65,026 research outputs found
Estimation in discretely observed diffusions killed at a threshold
Parameter estimation in diffusion processes from discrete observations up to
a first-hitting time is clearly of practical relevance, but does not seem to
have been studied so far. In neuroscience, many models for the membrane
potential evolution involve the presence of an upper threshold. Data are
modeled as discretely observed diffusions which are killed when the threshold
is reached. Statistical inference is often based on the misspecified likelihood
ignoring the presence of the threshold causing severe bias, e.g. the bias
incurred in the drift parameters of the Ornstein-Uhlenbeck model for biological
relevant parameters can be up to 25-100%. We calculate or approximate the
likelihood function of the killed process. When estimating from a single
trajectory, considerable bias may still be present, and the distribution of the
estimates can be heavily skewed and with a huge variance. Parametric bootstrap
is effective in correcting the bias. Standard asymptotic results do not apply,
but consistency and asymptotic normality may be recovered when multiple
trajectories are observed, if the mean first-passage time through the threshold
is finite. Numerical examples illustrate the results and an experimental data
set of intracellular recordings of the membrane potential of a motoneuron is
analyzed.Comment: 29 pages, 5 figure
Dwell time symmetry in random walks and molecular motors
The statistics of steps and dwell times in reversible molecular motors differ
from those of cycle completion in enzyme kinetics. The reason is that a step is
only one of several transitions in the mechanochemical cycle. As a result,
theoretical results for cycle completion in enzyme kinetics do not apply to
stepping data. To allow correct parameter estimation, and to guide data
analysis and experiment design, a theoretical treatment is needed that takes
this observation into account. In this paper, we model the distribution of
dwell times and number of forward and backward steps using first passage
processes, based on the assumption that forward and backward steps correspond
to different directions of the same transition. We extend recent results for
systems with a single cycle and consider the full dwell time distributions as
well as models with multiple pathways, detectable substeps, and detachments.
Our main results are a symmetry relation for the dwell time distributions in
reversible motors, and a relation between certain relative step frequencies and
the free energy per cycle. We demonstrate our results by analyzing recent
stepping data for a bacterial flagellar motor, and discuss the implications for
the efficiency and reversibility of the force-generating subunits. Key words:
motor proteins; single molecule kinetics; enzyme kinetics; flagellar motor;
Markov process; non-equilibrium fluctuations.Comment: revtex, 15 pages, 8 figures, 2 tables. v2: Minor revision, corrected
typos, added references, and moved mathematical parts to new appendice
Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation
We present computer-assisted methods for analyzing stochastic models of gene
regulatory networks. The main idea that underlies this equation-free analysis
is the design and execution of appropriately-initialized short bursts of
stochastic simulations; the results of these are processed to estimate
coarse-grained quantities of interest, such as mesoscopic transport
coefficients. In particular, using a simple model of a genetic toggle switch,
we illustrate the computation of an effective free energy and of a
state-dependent effective diffusion coefficient that characterize an
unavailable effective Fokker-Planck equation. Additionally we illustrate the
linking of equation-free techniques with continuation methods for performing a
form of stochastic "bifurcation analysis"; estimation of mean switching times
in the case of a bistable switch is also implemented in this equation-free
context. The accuracy of our methods is tested by direct comparison with
long-time stochastic simulations. This type of equation-free analysis appears
to be a promising approach to computing features of the long-time,
coarse-grained behavior of certain classes of complex stochastic models of gene
regulatory networks, circumventing the need for long Monte Carlo simulations.Comment: 33 pages, submitted to The Journal of Chemical Physic
Poliovirus intrahost evolution is required to overcome tissue-specific innate immune responses.
RNA viruses, such as poliovirus, have a great evolutionary capacity, allowing them to quickly adapt and overcome challenges encountered during infection. Here we show that poliovirus infection in immune-competent mice requires adaptation to tissue-specific innate immune microenvironments. The ability of the virus to establish robust infection and virulence correlates with its evolutionary capacity. We further identify a region in the multi-functional poliovirus protein 2B as a hotspot for the accumulation of minor alleles that facilitate a more effective suppression of the interferon response. We propose that population genetic dynamics enables poliovirus spread between tissues through optimization of the genetic composition of low frequency variants, which together cooperate to circumvent tissue-specific challenges. Thus, intrahost virus evolution determines pathogenesis, allowing a dynamic regulation of viral functions required to overcome barriers to infection.RNA viruses, such as polioviruses, have a great evolutionary capacity and can adapt quickly during infection. Here, the authors show that poliovirus infection in mice requires adaptation to innate immune microenvironments encountered in different tissues
Mechanism of unidirectional movement of kinesin motors
Kinesin motors have been studied extensively both experimentally and
theoretically. However, the microscopic mechanism of the processive movement of
kinesin is still an open question. In this paper, we propose a hand-over-hand
model for the processivity of kinesin, which is based on chemical, mechanical,
and electrical couplings. In the model the processive movement does not need to
rely on the two heads' coordination in their ATP hydrolysis and mechanical
cycles. Rather, the ATP hydrolyses at the two heads are independent. The much
higher ATPase rate at the trailing head than the leading head makes the motor
walk processively in a natural way, with one ATP being hydrolyzed per step. The
model is consistent with the structural study of kinesin and the measured
pathway of the kinesin ATPase. Using the model the estimated driving force of ~
5.8 pN is in agreements with the experimental results (5~7.5 pN). The
prediction of the moving time in one step (~10 microseconds) is also consistent
with the measured values of 0~50 microseconds. The previous observation of
substeps within the 8-nm step is explained. The shapes of velocity-load (both
positive and negative) curves show resemblance to previous experimental
results.Comment: 22 pages, 6 figure
A fast quantum interface between different spin qubit encodings
Single-spin qubits in semiconductor quantum dots proposed by Loss and
DiVincenzo (LD qubits) hold promise for universal quantum computation with
demonstrations of a high single-qubit gate fidelity above 99.9 % and two-qubit
gates in conjunction with a long coherence time. However, initialization and
readout of a qubit is orders of magnitude slower than control, which is
detrimental for implementing measurement-based protocols such as
error-correcting codes. In contrast, a singlet-triplet (ST) qubit, encoded in a
two-spin subspace, has the virtue of fast readout with high fidelity and
tunable coupling to the electric field. Here, we present a hybrid system which
benefits from the different advantages of these two distinct spin-qubit
implementations. A quantum interface between the two codes is realized by
electrically tunable inter-qubit exchange coupling. We demonstrate a
controlled-phase (CPHASE) gate that acts within 5.5 ns, much faster than the
measured dephasing time of 211 ns. The presented hybrid architecture will be
useful to settle remaining key problems with building scalable spin-based
quantum computers
High-fidelity single-shot readout for a spin qubit via an enhanced latching mechanism
The readout of semiconductor spin qubits based on spin blockade is fast but
suffers from a small charge signal. Previous work suggested large benefits from
additional charge mapping processes, however uncertainties remain about the
underlying mechanisms and achievable fidelity. In this work, we study the
single-shot fidelity and limiting mechanisms for two variations of an enhanced
latching readout. We achieve average single-shot readout fidelities > 99.3% and
> 99.86% for the conventional and enhanced readout respectively, the latter
being the highest to date for spin blockade. The signal amplitude is enhanced
to a full one-electron signal while preserving the readout speed. Furthermore,
layout constraints are relaxed because the charge sensor signal is no longer
dependent on being aligned with the conventional (2, 0) - (1, 1) charge dipole.
Silicon donor-quantum-dot qubits are used for this study, for which the dipole
insensitivity substantially relaxes donor placement requirements. One of the
readout variations also benefits from a parametric lifetime enhancement by
replacing the spin-relaxation process with a charge-metastable one. This
provides opportunities to further increase the fidelity. The relaxation
mechanisms in the different regimes are investigated. This work demonstrates a
readout that is fast, has one-electron signal and results in higher fidelity.
It further predicts that going beyond 99.9% fidelity in a few microseconds of
measurement time is within reach.Comment: Supplementary information is included with the pape
Global Control Methods for GHZ State Generation on 1-D Ising Chain
We discuss how to prepare an Ising chain in a GHZ state using a single global
control field only. This model does not require the spins to be individually
addressable and is applicable to quantum systems such as cold atoms in optical
lattices, some liquid- or solid-state NMR experiments, and many nano-scale
quantum structures. We show that GHZ states can always be reached
asymptotically from certain easy-to-prepare initial states using adiabatic
passage, and under certain conditions finite-time reachability can be ensured.
To provide a reference useful for future experimental implementations three
different control strategies to achieve the objective, adiabatic passage,
Lyapunov control and optimal control are compared, and their advantages and
disadvantages discussed, in particular in the presence of realistic
imperfections such as imperfect initial state preparation, system inhomogeneity
and dephasing.Comment: 13 pages, 11 figure
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