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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