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karin6

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Abstract
Tissues use feedback circuits in which cells send signals to each other to control their growth and survival. We show that such feedback circuits are inherently unstable to mutants that misread the signal level: Mutants have a growth advantage to take over the tissue, and cannot be eliminated by known cell-intrinsic mechanisms. To resolve this, we propose that tissues have biphasic responses in and the signal is toxic at both high and low levels, such as glucotoxicity of beta cells, excitotoxicity in neurons, and toxicity of growth factors to T cells. This gives most of these mutants a frequency-dependent selective disadvantage, which leads to their elimination. However, the biphasic mechanisms create a new unstable fixed point in the feedback circuit beyond which runaway processes can occur, leading to risk of diseases such as diabetes and neurodegenerative disease. Hence, glucotoxicity, which is a dangerous cause of diabetes, may have a protective anti-mutant effect. Biphasic responses in tissues may provide an evolutionary stable strategy that avoids invasion by commonly occurring mutants, but at the same time cause vulnerability to disease.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
Id Name Spatial dimensions Size
default 0.0 1.0
Id Name Initial quantity Compartment Fixed
zd zd 1.0 default
zs zs 0.5 default
zsm zsm 0.0 default

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
v1 v1 ∅ = zs

(2 * pr - 1) * lp * zs
v2 v2 ∅ = zsm

(2 * prm - 1) * lp * zsm
v3 v3 ∅ = zd

2 * (1 - pr) * lp * zs + 2 * (1 - prm) * lp * zsm - lm * zd

Global parameters

Id Value
k_pr 1.0
k_prm 0.15
lm 0.5
lp 1.0
pr nan
prm nan

Local parameters

Id Value Reaction

Assignment rules

Definition
pr = 1.0 / (1.0 + pow(k_pr * zd, 0.5))
prm = 1.0 / (1.0 + pow(k_prm * zd, 0.5))

Rate rules

Definition

Algebraic rules

Definition
Definition
Trigger Assignments
eq(time, 10) zsm = 0.01