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Fly eyes are composed of multiple units (ommatidia) that are disposed in a regular arrangement. The regularity of this pattern depends on the underlying molecular events that give rise to it. In order for it to form the cells that will compose the eye of the adult fly need to transition from an undifferentiated to a differentiated state. This is controlled by a network that acts like a bistable switch: it changes the concentrations of most of its components over time if specific ones are degraded at certain points during development. This model represents part of the network (molecular components and interactions) that occur in the cells giving rise to the fly eyes while they are differentiating in the larva. It is based on a map published by Li et al (2009). The model intends to explore how the different concentrations of the molecular components change if the concentrations of individual types are modified.
The model represents the network by concentrations of 11 molecular species corresponding to 6 fly genes (Yan, Phyl, Ttk69, Pnt-p1 and miR-7), their encoded products (messenger RNAs (mRNAs), microRNAs (miRs) and Proteins) and their interactions. Each molecular species is modeled by a stock (tank) representing the molecule amounts, each stock being affected by the rates at which new molecules of a particular product are synthesized or degraded. Also, the stocks interact with each other according to the certain molecular interactions. For each gene, except the microRNA miR-7, messenger RNAs are created according to the input concentration of other proteins called transcription factors (TF). This is controlled by four parameters (Hill Coefficient, K-activation-coefficient, beta-maximal-expression-promoter, and the TF-activator-concentration). Proteins are synthesized using its corresponding mRNA as template, so that the mRNA concentration determines the amounts of proteins made. Finally, a microRNA (miR-7) is made but not translated into protein and its amounts depend also on synthesis and degradation rates.
Both RNAs and Proteins are made and degraded according to independent rates. mRNA synthesis and degradation rates are the same. For proteins these are independent. Changes of the concentrations of the stocks are due to the interactions between the components of the network according to the following rules: 1) The YAN mRNA is decreased (down regulated more rapidly by increasing its degradation rate) when the miR-7 is made; 2) the YAN protein reduces the synthesis of the Phyl mRNA by enhancing its degradation rate; 3) YAN is down regulated by ERK, a signaling molecule that immediately targets it for degradation; 4) The PHYL protein helps degrade the TTK69 protein by enhancing its degradation rate; 5) TT69 is at TF that prevents the synthesis of the miR-7 when present (i.e. reduces its synthesis rate); 6) miR-7 feeds back into YAN negatively regulating the synthesis of its mRNA (i.e. reduces its synthesis rate); 7) the Pnt-P1 protein represses the synthesis of the yan mRNA (i.e. reduces its synthesis rate); 8) Pnt-P1 protein activates the synthesis of miR-7 (increasing its transcription rate); 9) Pnt-P1 is a self-activator; 10) Pnt-P2 competes with the YAN protein for the binding site of the Pnt-P1 repressing its synthesis when present (i.e. it reduces its synthesis rate).
The setup button fills the stocks with the conditions specified by the user: for each molecular species the user can decide its initial concentration. Also, the synthesis and degradation rates of the proteins can be controlled independently, but are the same for all of them. mRNA synthesis and degradation rates are controlled by four parameters: the K-activation coefficient, the beta-maximal expression for the promoter, the Hill Coefficient and the concentration of the activating TF. These are combined into a single value according to the Hill Function, determining both the synthesis and degradation rates of the mRNAs. ERK induced degradation can be turned on or off during the simulation affecting the concentrations of YAN protein as well as other molecules. The amount by which the YAN degradation rate changes is controlled by a slider and can be modified during the simulation. Counters also give precise numerical values of the molecular amounts for each chemical species. Finally, the go button starts running the simulation.
The network can reach a steady state from its starting point. In some few cases this does not happen and it just oscillates between different states. First press the go button and see if it converges or oscillates given a set of initial conditions. After setting the ERK slider, press the go button again and turn on the ERK signaling. This will cause a rapid degradation of the YAN protein. Turning it off will allow the levels of the YAN protein to rise again.
Slow down the speed at which the simulation runs to better observe if and how the network converges to a steady state. Try different synthesis and degradation rates for proteins and mRNAs. How does this affect the ability of the network to reach steady (non oscillatory) state? Do the convergence trajectories change? Also, turning on or off the and using different amounts of ERK signaling will induce a rapid degradation of the YAN protein and might result in different dynamics. How does this affect the network behavior?
One gene called TTK88 as well as the Notch signaling arm (see Li et all, 2009) have not been included in this model. They can be added to it. Each type of RNA and protein could have an individual synthesis and degradation rate. Also, their transcription and translation could have some noise being probabilistic rather than deterministic. Finally, a hybrid model where some of the stocks are expanded as agents could be implemented. Could you think about ways of creating this features in the model?
This model used the NetLogo Systems Dynamic Modeler to represent the part of the network required to define the cell fate of certain cells in the fly developing eye.
The Wolf Sheep predation model present in the NetLogo Model Library is to some extent related to this one. It uses similar modeling techniques and principles to represent the dynamics of system. The author does not know about any other model of the network modeled.
This Model is still under development. It has been created by Nicolas Pelaez at Northwestern University as part of the course work for the Agent-Based Modeling class taught by Uri Wilensky (Spring 2009).
A map of the network modeled and other relevant references can be found in:
Li X, Cassidy J.J. Reinke C.A. Fischboeck S and. Carthew R.W (2009) A MicroRNA Imparts Robustness against Environmental Fluctuation during Development Cell 137, 273�282, April 17, 2009.
to setup clear-all system-dynamics-setup end to go system-dynamics-go system-dynamics-do-plot if YAN-prot >= 5000 or PHYL-prot >= 5000 or ticks = 30 [ stop ] end