been produced. Additionally, online-measurement and high-resolution sampling timeseries allow to establish the current state of cellular growth. Since we decided not to account for filamentous
growth, we can assume that the liquid and cell-phases are well mixed and chemical conversions and cellular
growth can thus be modelled by Ordinary Differential Equations (ODEs).
2.1
Gas Exchange
Models on the physico-chemical properties of bioreactors, namely mass exchange between gas, liquid and
cell phases, have been developed by two groups attending the Mikulov meeting [11, 12]. This work will
be adapted to the specific chosen bioreactor system, where certain geometric (e. g. head-space vs. liquid
volume) and dynamic features (aeration rate, mixing) of the bioreactor allow to cut-down a full description which in principle would require high-dimensional ODE or Partial Differential Equation (PDE) systems - to
simplified ODE models. With this mathematical tool-set we will be able to directly establish and test possible
assumptions specific to the chosen bioreactor system, based on relative time-scales of three to four different
processes in the system, namely: (1) gas flow through the system (aeration rate), (2) exchange of a certain
molecule between gas and liquid (Henry’s law), (3) conversion of the gas in the liquid (e. g. bicarbonate
formation), and (4) exchange of the gas between liquid and cell phase (see below). Additionally, this work
will provide methods to quantitatively estimate cell:liquid gas exchange rates from dissolved concentration
measurements only.
2.2
Open Problems
Three caveats were raised during discussions in Mikulov.
• We may have to account for CELL BOUNDARY LAYERS, in which local concentration gradients form
around individual cells. This matters e. g. in cells taking up only CO2 (but not bicarbonate HCO−
3 ),
which is present in only low concentrations especially under alkaline conditions of typical cyanobacterial
growth, or if the cellular uptake rates are especially high. Strong stirring technology may circumvent
this problem by disrupting (shearing) boundary layers.
• Volatile substances (gases) may also be TRAPPED IN CONDENSATE forming in the head-space of a
reactor. This problem may be circumvented by cooling traps, as e. g. used to increase ethanol yield in
fermentation by yeast.
• In bigger reactor systems we may have to account for PRESSURE GRADIENTS in the reactor, which
again in principle would require PDE approaches.
2.3
Proposed Experiments & Model Development
Figure 1 gives an overview of the physico-chemical processes modelled. The basic gas-exchange behaviour
should be established in cell-free experiments, switching e. g. from bubbling with nitrogen to normal or
CO2 -enriched air, and measure both dissolved and off-gas concentrations of the gases of interest (for now O2 ,
CO2 and possibly N2 ).
Since at non-acidic conditions CO2 will rapidly react to HCO−
3 , we further need to establish their concentrations at different pH values. We can start with a full-scale model of all involved reactions based on the
recently published new parameter set for the respectice reactions [13], and formally map towards reduced
models based on equilibria between the fast reactions in the system and interaction with pH.
3
Figure 1: Gas Exchange Model. This figure has been created in CellDesigner, and thus can be extended
to a real ODE model encoded in SBML easily. In this case the model we already have fully parameterized
versions working as ODE models (except for N2 exchange) and will be made available on a file server, yet to
be established.
3
Cells I - Top-down Approach
From here it gets difficult, since we need to add cells to our bioreactor
Figure 2 gives a rough conceptual overview of the relevant processes as discussed in Mikulov. It thus
represents the first results of the top-down approach outlined above.
BLACK-BOX MODEL
MIKULOV RESULT: MODEL OF MAJOR MASS-FLUX
Figure 2: Overview of Photosynthetic Growth. Left: initial black-box Monod-type growth model;
Right: extended model featuring the relevant processes as discussed in Mikulov. A*/A: charged (reduced ferredoxin, NADPH, ATP) and uncharged (oxidized ferredoxin, NADP+ , ADP) currency metabolites;
COH/(COH)n : monomeric and polymeric (storage) carbohydrates, lipids; CNH: amino acids/nucleotides;
PC: cyanophycin/phycocyanin; PS: photosynthesis, carbon concentrating mechanism & Calvin-Benson cycle; cPS: cyclic electron transport; RC: glycolysis, TCA & respiration; BS: biosynthesis; MR: Mehler reaction;
NF: N2 fixation; pH: pH homeostasis; MT: maintenance.
4
3.1
Carbon & Oxygen
Table 1 lists the major sources and sinks of CO2 and O2 during cyanobacterial growth as enumerated
and discussed in Mikulov. Internally, these mass conversion processes are coupled via so-called currency
metabolites, mostly Adenosine-based compounds serving as hubs for exchange and interconversion of (electro)chemical and mechanical energy. The rough overall stoichiometries need to be established, and some more
details and issues raised in Mikulov are given in the next paragraphs.
PROCESS
Linear e-chain
FNR
Cyclic e-chain
Mehler Reaction
Photorespiration
Calvin Cycle
Carbon Storage
∆GP ∆Gox
+ATP +FDred
−FDred
+NADPH
+ATP
−NADPH
−ATP −NADPH
−ATP −NADPH
−ATP −NADH
Glycolysis/TCA
+ATP +NADH
Respiratory e-chain +ATP −NADH
∆ Gases ∆ Nutrients
+O2
−hν
−hν
−O2
−O2
−CO2
−CO2
+CO2
−O2
+COH
−COH
+(COH)n
−COH
Table 1: Oxygen, carbon & energy conversions during photosynthetic growth.
Carbon: Calvin-Cycle, Concentrating Mechanism and Cycling The majority of CO2 consumption
happens in the Calvin-Benson cycle. Rubisco is an especially ineffective enzyme and prefers O2 over CO2
initiating a reaction chain called photorespiration (see below). Photosynthetic organisms counteract this effect
by so-called carbon concentrating mechanims (CCM) [14]. At cellular pH-ranges, CO2 is rapidly converted
−
to bicarbonate HCO−
3 and the enzyme Carbonic Anhydrase (CA) can convert HCO3 back to CO2 against
the chemical equilibrium. In cyanobacteria Rubisco and CA are organized in so-called carboxysomes, with
the effect of locally increasing the concentration of CO2 at the site of assimilation. A detailed model [2] has
been discussed at the meeting and a first step of this project may be to make this model accessible for our
purposes, i. e. convert it to SBML, with annotation coherent with other models of the project.
Additionally cyanobacteria also change the extracellular equilibrium of CO2 and HCO−
3 an this carbon
cycling needs to be accounted for also in the liquid phase layer of the model.
Diverse anaplerotic reactions may be alternative sinks for CO2 , and are e. g. required to fill up core
carbon metabolism intermediates for both catabolic and anabolic use. Their significance and quantity for
cyanobacterial growth needs be established.
And finally, CO2 is released again during glycolytic and respiratory growth - mainly in dark phase, but also
in parallel to photosynthesis, peaking during certain phases in diurnal cycle [15].
Oxygen: Photosynthesis, Respiration & Mehler Reaction O2 is produced by the photosynthetic
and consumed by the respiratory electron chains, respectively. The latter exists in up to 10 different versions
in certain cyanobacteria, and we should establish or estimate their respective signficance and consequence.
Additionally O2 can be consumed by photorespiration, usually considered detrimental - but see [7]. However
a significant fraction of O2 can be consumed during photosynthesis - by the Mehler reaction.
Linear electron transport in principle produces both ATP and NADPH in the exact stoichiometry required
for the Calvin Cycle. The Mehler reaction can thus be used to supply ATP in the case where the Calvin cycle
is saturated (and NADPH can not be re-oxidized) and/or if only ATP is required for other cellular functions.
Alternatively, cyclic electron transport can produce ATP without concurrent NADPH production, however
it has been suggested at Mikulov that this is minor compared to the Mehler reaction and (in dark) respiration.
5
3.2
Nitrogen & Sulphur
The Ferredoxin/NADPH Hub The final electron acceptor of the photosynthetic electron transport is
ferredoxin, and from there electrons are distributed between different (assimilatory) processes, to mainly
Calvin-Benson cycle, nitrogen fixation or sulphate uptake pathways via NADPH or in some cases directly
via other ferredoxin reductases. Table 2 lists these additional processes and complements table 1 by adding
the sinks for products of all processes discussed so far in biosynthetic processes, i. e. in cell growth.
PROCESS
Nitrogen Fixation
Glutamate/AA
∆GP ∆Gox
−ATP −FDred
−NADH
Nitrogen Storage
−ATP
Sulphate Uptake
−ATP
Sulphite Reductase
Thiols
Maintenance
BioSynthesis
−ATP
−ATP
∆ Gases ∆ Nutrients
−N2
+NH4
−COH, −NH4
+CNH
−CNH
+(CNH)n
−NADPH
−SO2−
4
+SO2−
3
−FDred
+H2 S
−SO2−
3
−H2 S
−CNH
+CNSH
−NADPH
−NADPH −CO2
−(COH)n
−CN(S)H
+BIOMASS
Table 2: Nitrogen and Sulphur Assimilation, and Biosynthesis.
3.3
Open Problems
• CARBON FATES: what are the ATP & NADPH costs of CCM? Can we - for the top-down model simplify the process by considering the carboxysome (CA+Rubisco) as one big enzyme taking HCO3- as
input, and simply adjust total ATP/NADPH stoichiometries of the Calvin Cycle? Also, are there other
significant CO2 assimilating reactions, e. g. anaplerotic reactions, and do they use CO2 or HCO−
3?
• ATP SYNTHESIS: electron transport and ATP production are not stoichiometrically coupled (chemiosmotic theory). Do we need to separate these processes? Is e. g. proton leakage a variable process?
• O2 VS. N2 VS. H2 S: the final electron acceptor in photosynthesis is ferredoxin (see chapter 7) and from
3−
3
there electrons are re-distributed to CO2 , N2 /NO−
2 /NO3 − or SO4 uptake. However, O2 is supposed to
3−
block Nitrogenase, while H2 S (an intermediate of SO4 uptake) blocks photosynthetic and respiratory
electron transport. How does this relate to dark-phase nitrogen fixation in non-filamentous cyanos?
Can we assume a temporal separation of all three assimilatory processes?
• WHAT CAN WE MEASURE? And what can we learn about the basic stoichiometries and rates listed
in figure 3 from these measurements? Can we list the reaction stoichiometries and rates that we can
differentiate by the experiments suggested below?
• METABOLIC STATES: The stoichiometires and rates of reactions in figure 3 strongly depend on the
presence and intensity of light, and relative nutrient concentrations. Can we test different conditions to
learn more about the individual rates? Diurnal light/dark cycles and the circadian clock already impose
a cycle of changing growth conditions and recent circadian transcriptome data sets (Cyanothece sp.
ATCC 51142 [16, 17], or Synechococcus elongatus PCC 7942 [18]) reveal cohorts of co-expressed genes,
forming functionally coherent sets and indicating a natural cycle between certain defined metabolic
states. Can we use these transcriptome data sets and measurements over a diurnal light cycle to define
such states as subsets of the top-down model?
6
3.4
Proposed Experiments & Model Development
1. BIOMASS (in gram dry-cell weight) and its elemental composition, especially C and N content, need
to be measured for the selected growth conditions and e. g. as a time-course over a diurnal light/dark
cycle.
2. Dissolved and off-GAS MEASUREMENTS will complement biomass measurements and establish the
total mass exchange, i. e. the total stoichiometries of a Monod-type and derived top-down models of
growth.
3. MIMS (Membrane Inlet Mass Spectrometry) can identify dissolved gases and differentiate isotopes,
and the diverse reactions are supposed to have different isotope preferences. Do we have to account for
isotopes IN the models?
4. FLUORESCENCE of the photosystems only tells us the amount of light NOT actually used in photosynthesis. However, can we combine it with MIMS and employ the bubbling protocols of PSI photobioreactors to learn about the actual rates?
3.5
Conclusion
Figure 3: Cellular Mass Flux. The completeness of reactions, and their stoichiometries and rates needs
to be established in this project. Note, that this scheme assumes electron distribution at the end-point of
the photosynthetic electron transport chain between NADPH, N2 and SO−
3 reduction, and further collapses
carboxysomes into one enzyme containing both carbonic anhydrase (CA) and Rubisco.
Figure 3 extends the initial figure 2 by the specific currency metabolites as listed in tables 1 and 2. It is
thus a first draft of a model encompassing the relevant processes discussed for the top-down approach. The
reaction network already reaches a rather high complexity and it approaches the detailed bottom-up models
desribed in the next chapter. Tables 1 and 2 may in fact be considered a precursor of a stoichiometric matrix
defined by metabolic network models. Mapping of the top-down models to full-scale metabolic models may be
instrumental in defining the exact stoichiometries, especially with respect to the final biomass stoichiometries,
and thus complementary to the experiments suggested above. This approach will be outlined in the next
chapter 4.
7
4
Cells II - Bottom-up Approach
Several models at different levels of detail and timescale are available to us, i. e. have been constructed
by participants of the Mikulov meeting. First it has
to be mentioned that a very comprehensive model
which maps photosynthetic rates to the final biomass
yield exists already [6], see figure 4. This model
however is designed for and calibrated to eukaryotic
algae living in open water (rather then controlled
bioreactor), has a heavy focus on electron transport
chain and photosynthesis, but does e. g. not account
for (circadian) gene regulation and captures the bulk
of metabolism only very roughly. It may be a great
benchmark and reference model for our project.
In the following sections we will list available mod- Figure 4: Comprehensive model of photosynthetic
els and their features, and analyze how we can adapt growth from reference [6].
and integrate them.
4.1
Kinetic Models
Figure 5: Carbon Concentrating Mechanism and Carbon Cycling: two models available to us. Left: from
reference [2], right: from [19]
Aaron Kaplan, Silke Thoms, Jiry Jablonsky, Dusan Lazar
4.2
Metabolic Models
metabolic network by Knoop and Steuer [7] and others [20]
Flux Balance Analysis and the Biomass Objective Function
8
Figure 6: Conceptual view of a genome-scale metabolic network reconstruction of Synecchocystis sp. PCC
6803 from [7]
4.3
Open Problems
4.4
Proposed Experiments & Model Development
5
Cells III - Dynamics & Regulation
* METABOLIC STATES over the diurnal cycle, e. g. O2 production vs. respiration vs. N fixation , vs.
modules
* CONDITIONS: aerob/anaerob, different nutrient levels
* cell cycle not well understood
* population structure: Dynamics of the Average vs. Average of the Dynamics
* Top-down: use transcriptome data and knowledge, to define relevant sub-states, or measure various
stoichiometries & rates, generate hypothesis on gene regulation, e. g. DNA supercoiling vs ATP vs. KaiABC
* Bottom-up: use metabolic models and FBA with BOF for defined sub-states
9
5.1
Circadian Cycles
Figure 7: Metabolic states of Cyanothece sp. ATCC 51142 over a diurnal cycle, as indicated by transcriptome
measurements in [16]
5.2
Yeast Respiratory Oscillations as a Benchmark System
* transcriptome: global vs. local regulation & DNA structure
* anaplerotic reaction & evolutionary conserved switching around the amphibolic core carbon backbone
5.3
Open Problems
Available data:
* transcriptome
* proteome
* metabolome
5.4
Proposed Experiments & Model Development
To be measured under our conditions and with chosen photo-bug:
* transcriptome
* proteome
10
* enyzmatic activity of core enzymes
* metabolome
6
How to Model: Concepts & Methodology
basics: SBML+MIRIAM, annotation scheme, e-photosynthesis,
... Coherent modeling, use platform (forums, http://www.e-photosynthesis.org, example: http://www.
comp-sys-bio.org/yeastnet/), and defined species & compartments (SBML + MIRIAM) ...
Top-down vs. bottom-up
FBA vs. ODE: integrated approach? Or can FBA help in finding stoichiometries (for different metabolic
states, for biomass)?
Biomass Equation: re-measure, at different states/conditions
ODE vs. Discrete (Boolean and/or Logical Models)
Metabolic states vs. Modules:
* metabolic states may help to define coarse-grained models
* in certain metabolic states, some processes may be represented only in a coarse-grained manner (rough
input/output) and/or with different stoichiometries (swiss-cross)
Modules with defined input/output functions, Westerhoff project on yeast
Dynamics of the Average vs. Average of the Dynamics
7
Conclusion: Proposed Models
* Rainer Machne, Stefan Mueller, Lada Nedbal, Jan Cerveny: Gas Exchange
* Aaron Kaplan, Silke Thoms: Carbon Concentrating Mechanism and Ci Cycling
* Dusan Lazar: Photosynthetic e-chain
* Jiry Jablonsky: Calvin-Benson Cycle & Storage COH
* Silke Thoms: C vs. N Fixation:
uptake, assimilation and allocation
CCM, PS light reaction, Distribution of electrons at ferredoxin: N vs. C
7.1
Modelling Teams
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