Translation regulation dynamics


This Java applet
(Java 1.4) models the dynamics of translation regulation in the Unfolded Protein Response in yeast.

The background picture is a conceptual visualisation of the relevant cellular compartments: the overall cell, the nucleus and the endoplasmic reticulum. The box in the upper right corner is the legend. The colors in the lower right graph corresponds to the

The simulation starts automatically with initially low concentration of unfolded proteins. The other concentrations then settles at their respective steady state levels.

There are three buttons: Shock, break, and init. The Shock button shocks the system by transiently increasing the unfolding rate by 50-fold. Clicking repeatedly on this button will cause a resetting (since the cell will most probably die from too high unfolding rates). To study the dynamical profile the break button can be pressed to freeze the current picture. To restart the simulation the init button will clear the cell of unfolded protein to the standard level, and the system will once again be sensitive to a shock. The textfield displays the value of t*, which can be interactively set to values between 1 and 25.

The ODE equations are integrated by solving the fast chemistry (red/blue arrows) adiabatically since these are strongly nonlinear and contains rates which are 10 orders of magnitude larger than the soft equations describing proteins synthesis, mRNA conversion and protein folding. In the paper the equations were properly integrated by a second order implicit differentiating and automatic timestep adjustment algorithm in MATLAB (ode23s). In this version we display the extended model where the folded/unfolded dynamics is displayed for clarity.


Quantifying the benefits of translation regulation in the unfolded protein response

J.B. Axelsen and K. Sneppen

(A mathematical model for the dynamics of translation regulation)

The model deals with the dynamics of having a stock of passive mRNA (m) for rapid conversion to active mRNA (m*). (1) The moment the cell experiences a shock in the form of vastly increased levels of unfolded proteins (U), the folding chaperone (BiP) is released from a complex with an endonuclease (Ire1p). This endonuclease then (2) cleaves passive mRNA into (3) active mRNA, which then opens for parallel production (4) of a signalling protein (Hac1p) which then initiates transcription (5) of the folding chaperone (BiP). The chaperone brings the unfolded protein levels down, and the loop is closed.
In the paper we analyse the model and discuss the relevant parameters for making this system work. We found that there exists a relation between degradation times for the mRNAs (tm,t*) and the rate with which Ire1p converts passive to active mRNA (c): c~1/tm << 1/t*.
The degradation time for the passive mRNA should match the conversion rate because otherwise sensitivity is lost (This can be realised from the steady state condition). The short lifetime of m* is necessary for an overshooting effect of the concentration of Hac1p. The overshooting will bring BiP faster to its required level, since the change in BiP is a direct function of Hac1p.
Parameters derived from both in vivo and in vitro experiments shows that the relation above holds. However, as discussed in the paper, by varying the model parameters we found that the model is most sensitive to t*, which lead to a reinterpretation of raw data in order to match the peak times of measured mRNA for Hac1p. This is perfectly in line with the philosophy of the model which states that t* is limiting.
This model is the first of its kind, since the demands on biological information is quite high and the system is novel in its design. Especially the transmembrane kinase/endonuclease Ire1p is a remarkable feat of evolution. The system is also present in mammals in a sligthly modified form.