72 research outputs found
Optimal localization patterns in bacterial protein synthesis
In bacterium, the molecular compounds involved in
protein synthesis, messenger RNAs (mRNAs) and ribosomes, show marked
intracellular localization patterns. Yet a quantitative understanding of the
physical principles which would allow one to control protein synthesis by
designing, bioengineering, and optimizing these localization patterns is still
lacking. In this study, we consider a scenario where a synthetic modification
of mRNA reaction-diffusion properties allows for controlling the localization
and stoichiometry of mRNAs and polysomescomplexes of multiple
ribosomes bound to mRNAs. Our analysis demonstrates that protein synthesis can
be controlled, e.g., optimally enhanced or inhibited, by leveraging mRNA
spatial localization and stoichiometry only, without resorting to alterations
of mRNA expression levels. We identify the physical mechanisms that control the
protein-synthesis rate, highlighting the importance of colocalization between
mRNAs and freely diffusing ribosomes, and the interplay between polysome
stoichiometry and excluded-volume effects due to the DNA nucleoid. The
genome-wide, quantitative predictions of our work may allow for a direct
verification and implementation in cell-biology experiments, where localization
patterns and protein-synthesis rates may be monitored by fluorescence
microscopy in single cells and populations
Non-perturbative effects in spin glasses
We present a numerical study of an Ising spin glass with hierarchical
interactions - the hierarchical Edwards-Anderson model with an external
magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in
the mean-field (MF) and non-mean-field (NMF) regions corresponding to
and for the -dimensional ferromagnetic Ising model respectively. We
compare the MC results with those of a renormalization-group (RG) study where
the critical fixed point is treated as a perturbation of the MF one, along the
same lines as in the -expansion for the Ising model. The MC and the
RG method agree in the MF region, predicting the existence of a transition and
compatible values of the critical exponents. Conversely, the two approaches
markedly disagree in the NMF case, where the MC data indicates a transition,
while the RG analysis predicts that no perturbative critical fixed point
exists. Also, the MC estimate of the critical exponent in the NMF region
is about twice as large as its classical value, even if the analog of the
system dimension is within only from its upper-critical-dimension
value. Taken together, these results indicate that the transition in the NMF
region is governed by strong non-perturbative effects
A renormalization group computation of the critical exponents of hierarchical spin glasses
The infrared behaviour of a non-mean field spin-glass system is analysed, and
the critical exponent related to the divergence of the correlation length is
computed at two loops within the epsilon-expansion technique with two
independent methods. Both methods yield the same result confirming that the
infrared behaviour of the theory if well-defined and the underlying ideas of
the Renormalization Group hold also in such non-mean field disordered model. By
pushing such calculation to high orders in epsilon, a consistent and predictive
non-mean field theory for such disordered system could be established
Free-energy bounds for hierarchical spin models
In this paper we study two non-mean-field spin models built on a hierarchical
lattice: The hierarchical Edward-Anderson model (HEA) of a spin glass, and
Dyson's hierarchical model (DHM) of a ferromagnet. For the HEA, we prove the
existence of the thermodynamic limit of the free energy and the
replica-symmetry-breaking (RSB) free-energy bounds previously derived for the
Sherrington-Kirkpatrick model of a spin glass. These RSB mean-field bounds are
exact only if the order-parameter fluctuations (OPF) vanish: Given that such
fluctuations are not negligible in non-mean-field models, we develop a novel
strategy to tackle part of OPF in hierarchical models. The method is based on
absorbing part of OPF of a block of spins into an effective Hamiltonian of the
underlying spin blocks. We illustrate this method for DHM and show that,
compared to the mean-field bound for the free energy, it provides a tighter
non-mean-field bound, with a critical temperature closer to the exact one. To
extend this method to the HEA model, a suitable generalization of Griffith's
correlation inequalities for Ising ferromagnets is needed: Since correlation
inequalities for spin glasses are still an open topic, we leave the extension
of this method to hierarchical spin glasses as a future perspective
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