In Silico Evolution of early Metabolism.
Alexander Ullrich, Christoph Flamm,
Markus Rohrschneider, Peter F. Stadler
Abstract
Scenarios of Evolution
We developed a simulation tool for the evolution of
early metabolism, allowing us to speculate on the formation of metabolic pathways from catalyzed chemical reactions and network properties. Our model
consists of a protocellular entity with a simple RNAbased genetic system and an evolving metabolism
of catalytically active ribozymes that manipulate a
rich underlying chemistry. Ensuring an almost openended and fairly realistic simulation is crucial for understanding the first steps in metabolic evolution. We
show here how our simulation tool can be helpful in
arguing for or against hypotheses on the evolution of
metabolic pathways. We demonstrate that seemingly
mutually exclusive hypotheses may well be compatible when we take into account that different processes dominate different phases in the evolution of
a metabolic system. Our results suggest that forward
evolution shapes metabolic network in the very early
steps of evolution. In later and more complex stages,
enzyme recruitment supersedes forward evolution,
keeping a core set of pathways from the early phase.
Energy
Energy
Energy
Energy
Energy
Energy
Biomass Biomass
Biomass
(a)
(b)
Forward Evolution
Assumes that an organism is able to make use of certain
molecules from the environment. Individuals that can produce these beneficial molecules by themselves gain an advantage in selection in the case of depletion of the “food
source”. Therefore, new chemical reactions are added that
produce beneficial molecules from precursors that are abundant in the environment or that are produced in turn by the
organism’s metabolism. As a consequence, one should observe more ancient enzymes downstream in present-day
metabolic pathways. Towards the entry point of the pathway, younger and younger going enzymes should be found.
Forward evolution could be seen as an extension or counterpart of the backward evolution hypothesis, reversing the
direction of pathway evolution. Granick, and later Cordon,
argue for a pathway evolution in forward direction, requiring
that the intermediates are already beneficial to the organism. This is in particular plausible for catabolic pathways,
where the organism can extract more energy by breaking
food molecules downs to simpler and simpler end products.
Older enzymes are then expected to be upstream in the
pathway, with younger enzymes appearing further downstream.
Patchwork Model
Shell Hypothesis
The patchwork model explains the formation of pathways
by recruiting enzymes from existing pathways. The recruited enzymes may change their reaction chemistry and
metabolic function in the new pathways and specialize later
trough evolution. This introduction of new catalytic activities
lead to a selective advantage. Looking at the constitution
of a pathway formed by enzyme recruitment, we should observe a mosaic-like picture of older and younger enzymes
mixed throughout the pathway.
The shell hypothesis was proposed by Morowitz. It argues
for the case of the reductive citric acid cycle that in the beginning an auto-catalytic core is formed from which new catalytic activities and pathways could be recruited and fed.
Thus a metabolic shell would form around this core. Enzymes in the core would likely be less prone to mutational
changes because they are essential for the organism. Thus,
one should still be able to observe a core of ancient enzymes.
Existing
New
Existing
Backward Evolution
same
chemistry
Core
Shell
Recruit
(c)
(d)
Hypotheses about the formation and evolution of metabolic pathways [1]. (a) Backward evolution, (b)
Forward evolution, (c) Patchwork model, (d) Shell hypothesis. Colored squares represent enzymes, gray
circles are metabolites. Color encoding for enzymes stand for their age, red being older and blue being
younger enzymes.
classification tree of organic reactions for functional
assignment of the catalytic set (Step B). Thus we have
implemented an evolvable sequence-to-function map,
allowing the metabolic organization to escape from the
confines of the chemical space set by the initial conditions of the simulation.
The metabolic subsystem is built upon a graph-based
artificial chemistry endowed with a built-in thermodynamics. To generate the metabolic reaction network,
induced by the catalytic set on the set of metabolites, a
rule-based stochastic simulation is performed. Reaction rates are calculated “on the fly” from the chemical
graphs of the reactants.
To identify the elementary flux modes, i.e., extreme pathways, of the resulting reaction network, a
metabolic flux analysis is performed. (Step D). The
fitness of an organism is computed as the maximum
of the yield function (e.g. biomass production) over all
extreme pathways. Finally, genetic variation operators
are applied to the genome (Step E).
U
A CC UG
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flux v
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The computational model ([2]) is composed of a genetic and a metabolic subsystem. The genetic subsystem is implemented as a cyclic RNA genome. A
special sequence motif indicates the start of genes
which are of constant length. The RNA sequence
corresponding to the “coding sequence” of a gene
is folded into the (secondary) structure using the
Vienna RNA Package(Step A).
During chemical reactions, bond formation/breaking
is confined to a small subset of atoms of the reacting molecules. A cyclic graph abstraction, called the
imaginary transition state (ITS) [3], can be used to
capture the changes in the reactive center. Furthermore, over 90% of all known organic reactions can
be classified by their ITS and organized in a hierarchical structure [3]. Sequence and structure features
of the folded RNA gene products are mapped into the
flu
x
Computational Model
O
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flux v
O
A
Scheme of the simulation system. (A) Decoding of (RNA-)genes to catalytic molecules; (B) Assignment of catalytic functions to “ribozymes”, through mapping from structural and sequential information of
the RNA molecule to a reaction logo in the hierarchy [3]; (C) Construction and stochastic simulation of the metabolic network; (D) Metabolic Flux analysis and fitness evaluation; (E) Application of genetic
variation operators.
Results
For this study, we performed 100 runs with a population size of 100 cells running for 100 generations
and performing 100 network expansion (stochastic
simulation) steps per generation, the input molecules
were cyclobutadiene, ethenol, phthalic anhydride,
methylbutadiene, and cyclohexa-1,3-diene.
We use data from a simple simulation run, starting
with only two input molecules and developing only
few enzymes, for the visualization of an evolutionary
time series and the reaction lifetime overview. Another, more complex, setting is used in a simulation
run in which we investigate the evolutionary history
of the involved genes/enzymes, depicted in the catalytic function genealogy for all generations.
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Average relative connectivity of (left) enzymes and (right) metabolites introduced in the same generation, for
100 generations. The height of the bars shows the fraction of the overall connections that are accounted by
enzymes/metabolites from a particular generation. All values are averages over 100 simulation runs. Input
molecules are not considered in the statistic, they account for nearly 50 percent of metabolite connectivity.
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A series of simulated metabolic networks after (a) 10, (b) 30, (c) 66, and (d) 100 generations. Colored
squares represent chemical reactions, gray circles represent metabolites. Metabolites involved in a reaction
are connected to it in the network graph. The coloring for the reactions encode their age, where red stands
for older (occurrence in early generation) and blue for newer (later generation) reactions.
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We have introduced a simulation tool that
models the early evolution of metabolism
in a quite realistic setting and provides
many tools for the detailed investigation
of metabolic evolution. Using both simple
example and a series of more complex simulation runs, the evolution of the components
on the small scale (metabolites, enzymes)
as well as on systems (pathways, networks)
was investigated. The simulations allow to
discriminate between different scenarios for
the evolution of metabolic pathways. Based
on the observations from this study, we
argue that the different evolutionary hypotheses can be reconciled, in that they act in
different phases of evolution, i.e. in different
scenarios we might observe another strategy at work. Here, we suggest that forward
evolution dominates in the earliest steps and
is then superseded by a phase of enzyme
recruitment, however, leaving behind a trace
in form of a core set of forward evolved
pathways.
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Evolutionary history of simulated metabolic networks. For the first 100 generations, we show the number of
links and pathways that conform to the forward and backward evolution scenarios, respectively. Links are
pairs of (left) consecutive reactions or (right) consecutive metabolites along a pathway. A pathway is
identified as “forward-evolved” if at least one of its links is forward and none backward. In the first
generations, the network consists predominantly of forward (reaction) links and pathways. After about 20
generations, the relative abundance of forward pathways decreases drastically but quickly reaches a
persistent plateau value.
We find that enzymes from earlier stages are significantly higher connected than those from later stages.
Further, we observe forward evolution in the first
period succeeded by patchwork evolution, however
keeping a core set of pathways from the early steps.
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Life Time
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Life-time diagram for metabolic reactions. (left) Life-time of reactions, (right) union network graph over all 100
generations. The reactions in the life-time diagram are positioned corresponding to their position in the union
network graph. The rows have colored entries if the corresponding reaction was present at a certain
generation (columns 1-100). Older reactions are red, newer blue. The colored bars show the age distribution
of reactions in the network in the same order as in the lifetime overview. The first bar represents our results,
following the pattern for backward evolution, forward evolution and the patchwork model.
In an early and simple environment forward evolution
is the main evolutionary force in our simulations. In
longer simulations we observe all kinds of evolutionary events, such as divergence, convergence, multiplication and deletion.
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Genealogy of catalytic functions and gene dosage over 2000 generations. Each row represents an
observed catalytic function. Black horizontal lines indicate time intervals in which genes coding for that
catalytic function were present in the genome (0-200: from left to right). The thickness of the black
lines indicates the number genes with a given function. Thin vertical red lines indicate points where
the accumulation of mutations caused a transitions between catalytic functions. If the number of genes
copies in a function class increases without a transition from another gene, then the increase is due to
a gene duplication. A new gene can be created in the genome through the fortuitous formation of a
TATA-box. Conversely, a gene can vanish if its TATA-box is destroyed by mutation. On the left of the
chart a numerical encoding of the graph transformations performed by the “enzyme” is plotted.
References
[1] G. Caetano-Anolles et. al. The origin and evolution of modern metabolism. Inter J Biochem and Cell Biol (2009).
[2] Flamm et. al. Evolution of metabolic networks: A computational framework. J. Syst. Chem. (2010)
[3] J.B. Hendrickson. Comprehensive system for classification and nomenclature of organic reactions. J Chem Inf ComputSci (1997)
Albeit our simulation environment is still
a drastic simplification of chemistry, it is
realistic enough to investigate the evolution
of early metabolism. Computer simulations
like this one are likely to provide new insights
about the general evolutionary mechanisms
governing biological systems in particular in
regimes that are not readily observable. Our
approach of a realistic, yet computationally
feasible, model appears to be a promising
step in this direction.