Supplemental material for the paper : Noise analysis of genome-scale protein synthesis using a discrete computational model of translation

aLaboratory of Computational Systems Biotechnology, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland bSwiss Institute of Bioinformatics (SIB), CH-1015 Lausanne, Switzerland cCurrent address: Computational Cancer Biology Lab, Ludwig Center for Cancer Research, University of Lausanne, CH-1066 Epalinges, Switzerland dCurrent address: Via Loreto 24, CH-6900 Lugano, Switzerland


FIGURE S2 Runtime of the simulations. (a) Comparison of the runtime using
Gillespie's optimized direct method or our stochastic translation algorithmthese simulations were implemented in MATLAB.Five simulations with randomly selected genes were performed for each value of total mRNA copy number.(b) The runtime with our stochastic translation algorithm, for simulations optimized in C++, scales only linearly with the total number of mRNA copies present.(The coefficient of determination R 2 of the linear fitting is 0.97).The simulations were performed on Mac Pro computer, with a 2 x 2.93 GHz Quad-Core Intel Xeon processor, on a C++ implementation of the algorithm that was not parallelized.The final time in these simulations was taken as 1000 seconds.

FIGURE S3
Synthesis rate profiles for suboptimal conditions.Similar profiles to Fig. 3 are shown but for conditions of initiation/termination rate constants that are suboptimal.See Fig. 3 for a description of the legend.Parameter values used for the simulations for these profiles are given in Table S1.

FIGURE S4
Estimating protein abundances and noise on the protein abundance.The simulations are performed as described in Appendix A, and assuming the translation profiles of the genes are the optimal ones (Fig. 3).
(a-b) Protein abundance (a) and coefficient of variation (b) versus the ribosomal density of the mRNA, for a protein with a half-life of 20 minutes.
(c) Coefficient of variation for proteins with different half-lives, assuming their mRNA is translated at a ribosomal density of 0.2.

FIGURE S5 Evolution of the instantaneous ribosomal density, with
parameters giving maximal synthesis rate (blue curve, r = 0.76 ) or suboptimal parameters (green curve, r = 0.69 ).

Figure S6
Comparing the results with a background pool of genes or without.(a) Distribution of the number of free ribosomes during the evolution of the two background pools of genes.(b) Protein synthesis rates when the "marker" gene is isolated or competing with a background pool of genes using two different backgrounds; results are showed for various mean ribosomal densities of the "marker" gene (indicated on the x-axis).Note that for the simulations with the marker gene observed in isolation, a constant number of 17670 free ribosomes was used.

FIGURE S7
Probability distribution of the specific synthesis rates at various densities and resulting distribution after a change of 50% of the given input parameter (given in the legend at the right of each row).The mean densities for the unperturbed cases are given at the top of each column.

FIGURE S8
Probability distribution of the ribosomal densities at various mean densities and resulting distribution after a change of 50% of the given input parameter (given in the legend at the right of each row).The mean densities for the unperturbed cases are given at the top of each column.

FIGURE S12
Allowing for ribosomes unbinding from initiation site.The rates of translation initiation and reverse-initiation were simultaneously varied in order to keep the same average protein synthesis rates.The corresponding mean ribosomal densities and synthesis rates for 4 different cases are indicated on the figure.The left-most values of kI for each "line" denotes the minimal kI value needed to reach the given synthesis rate and ribosomal density (i.e. when k-I = 0).(a) Coefficient of variation on the rate for all ribosome binding events.(b) Coefficient of variation on the rate for the ribosome binding events that are followed by translation elongation (i.e. in (a) all events of initiation are recorded, even those that are followed by the ribosome unbinding from initiation site, while in (b) only the events of initiation that are followed by translation and protein synthesis are recorded).(c) Coefficient of variation on the rate of protein synthesis.(d) Mean initiation delay, i.e. delay during which the translation initiation site is occupied by a ribosome before this ribosome translated the first L codons of the mRNA, allowing for a new ribosome to bind (the delay reported here only accounts for the ribosomes that perform a full protein translation).(e) Mean translation delay, time needed by a ribosome to fully translate the protein, between the translation initiation event and translation termination.Table S1: Parameter values used for the main simulations without a background pool of genes in the case of optimal or suboptimal synthesis profiles.In these simulations the total number of free ribosomes was kept constant.tend describes the time until which the simulations where performed to compute the statistics of protein synthesis.See Table 1 and method section for the parameters definition.As the system is characterized by a single steady state at each parameter set, and the recording starts after the steady state was reached, each state is simulated with a single simulation with a late end-time (2  10 6 s) which is equivalent to doing for example 1000 repetitions of the simulations during 2  10 3 s.

FIGURE
FIGURE S9 Probability density value of the protein synthesis rate (a) and ribosomal densities (b) for various sets of parameters and after different changes on the given input parameters.The input parameters (initiation (1 st column), elongation (2 nd column) and termination (3 rd column) rate constants: kI, kE, kT) were varied one at a time by various amounts (±10, 50 and 90% with respect to the original values), and the resulting pdf value for the synthesis rate (a) and ribosomal densities (b) are presented.This was repeated for multiple sets of input parameters that gave rise to different mean ribosomal densities (the various rows of subfigures; the value of ribosomal density given on the left correspond to the mean ribosomal density with the original parameter value sets).

FIGURE
FIGURE S13Probability density functions of the instantaneous specific synthesis rates for our full model (model 1) and for three simpler models.Showing these distributions at various mean ribosomal densities as indicated in the titles.