Thesis Hugo van den Berg
Chapter summaries
Chapter 1: Introduction
The main ideas and concepts in the thesis are introduced.
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Chapter 2: Classic models and metabolic shutdown
General theoretical aspects are reviewed of models for microbial growth
and endogenous metabolism. The focus is on a generic cell model with
two components.
Growth is represented as the increase of one of these
components (the structural scaffolding or `frame'). A novel feature of
the present generic model is the explicit modelling of (partial)
metabolic shutdown under conditions where maintenance requirements
cannot be met.
Two different approaches to mechanistic underpinnings for the classic
models are outlined. The first approach is based on a bimolecular
reaction between the non-permanent biomass component and the permanent
(frame)
biomass component. The second approach is based on cellular control
systems.
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Chapter 3: Nutrient limitation
Liebig's Law of the Minimum is reformulated in terms of biomass
composition dynamics. The doctrine of the single limiting
nutrient is shown to be invalid generally.
The nutritional status of a unicellular organism is expressed in terms
of state variables; one which represents the subsistence composition
and a number of `reserve surplus'-related variables.
It is proposed that ``being limiting'' should be defined in terms of
these `reserve surplus' variables. On the basis of this definition, it
can be decided whether a nutrient, or combination of nutrients, is
`limiting', both in transient and steady states. `Multiple limitation'
is shown to have two distinct meanings on these definitions.
A `non-interactive' minimum model, based on a `hard' minimum operator,
is introduced. Smooth `interactive' models may be formulated which
have this minimum model as a limiting case. One such model is
described. Numerical simulations show how the behaviour of this smooth
model can approximate that of the minimum model: apparently hard
non-linearities can arise in the smooth model, through time-scale
separation.
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Chapter 4: Redox and light limitation
A microbial trichome extracts nutrients from its immediate
surroundings. It may also oxidize electron donors, reduce electron
acceptors, and exude the `waste' products of endogenous redox
metabolism. Finally, it may effect light harvesting.
These exchange fluxes are summed up in a generic model, which covers
photoautotrophs as well as chemoheterotrophs. The focus is on
endogenous metabolism and the cellular homeostasis of both reducing and
phosphorylating equivalents.
A novel result is the formulation of four `rules', akin to the Pasteur
effect, which govern the compatibility of endogenous metabolism with
various assimilatory processes.
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Chapter 5: Adaptive re-allocation
This chapter looks at a microbial trichome and its biochemical exchange
fluxes with the ambient. A difficulty in modelling these fluxes is the
need to accomodate several environmental influences.
This problem is tackled on the assumption that the environmental
influences may be represented as a set of `saturation factors', each
corresponding to a distinct assimilatory pathway.
On the adaptive re-allocation concept proposed in this paper, the
saturation factors can be used to find a scalar `diet functional
response'. Biogeochemical exchange fluxes are given as a linear
function of this diet functional response.
To achieve the diet functional response, the microbial trichome needs
to minimize surplus reserves; this is nutritional balancing. This
nutritional
balancing in turn necessitates a re-allocation of molecular building
blocks among the catalytic machineries that underly the various
assimilatory pathways.
It is shown how a regulatory feedback mechanism which monitors the
internal surpluses can achieve such re-allocation. At steady state,
under stationary but arbitrary ambient saturation factors, the model
trichome attains the diet functional response.
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Chapter 6: Uptake versus growth
A microbial trichome grows by assimilating nutrients from its
environment, and converting these into catalytic macro-molecular
machinery. This machinery may be divided into assimilatory machinery
and proliferative machinery. Assimilatory machinery is involved in
nutrient uptake, whereas proliferative machinery enables the trichome
to grow.
The cells in the trichome are faced with an allocation problem: given
the availability of nutrients in the environment, how many
macro-molecular building blocks should be allocated to the synthesis of
assimilatory machinery, and how many to the synthesis of proliferative
machinery?
We answer this question for a particular model, which is a
generalization of the Droop quota model. We formulate a
two-dimensional non-linear optimal control problem, corresponding to
this model.
An optimal allocation regime with a singular segment is derived, based
on Pontryagin's maximum principle. We give a direct proof of
optimality. We discuss how actual biological cells might implement
this optimal regime.
This chapter was written in collaboration with
Mikhail Orlov
and Yuri Kiselev.
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Chapter 7: Bottom:Up versus Top:Down
Fluxes of matter through an ecosystem are subject to influences arising
in its external surroundings. Variations of these influences lead to
changes in the flux pattern of the ecosystem. Straightforward
application of the Chain Rule shows how the sensitivity of the steady
state can be resolved into a matrix containing the direct external
influences on the ecosystem's fluxes premultiplied by the inverse of
the community matrix.
An example of this formalism is given, and various ways to model flux
functions are briefly reviewed. The formalism is applies to Trophic
Cascades Theory, which was later assimilated into the
Bottom-Up:Top-Down Theory. A consistency check on this model is
given.
The concept of ratio-dependence has been put forward as an explanation
of why trophic cascades must peter out, away from the locus of direct
perturbation. It is shown that ratio-dependence achieves this
petering out effect in
virtue of satisfying a more general condition on so-called `coupling
strengths'.
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Chapter 8: Dimethyl sulfide emission from a microbial mat
This modelling study relates dimethylsulfide DMS emission from a
microbial mat to the flux of dimethylsulfoniopropionate DMSP that is
exuded into the interstitial space of the mat by phototrophs.
DMSP may be either cleaved or demethylated. Only cleavage results in
the production of DMS, which itself is further oxidized or escapes from
the mat. The fate of DMSP depends on the functional group composition
of the mat, the physiological characteristics of these groups, and the
eco-physiological conditions oxic/anoxic and light/dark, which both
vary in a diel cycle.
These three factors are accounted for in a mathematical model of a
microbial mat typical of estuaries on the Wadden Islands of The Netherlands and
Germany. Model simulations quantify increased DMS production under
alkaline stress as well as additional DMSP loads.
This chapter was written in collaboration with
Henk Jonkers
and Stef van Bergeijk.
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Chapter 9: General discussion
The main ideas and concepts in the thesis are discussed.
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