76 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
Reply to comment on 'Real-space renormalization-group methods for hierarchical spin glasses'
In their comment, Angelini et al. object to the conclusion of [J. Phys. A:
Math. Theor., 52:445002, 2019] (1), where we show that in [Phys. Rev. B,
87:134201, 2013] the exponent has been obtained by applying a
mathematical relation in a regime where this relation is not valid. We observe
that the criticism above on the mathematical validity of such relation has not
been addressed in the comment. Our criticism thus remains valid, and disproves
the conclusions of the comment. This constitutes the main point of this reply.
We also provide a point-by-point response and discussion of Angelini et al.'s
claims. First, Angelini et al. claim that the prediction of [1]
is incorrect, because it results from the relation between the largest eigenvalue of the linearized
renormalization-group (RG) transformation and , which cannot be applied to
the ensemble renormalization group (ERG) method, because for the ERG
. However, the feature is specific
to the ERG transformation and it does not give any grounds for questioning the
validity of the general relation specifically for
the ERG transformation. Second, Angelini et al. claim that should be
extracted from an early RG regime (A), as opposed to the asymptotic regime (B)
used to estimate in [1] and that (B) is dominated by finite-size effects.
Still, (A) is a small-wavelength, non-critical regime, which cannot
characterize the critical exponent related to the divergence of the
correlation length. Also, the fact that (B) involves finite-size effects is a
feature specific to the ERG, and gives no rationale for extracting from
(A).
Finally, we refute the remaining claims made by Angelini et al., and thus
stand by our assertion that the ERG method yields a prediction given by
.Comment: Reply to arXiv:1911.0232
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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