Variability in mRNA translation: a random matrix theory approach

AbstractThe rate of mRNA translation depends on the initiation, elongation, and termination rates of ribosomes along the mRNA. These rates depend on many “local” factors like the abundance of free ribosomes and tRNA molecules in the vicinity of the mRNA molecule. All these factors are stochastic and their experimental measurements are also noisy. An important question is how protein production in the cell is affected by this considerable variability. We develop a new theoretical framework for addressing this question by modeling the rates as identically and independently distributed random variables and using tools from random matrix theory to analyze the steady-state production rate. The analysis reveals a principle of universality: the average protein production rate depends only on the of the set of possible values that the random variable may attain. This explains how total protein production can be stabilized despite the overwhelming stochasticticity underlying cellular processes.

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Implementing nonuniversal features with a random matrix theory approach: Application to space-to-configuration multiplexing

Physical Review E ◽

10.1103/physreve.102.010201 ◽

2020 ◽

Vol 102 (1) ◽

Cited By ~ 1

Author(s):

Philipp del Hougne ◽

Dmitry V. Savin ◽

Olivier Legrand ◽

Ulrich Kuhl

Keyword(s):

Random Matrix Theory ◽

Random Matrix ◽

Matrix Theory ◽

Theory Approach

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Texture classification from single uncalibrated images: Random matrix theory approach

2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP) ◽

10.1109/mlsp.2017.8168115 ◽

2017 ◽

Author(s):

E. S. Nadimi ◽

J. Herp ◽

M. M. Buijs ◽

V. Blanes-Vidal

Keyword(s):

Random Matrix Theory ◽

Random Matrix ◽

Matrix Theory ◽

Texture Classification ◽

Theory Approach ◽

Uncalibrated Images

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Random matrix theory approach to vibrations near the jamming transition

JETP Letters ◽

10.1134/s0021364015050033 ◽

2015 ◽

Vol 101 (5) ◽

pp. 345-349 ◽

Cited By ~ 9

Author(s):

Y. M. Beltukov

Keyword(s):

Random Matrix Theory ◽

Random Matrix ◽

Matrix Theory ◽

Theory Approach ◽

Jamming Transition

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On the empirical spectral distribution for certain models related to sample covariance matrices with different correlations

Random Matrices Theory and Application ◽

10.1142/s2010326322500307 ◽

2021 ◽

Author(s):

Alicja Dembczak-Kołodziejczyk ◽

Anna Lytova

Keyword(s):

Random Matrix Theory ◽

Random Matrix ◽

Spectral Distribution ◽

Matrix Theory ◽

Random Variable ◽

Covariance Matrices ◽

Convergence In Probability ◽

Stat Phys ◽

Sample Covariance ◽

Arbitrary Space

Given [Formula: see text], we study two classes of large random matrices of the form [Formula: see text] where for every [Formula: see text], [Formula: see text] are iid copies of a random variable [Formula: see text], [Formula: see text], [Formula: see text] are two (not necessarily independent) sets of independent random vectors having different covariance matrices and generating well concentrated bilinear forms. We consider two main asymptotic regimes as [Formula: see text]: a standard one, where [Formula: see text], and a slightly modified one, where [Formula: see text] and [Formula: see text] while [Formula: see text] for some [Formula: see text]. Assuming that vectors [Formula: see text] and [Formula: see text] are normalized and isotropic “in average”, we prove the convergence in probability of the empirical spectral distributions of [Formula: see text] and [Formula: see text] to a version of the Marchenko–Pastur law and the so-called effective medium spectral distribution, correspondingly. In particular, choosing normalized Rademacher random variables as [Formula: see text], in the modified regime one can get a shifted semicircle and semicircle laws. We also apply our results to the certain classes of matrices having block structures, which were studied in [G. M. Cicuta, J. Krausser, R. Milkus and A. Zaccone, Unifying model for random matrix theory in arbitrary space dimensions, Phys. Rev. E 97(3) (2018) 032113, MR3789138; M. Pernici and G. M. Cicuta, Proof of a conjecture on the infinite dimension limit of a unifying model for random matrix theory, J. Stat. Phys. 175(2) (2019) 384–401, MR3968860].

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