10,439 research outputs found
Modelling protein localisation and positional information in subcellular systems
Cells and their component structures are highly organised. The correct function of
many biological systems relies upon not only temporal control of protein levels but
also spatial control of protein localisation within cells. Mathematical modelling allows
us to quantitatively test potential mechanisms for protein localisation and spatial
organisation. Here we present models of three examples of spatial organisation within
individual cells.
In the bacterium E. coli, the site of cell division is partly determined by the Min
proteins. The Min proteins oscillate between the cell poles and suppress formation of
the division ring here, thereby restricting division to midcell. We present a stochastic
model of the Min protein dynamics, and use this model to investigate partitioning of
the Min proteins between the daughter cells during cell division.
The Min proteins determine the correct position for cell division by forming a timeaveraged
concentration gradient which is minimal at midcell. Concentration gradients
are involved in a range of subcellular processes, and are particularly important for
obtaining positional information. By analysing the low copy number spatiotemporal
uctuations in protein concentrations for a single polar gradient and two oppositelydirected
gradients, we estimate the positional precision that can be achieved in vivo.
We nd that time-averaging is vital for high precision.
The embryo of the nematode C. elegans has become a model system for the study
of cell polarity. At the one-cell stage, the PAR proteins form anterior and posterior
domains in a dynamic process driven by contraction of cortical actomyosin. We
present a continuum model for this system, including a highly simpli ed model of the
actomyosin dynamics. Our model suggests that the known PAR protein interactions
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are insu cient to explain the experimentally observed cytoplasmic polarity. We discuss
a number of modi cations to the model which reproduce the correct cytoplasmic
distributions
Thermalization near integrability in a dipolar quantum Newton's cradle
Isolated quantum many-body systems with integrable dynamics generically do
not thermalize when taken far from equilibrium. As one perturbs such systems
away from the integrable point, thermalization sets in, but the nature of the
crossover from integrable to thermalizing behavior is an unresolved and
actively discussed question. We explore this question by studying the dynamics
of the momentum distribution function in a dipolar quantum Newton's cradle
consisting of highly magnetic dysprosium atoms. This is accomplished by
creating the first one-dimensional Bose gas with strong magnetic dipole-dipole
interactions. These interactions provide tunability of both the strength of the
integrability-breaking perturbation and the nature of the near-integrable
dynamics. We provide the first experimental evidence that thermalization close
to a strongly interacting integrable point occurs in two steps:
prethermalization followed by near-exponential thermalization. Exact numerical
calculations on a two-rung lattice model yield a similar two-timescale process,
suggesting that this is generic in strongly interacting near-integrable models.
Moreover, the measured thermalization rate is consistent with a parameter-free
theoretical estimate, based on identifying the types of collisions that
dominate thermalization. By providing tunability between regimes of integrable
and nonintegrable dynamics, our work sheds light both on the mechanisms by
which isolated quantum many-body systems thermalize, and on the temporal
structure of the onset of thermalization.Comment: 6 figures, 9 pages main text; 12 appendices with 12 figure
Dissipative Transport of a Bose-Einstein Condensate
We investigate the effects of impurities, either correlated disorder or a
single Gaussian defect, on the collective dipole motion of a Bose-Einstein
condensate of Li in an optical trap. We find that this motion is damped at
a rate dependent on the impurity strength, condensate center-of-mass velocity,
and interatomic interactions. Damping in the Thomas-Fermi regime depends
universally on the disordered potential strength scaled to the condensate
chemical potential and the condensate velocity scaled to the peak speed of
sound. The damping rate is comparatively small in the weakly interacting
regime, and the damping in this case is accompanied by strong condensate
fragmentation. \textit{In situ} and time-of-flight images of the atomic cloud
provide evidence that this fragmentation is driven by dark soliton formation.Comment: 14 pages, 20 figure
Ultracold Neutral Plasmas
Ultracold neutral plasmas, formed by photoionizing laser-cooled atoms near
the ionization threshold, have electron temperatures in the 1-1000 kelvin range
and ion temperatures from tens of millikelvin to a few kelvin. They represent a
new frontier in the study of neutral plasmas, which traditionally deals with
much hotter systems, but they also blur the boundaries of plasma, atomic,
condensed matter, and low temperature physics. Modelling these plasmas
challenges computational techniques and theories of non-equilibrium systems, so
the field has attracted great interest from the theoretical and computational
physics communities. By varying laser intensities and wavelengths it is
possible to accurately set the initial plasma density and energy, and
charged-particle-detection and optical diagnostics allow precise measurements
for comparison with theoretical predictions. Recent experiments using optical
probes demonstrated that ions in the plasma equilibrate in a strongly coupled
fluid phase. Strongly coupled plasmas, in which the electrical interaction
energy between charged particles exceeds the average kinetic energy, reverse
the traditional energy hierarchy underlying basic plasma concepts such as Debye
screening and hydrodynamics. Equilibration in this regime is of particular
interest because it involves the establishment of spatial correlations between
particles, and it connects to the physics of the interiors of gas-giant planets
and inertial confinement fusion devices.Comment: 89 pages, 54 image
Exploring the ferromagnetic behaviour of a repulsive Fermi gas via spin dynamics
Ferromagnetism is a manifestation of strong repulsive interactions between
itinerant fermions in condensed matter. Whether short-ranged repulsion alone is
sufficient to stabilize ferromagnetic correlations in the absence of other
effects, like peculiar band dispersions or orbital couplings, is however
unclear. Here, we investigate ferromagnetism in the minimal framework of an
ultracold Fermi gas with short-range repulsive interactions tuned via a
Feshbach resonance. While fermion pairing characterises the ground state, our
experiments provide signatures suggestive of a metastable Stoner-like
ferromagnetic phase supported by strong repulsion in excited scattering states.
We probe the collective spin response of a two-spin mixture engineered in a
magnetic domain-wall-like configuration, and reveal a substantial increase of
spin susceptibility while approaching a critical repulsion strength. Beyond
this value, we observe the emergence of a time-window of domain immiscibility,
indicating the metastability of the initial ferromagnetic state. Our findings
establish an important connection between dynamical and equilibrium properties
of strongly-correlated Fermi gases, pointing to the existence of a
ferromagnetic instability.Comment: 8 + 17 pages, 4 + 8 figures, 44 + 19 reference
Probing many-body dynamics on a 51-atom quantum simulator
Controllable, coherent many-body systems can provide insights into the
fundamental properties of quantum matter, enable the realization of new quantum
phases and could ultimately lead to computational systems that outperform
existing computers based on classical approaches. Here we demonstrate a method
for creating controlled many-body quantum matter that combines
deterministically prepared, reconfigurable arrays of individually trapped cold
atoms with strong, coherent interactions enabled by excitation to Rydberg
states. We realize a programmable Ising-type quantum spin model with tunable
interactions and system sizes of up to 51 qubits. Within this model, we observe
phase transitions into spatially ordered states that break various discrete
symmetries, verify the high-fidelity preparation of these states and
investigate the dynamics across the phase transition in large arrays of atoms.
In particular, we observe robust manybody dynamics corresponding to persistent
oscillations of the order after a rapid quantum quench that results from a
sudden transition across the phase boundary. Our method provides a way of
exploring many-body phenomena on a programmable quantum simulator and could
enable realizations of new quantum algorithms.Comment: 17 pages, 13 figure
The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems
There are numerous examples of morphogen gradients controlling long range signalling in developmental and cellular systems. The prospect of two such interacting morphogens instigating long range self-organisation in biological systems via a Turing bifurcation has been explored, postulated, or implicated in the context of numerous developmental processes. However, modelling investigations of cellular systems typically neglect the influence of gene expression on such dynamics, even though transcription and translation are observed to be important in morphogenetic systems. In particular, the influence of gene expression on a large class of Turing bifurcation models, namely those with pure kinetics such as the Gierer–Meinhardt system, is unexplored. Our investigations demonstrate that the behaviour of the Gierer–Meinhardt model profoundly changes on the inclusion of gene expression dynamics and is sensitive to the sub-cellular details of gene expression. Features such as concentration blow up, morphogen oscillations and radical sensitivities to the duration of gene expression are observed and, at best, severely restrict the possible parameter spaces for feasible biological behaviour. These results also indicate that the behaviour of Turing pattern formation systems on the inclusion of gene expression time delays may provide a means of distinguishing between possible forms of interaction kinetics. Finally, this study also emphasises that sub-cellular and gene expression dynamics should not be simply neglected in models of long range biological pattern formation via morphogens
Cloud fluid models of gas dynamics and star formation in galaxies
The large dynamic range of star formation in galaxies, and the apparently complex environmental influences involved in triggering or suppressing star formation, challenges the understanding. The key to this understanding may be the detailed study of simple physical models for the dominant nonlinear interactions in interstellar cloud systems. One such model is described, a generalized Oort model cloud fluid, and two simple applications of it are explored. The first of these is the relaxation of an isolated volume of cloud fluid following a disturbance. Though very idealized, this closed box study suggests a physical mechanism for starbursts, which is based on the approximate commensurability of massive cloud lifetimes and cloud collisional growth times. The second application is to the modeling of colliding ring galaxies. In this case, the driving processes operating on a dynamical timescale interact with the local cloud processes operating on the above timescale. The results is a variety of interesting nonequilibrium behaviors, including spatial variations of star formation that do not depend monotonically on gas density
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