Toolbox: symbi

Interaction between hosts and symbionts in reactors:

symbi

host: 1 reserve, 1 structure, V1-morph
symbiont: 2 reserves, 1 structure, V1-morph
Demo that runs: The theory for the model can be found in:
Kooijman, S. A. L. M. 2002 Van herbivorie, via symbiose naar mixotrofie. In: Heesterbeek, H., Diekmann, O. en Metz, J. A. J. Theoretische Biologie. Epsilon-uitgevers, Utrecht. (subm)

The paper describes the trophic relationships between autothrophs and herbivores, and how herbivory can make a smooth transition to symbiosis. The basis is that herbivores consume the structure and, more important, the reserves of the autotrophs. Autotrophs also have to excrete some reserves in the environment, which can be taken up by the herbivores as well. Stoichiometric constraints and conversion efficiencies dominate the relationships between the partners.

Populations of autotrophs and heterotrophs live in a reactor; Model elements are:

Example of use after (optionally) editing file pars_symbi.m: symbi


pars_symbi

Set the parameters by editing file pars_symbi.m in toolbox symbi.

shtime_symbi

Batch reactor; Initial conditions can be changed by editing the file shtime_symbi.m. See pages {340} ff of the DEB-book.
Four figures are shown of variables against time

fig 1
Reserves in Molar: N-reserve (blue) and C-reserve (brown) of autotroph, and reserve (red) of heterotroph

fig 2
Nutrient and substrates in Molar: nitrogen (blue), carbohydrate (brown) and substrate (red)

fig 3
Structural masses in Molar: autotroph (green), heterotroph (red)

fig 4
Total organic carbon (brown) and nitrogen (blue) in the reactor.

Example of use after editing pars_symbi.m: clear all; pars_symbi; shtime_symbi
The command clear; pars_symbi; shtime_symbi(4) will only plot fig 4.


shsubstr2graz

Chemostat in equilibrium

Three figures are shown of autotrophs, heterotrophs and their ratio as functions of the substrate concentration in the feed, and the grazing intensity of the herbivores (that is: the preference for living autotrophic structure set by the parameter b_VA).

The range of values for the substrate concentration and grazing intensity can be changed by editing file shsubstr2graz.m

fig 1
Autotrophic structure in Molar

fig 2
Heterotrophic structure in Molar

fig 3
Ratio of autotrophic and heterotrophic structure in Molar/Molar

Example of use after editing pars_symbi.m: clear all; pars_symbi; shsubstr2graz.
The command clear all; pars_symbi; shsubstr2graz(3) will only plot fig 3.


shsubstr2nitro

Chemostat in equilibrium

Three figures are shown of autotrophs, heterotrophs and their ratio as functions of the substrate and the nitrogen concentration in the feed.

The range of values for the substrate and the nitrogen concentration can be changed by editing file shsubstr2nitro.m

fig 1
Autotrophic structure in Molar

fig 2
Heterotrophic structure in Molar

fig 3
Ratio of autotrophic and heterotrophic structure in Molar/Molar

Example of use after editing pars_symbi.m: clear all; pars_symbi; shsubstr2nitro.
The command clear; pars_symbi; shsubstr2nitro (3) will only plot fig 3.


shsubstr2throu

Chemostat in equilibrium

Three figures are shown of autotrophs, heterotrophs and their ratio as functions of the substrate concentration in the feed, and the throughput rate.

The range of values for the substrate concentration and throughput rate can be changed by editing file shsubstr2throu.m

fig 1
Autotrophic structure in Molar

fig 2
Heterotrophic structure in Molar

fig 3
Ratio of autotrophic and heterotrophic structure in Molar/Molar

Example of use after editing pars_symbi.m: clear all; pars_symbi; shsubstr2throu.
The command clear; pars_symbi; shsubstr2throu (3) will only plot fig 3.


shthrou2graz

Chemostat in equilibrium

Three figures are shown of autotrophs, heterotrophs and their ratio as functions of the throughput rate, and the grazing intensity of the herbivores (that is: the preference for living autotrophic structure set by the parameter b_VA).

The range of values for the throughput rate and grazing intensity can be changed by editing file shthrou2graz.m

fig 1
Autotrophic structure in Molar

fig 2
Heterotrophic structure in Molar

fig 3
Ratio of autotrophic and heterotrophic structure in Molar/Molar

Example of use after editing pars_symbi.m: clear all; pars_symbi; shthrou2graz.
The command clear; pars_symbi; shthrou2graz (3) will only plot fig 3.



endosym

Stepwise integration of two interacting population, via endosymbiosis to single population in a reactor:
future host: 1 reserve, 1 structure, V1-morph feeding on one substrate and one product made by future endosymbiont
future endosymbiont: 1 reserve, 1 structure, V1-morph feeding on one substrate and one product made by future host
final endosymbiosis: 1 reserve, 1 structure, V1-morph feeding on two substrates
Demo that runs: where * is an integer number in the range 0-8, that represents the degree (level) of integration (merging) of the two populations into a single one. The integration levels are:

The theory for the models can be found in:
S. A. L. M. Kooijman, P. Auger, J. C. Poggiale and B. W. Kooi 2003 Quantitative steps in symbiogenesis and the evolution of homeostasis.

The paper describes the trophic relationships between two species that become fully interlocked in an endosymbiontic relationship in 8 steps starting from complete independence. Each species feeds on a single substrate and produces a single product, which is taken up by the other species. The substrate and product for each species are initially substitutable, and then become complementary. The species initially live freely in a homogeneous reactor; later the future endosymbiont has three populations: free-living, inside the mantle space of the future host, and inside the host. Each species initially has a single reserve and single structure. First the structures merge, then the reserves. Eventually a single species with one structure and one reserve emerges.

The two (and later one) populations of live in a homogeous generalized reactor, where feeding rates of substrates and leaking rates of state variable are each controlled by parameters; The steady state analysis is just for chemostats, where the specific leaking rates of all state variables are equal, and the feeding rates are proportional to the leaking rates.

Example of use after (optionally) editing file pars*.m: endosym


pars*

Read pars*.m as one of the folling options: pars_endosym.m, pars0.m, pars1.m, .., pars8.m. The * refers to the level of merging between hosts and symbionts, see above. The file pars_endosym.m specifies the parameters of all levels simultaneously. The present version of shtime* and shstate* all make use of this single file.

Set the parameters by editing file pars*.m in toolbox endosym. The parameter vector istate* initializes the state variables for integration in shtime*.


shtime*

Read shtime* as one of the folling options: shtime0, shtime1, .., shtime8. The * refers to the level of merging between hosts and symbionts, see above.

Generalized reactor; Initial conditions can be changed by editing the file pars*.m.
The figures depent on the choice of merging level (0-8). They show variables as functions of time. Some also show ratio's of structures and reserves, to illustrate the degree of homeostasis.

Example of use after editing pars*.m: clear all; shtime*.
The command clear; shtime6 (4) will only plot fig 4 at merging level 6.


shstate*

Read shstate* as one of the folling options: shstate0, shstate1, .., shstate8. The * refers to the level of merging between hosts and symbionts, see above.

Chemostat in equilibrium for all not-trivial throughput rates; the computations might take some time. If continuation fails, time-integration is used to arrive at a initial guess of the states of the system.

The figures depent on the choice of merging level (0-8). They show variables as functions of te throughput rate. Some also show ratio's of structures and reserves, to illustrate the degree of homeostasis.

Example of use after editing pars*.m: clear all; shstate*.
The command clear; shstate6 (3) will only plot fig 3 at merging level 6.


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