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Scientific Report 2007-2009
Condensed matter physics and biophysics
C14. Statistical Biophysics
Cellular metabolism is to a large extent inaccessible
to experiments. The best experimental technique available
to date to probe intracellular reactions rely on C13-
based flux analysis: basically, a population of cells (eg
bacteria) is prepared to grow in a medium with a labeled
carbon source (eg glucose). After a transient, the marker
reaches a steady distribution over cells, and the mass-tocharge
ratio distribution in certain target compounds (eg
alanine) can be detected via mass or NMR spectroscopy.
From this, reaction fluxes can be inferred. In a model
system like the bacterium E.Coli, this allows to infer
the values of a few tens of fluxes (all from the major
carbohydrate-processing pathways) out of the roughly
1100 forming its metabolism. Much less is known about
eukaryotic cells, and only a handful of data cover human
cells (including the highly important red blood cells).
The inherent difficulty of gathering experimental evidence
makes theoretical approaches a necessary instrument
to reconstruct the global organization of fluxes at
the cellular level, both to predict responses to environmental
perturbations, drugs, or gene knockouts, and to
infer the critical epistatic interactions between metabolic
genes. Several methods are currently available to compute
reaction fluxes from the known stoichiometry, one
prominent example being flux balance analysis. The pillars
on which all of them rest are the assumptions that
(a) metabolite concentrations and reaction fluxes are at
a steady state, and (b) the cell’s overall activity aims
at maximizing the production and/or the consumption
of a given set of metabolites. The latter condition is
typically expressed via a linear optimization problem.
Biomass maximization and ATP maximization, glucose
consumption minimization or total flux minimization are
all examples of this kind of approach.
Some experimental evidence indeed has shown that E.
Coli under evolutionary pressure evolves towards states
of maximal biomass production in nutrient rich environments.
These models are able to reproduce the limited
empirical evidence with a varying degree of success. In
particular, if wild type cells in certain environments may
be reasonably well described by a biomass optimization
principle, after a knockout they are best described by
a principle of minimal flux adjustment with respect to
the wild type. Over the last few years, however, several
limitations of the existing theories have emerged, most
strikingly in the proliferation of objective functions that
are needed to describe different cells, environments and
cell mutants. By standard approaches it is not possible
to predict the biomass composition given the cell and
its environment: rather, the detailed biomass composition
is a key input of the models. A further drawback
of available theories is that by linear optimization they
systematically reduce the space of feasible flux states to
a single point (the optimum). Most of the biological
features requiring high flexibility, like metabolic pathways
coregulation or flux reorganization after knockouts
or environmental changes, are unlikely to be captured by
a simple optimization scheme.
Understanding the cell’s response to perturbations at
the metabolic level requires a deeper analysis of the existing
data and theories, besides new heuristics to explore
different directions. Our group has tackled such
problem within Von Neumann’s maximal producibility
framework. The scientific novelty of our research lies essentially
in the possibility to identify essential reactions
(or genes) as dynamically stiff ones, thus linking directly
to the genetic level. Results obtained so far reproduce
the experimental evidence and allow to infer (rather than
assume) the biomass composition. Many interesting extensions
are currently being analyzed.
Figure 1: E. coli’s central metabolism: nodes represent
metabolites, an arrow joining two nodes is present when a
reaction exists converting one into the other. Red reactions
turn out to be “frozen”, i.e. dynamically stiff.
References
1. C. Martelli, et al., PNAS 106, 2607 (2009).
2. A. De Martino ,et al., ‘ Europhys. Lett. 85, 38007 (2009).
3. A. De Martino ,et al., J Stat P05012 (2007)
Authors
A. De Martino 3 , E. Marinari, C. Martelli
Sapienza Università di Roma 67 Dipartimento di Fisica