119 research outputs found
Mathematical model of SARS-Cov-2 propagation versus ACE2 fits COVID-19 lethality across age and sex and predicts that of SARS, supporting possible therapy
The fatality rate of Covid-19 escalates with age and is larger in men than
women. I show that these variations correlate strongly with the level of the
viral receptor protein ACE2 in rat lungs, which is consistent with the still
limited and apparently contradictory data on human ACE2. Surprisingly, lower
levels of the receptor correlate with higher fatality. However, a previous
mathematical model predicts that the speed of viral progression in the organism
has a maximum and then declines with the receptor level. Moreover, many
manifestations of severe CoViD-19, such as severe lung injury, exacerbated
inflammatory response and thrombotic problems may derive from increased
Angiotensin II (Ang-II) level that results from degradation of ACE2 by the
virus. I present here a mathematical model based on the influence of ACE2 on
viral propagation and disease severity. The model fits Covid-19 fatality rate
across age and sex with high accuracy () under the hypothesis that
SARS-CoV-2 infections are in the dynamical regimes in which increased receptor
slows down viral propagation. Moreover, rescaling the model parameters by the
ratio of the binding rates of the spike proteins of SARS-CoV and SARS-CoV-2
allows predicting the fatality rate of SARS-CoV across age and sex, thus
linking the molecular and epidemiological levels. The presented model opposes
the fear that angiotensin receptor blockers (ARB), suggested as a therapy
against the most adverse effects of CoViD-19, may favour viral propagation, and
suggests that Ang-II and ACE2 are candidate prognostic factors for detecting
population that needs stronger protection.Comment: 1 figur
Structurally constrained protein evolution: results from a lattice simulation
We simulate the evolution of a protein-like sequence subject to point
mutations, imposing conservation of the ground state, thermodynamic stability
and fast folding. Our model is aimed at describing neutral evolution of natural
proteins. We use a cubic lattice model of the protein structure and test the
neutrality conditions by extensive Monte Carlo simulations. We observe that
sequence space is traversed by neutral networks, i.e. sets of sequences with
the same fold connected by point mutations. Typical pairs of sequences on a
neutral network are nearly as different as randomly chosen sequences. The
fraction of neutral neighbors has strong sequence to sequence variations, which
influence the rate of neutral evolution. In this paper we study the
thermodynamic stability of different protein sequences. We relate the high
variability of the fraction of neutral mutations to the complex energy
landscape within a neutral network, arguing that valleys in this landscape are
associated to high values of the neutral mutation rate. We find that when a
point mutation produces a sequence with a new ground state, this is likely to
have a low stability. Thus we tentatively conjecture that neutral networks of
different structures are typically well separated in sequence space. This
results indicates that changing significantly a protein structure through a
biologically acceptable chain of point mutations is a rare, although possible,
event.Comment: added reference, to appear on European Physical Journal
Can Conformational Changes of Proteins Be Represented in Torsion Angle Space? A Study with Rescaled Ridge Regression
Torsion angles are the natural degrees of freedom of protein structures. The ability to determine torsional variations corresponding to observed changes in Cartesian coordinates is highly valuable, notably to investigate the mechanisms of functional conformational changes or to develop computational models of protein dynamics. This issue is far from trivial in practice since the impact of modifying one torsion angle strongly depends on all other angles, and the compounding effects of small variations in bond lengths and valence angles can completely disrupt a protein fold. We demonstrate that naive strategies, such as directly comparing torsion angles between structures without correcting for variations in bond lengths and valence angles or fitting torsional variations without a proper regularization scheme, fail at producing an adequate representation of conformational changes in internal coordinates. In contrast, rescaled ridge regression, a method recently introduced to regularize multidimensional regressions with correlated explanatory variables, is shown to consistently identify a minimal set of torsion angles variations that closely reproduce changes in Cartesian coordinates. This torsional representation of conformational changes is shown to be robust to the choice of experimental structures. It also provides a better agreement with theoretical models of protein dynamics than the Cartesian representation, regarding notably the predominance of low-frequency normal modes in functional motions and the presence, in predicted equilibrium dynamics, of hints of natural selection for specific functional motions. The software is available at https://github.com/ugobas/tnm.Ministery of Economy, grant BIO2016-79043-P. Research at the CBMSO is facilitated by the Fundacion Ramon Arece
Replica-symmetry breaking in dynamical glasses
Systems of globally coupled logistic maps (GCLM) can display complex
collective behaviour characterized by the formation of synchronous clusters. In
the dynamical clustering regime, such systems possess a large number of
coexisting attractors and might be viewed as dynamical glasses. Glass
properties of GCLM in the thermodynamical limit of large system sizes are
investigated. Replicas, representing orbits that start from various initial
conditions, are introduced and distributions of their overlaps are numerically
determined. We show that for fixed-field ensembles of initial conditions, as
used in previous numerical studies, all attractors of the system become
identical in the thermodynamical limit up to variations of order
because the initial value of the coupling field is characterized by vanishing
fluctuations, and thus replica symmetry is recovered for . In
contrast to this, when random-field ensembles of initial conditions are chosen,
replica symmetry remains broken in the thermodynamical limit.Comment: 19 pages, 18 figure
Biodiversity in model ecosystems, II: Species assembly and food web structure
This is the second of two papers dedicated to the relationship between
population models of competition and biodiversity. Here we consider species
assembly models where the population dynamics is kept far from fixed points
through the continuous introduction of new species, and generalize to such
models thecoexistence condition derived for systems at the fixed point. The
ecological overlap between species with shared preys, that we define here,
provides a quantitative measure of the effective interspecies competition and
of the trophic network topology. We obtain distributions of the overlap from
simulations of a new model based both on immigration and speciation, and show
that they are in good agreement with those measured for three large natural
food webs. As discussed in the first paper, rapid environmental fluctuations,
interacting with the condition for coexistence of competing species, limit the
maximal biodiversity that a trophic level can host. This horizontal limitation
to biodiversity is here combined with either dissipation of energy or growth of
fluctuations, which in our model limit the length of food webs in the vertical
direction. These ingredients yield an effective model of food webs that produce
a biodiversity profile with a maximum at an intermediate trophic level, in
agreement with field studies
Statistical properties of neutral evolution
Neutral evolution is the simplest model of molecular evolution and thus it is
most amenable to a comprehensive theoretical investigation. In this paper, we
characterize the statistical properties of neutral evolution of proteins under
the requirement that the native state remains thermodynamically stable, and
compare them to the ones of Kimura's model of neutral evolution. Our study is
based on the Structurally Constrained Neutral (SCN) model which we recently
proposed. We show that, in the SCN model, the substitution rate decreases as
longer time intervals are considered, and fluctuates strongly from one branch
of the evolutionary tree to another, leading to a non-Poissonian statistics for
the substitution process. Such strong fluctuations are also due to the fact
that neutral substitution rates for individual residues are strongly correlated
for most residue pairs. Interestingly, structurally conserved residues,
characterized by a much below average substitution rate, are also much less
correlated to other residues and evolve in a much more regular way. Our results
could improve methods aimed at distinguishing between neutral and adaptive
substitutions as well as methods for computing the expected number of
substitutions occurred since the divergence of two protein sequences.Comment: 17 pages, 11 figure
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