An algorithmic framework for genome-wide modeling and analysis of translation networks - PubMed (original) (raw)

An algorithmic framework for genome-wide modeling and analysis of translation networks

Amit Mehra et al. Biophys J. 2006.

Abstract

The sequencing of genomes of several organisms and advances in high throughput technologies for transcriptome and proteome analysis has allowed detailed mechanistic studies of transcription and translation using mathematical frameworks that allow integration of both sequence-specific and kinetic properties of these fundamental cellular processes. To understand how perturbations in mRNA levels affect the synthesis of individual proteins within a large protein synthesis network, we consider here a genome-scale codon-wide model of the translation machinery with explicit description of the processes of initiation, elongation, and termination. The mechanistic codon-wide description of the translation process and the large number of mRNAs competing for resources, such as ribosomes, requires the use of novel efficient algorithmic approaches. We have developed such an efficient algorithmic framework for genome-scale models of protein synthesis. The mathematical and computational framework was applied to the analysis of the sensitivity of a translation network to perturbation in the rate constants and in the mRNA levels in the system. Our studies suggest that the highest specific protein synthesis rate (protein synthesis rate per mRNA molecule) is achieved when translation is elongation-limited. We find that the mRNA species with the highest number of actively translating ribosomes exerts maximum control on the synthesis of every protein, and the response of protein synthesis rates to mRNA expression variation is a function of the strength of initiation of translation at different mRNA species. Such quantitative understanding of the sensitivity of protein synthesis to the variation of mRNA expression can provide insights into cellular robustness mechanisms and guide the design of protein production systems.

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Figures

FIGURE 1

FIGURE 1

Schematic of the translational machinery. Translation comprises three key steps: initiation, elongation, and termination. The value n is the length of the mRNA template; γ and β are the scaled initiation and termination rate constants, respectively; λ is the ribosomal binding affinity; and L is the number of codons occupied by a ribosome.

FIGURE 2

FIGURE 2

The objective of the outer problem, formula image is a convex function of the fraction of free ribosomes, r. Convexity of the objective allows use of bisection method to estimate the fraction of free ribosomes.

FIGURE 3

FIGURE 3

Diagrammatic description of the bilevel algorithmic framework.

FIGURE 4

FIGURE 4

Distribution of sensitivities of protein synthesis rates from all mRNA species to their initiation (a), elongation (b), and termination (c) rate constants, respectively.

FIGURE 5

FIGURE 5

The elongation-limited mRNA species have higher protein synthesis rates than the initiation-limited mRNA species. (a) Sensitivity of the protein synthesis rates from every mRNA species to their initiation (+), elongation (□), and termination (•) rate constants as a function of ribosome density, ρ (the fraction of the mRNA covered by ribosomes). (b) Specific scaled protein synthesis rates from every mRNA species as a function of ribosome density, ρ.

FIGURE 6

FIGURE 6

Distribution of fold changes in protein synthesis rate from unperturbed mRNA species in response to (a) overexpression by fivefold of the mRNA species with low expression levels, and (b) underexpression by fivefold of the mRNA species with high expression levels.

FIGURE 7

FIGURE 7

Distribution of relative changes in the number of free ribosomes to changes in mRNA concentration estimated by increasing (a) or decreasing (b) the number of copies of each mRNA species by 1. (c) Relative changes in number of free ribosomes to increase (□) or decrease (×) in mRNA concentration is a linear function of the number of ribosomes associated with each mRNA.

FIGURE 8

FIGURE 8

Relative changes in the rates of protein synthesis from all unperturbed mRNAs,

formula image

as a function of the polysome size of the perturbed mRNA species. The perturbations correspond to an increase in the number of an individual mRNA species by one copy.

FIGURE 9

FIGURE 9

Relative changes in rate of protein synthesis from all mRNA species (a), and relative changes in the polysome size of each mRNA species (b), in response to a change in the concentration of the mRNA species with highest polysome size are a function of the scaled initiation rate constant, γ. Relative changes are calculated by increasing (I, ○) or decreasing (II, ⋄) the number of the mRNA species with highest polysome size by one copy. The ribosome density of each mRNA species is an increasing function of its scaled initiation rate constant, γ (c).

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