Terasaki spiral ramps and intracellular diffusion

The sheet-like endoplasmic reticulum (ER) of eukaryotic cells has been found to be riddled with spiral dislocations, known as 'Terasaki ramps', in the vicinity of which the doubled bilayer membranes which make up ER sheets can be approximately modeled by helicoids. Here we analyze diffusion on a surface with locally helicoidal topological dislocations, and use the results to argue that the Terasaki ramps facilitate a highly efficient transport of water-soluble molecules within the lumen of the endoplasmic reticulum

Aggregation-fragmentation-diffusion model for trail dynamics

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one, and also one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail P(w)~w-γ for small weight w. We obtain the exponent γ analytically and find that it varies continuously with the two model parameters. The exponent γ can be positive or negative, so that in one range of parameters small-weight trails are abundant and in the complementary range they are rare

Outcome prediction in mathematical models of immune response to infection

Clinicians need to predict patient outcomes with high accuracy as early as possible after disease inception. In this manuscript, we show that patient-to-patient variability sets a fundamental limit on outcome prediction accuracy for a general class of mathematical models for the immune response to infection. However, accuracy can be increased at the expense of delayed prognosis. We investigate several systems of ordinary differential equations (ODEs) that model the host immune response to a pathogen load. Advantages of systems of ODEs for investigating the immune response to infection include the ability to collect data on large numbers of `virtual patients', each with a given set of model parameters, and obtain many time points during the course of the infection. We implement patient-to-patient variability $v$ in the ODE models by randomly selecting the model parameters from Gaussian distributions with variance $v$ that are centered on physiological values. We use logistic regression with one-versus-all classification to predict the discrete steady-state outcomes of the system. We find that the prediction algorithm achieves near $100\%$ accuracy for $v=0$, and the accuracy decreases with increasing $v$ for all ODE models studied. The fact that multiple steady-state outcomes can be obtained for a given initial condition, i.e. the basins of attraction overlap in the space of initial conditions, limits the prediction accuracy for $v>0$. Increasing the elapsed time of the variables used to train and test the classifier, increases the prediction accuracy, while adding explicit external noise to the ODE models decreases the prediction accuracy. Our results quantify the competition between early prognosis and high prediction accuracy that is frequently encountered by clinicians.Comment: 14 pages, 7 figure

Persistent stability of a chaotic system

We report that trajectories of a one-dimensional model for inertial particles in a random velocity field can remain stable for a surprisingly long time, despite the fact that the system is chaotic. We provide a detailed quantitative description of this effect by developing the large-deviation theory for fluctuations of the finite-time Lyapunov exponent of this system. Specifically, the determination of the entropy function for the distribution reduces to the analysis of a Schrödinger equation, which is tackled by semi-classical methods. The system has generic instability properties, and we consider the broader implications of our observation of long-term stability in chaotic systems

Persistent features of intermittent transcription

Single-cell RNA sequencing is a powerful tool for exploring gene expression heterogeneity, but the results may be obscured by technical noise inherent in the experimental procedure. Here we introduce a novel parametrisation of sc-RNA data, giving estimates of the probability of activation of a gene and its peak transcription rate, which are agnostic about the mechanism underlying the fluctuations in the counts. Applying this approach to single cell mRNA counts across different tissues of adult mice, we find that peak transcription levels are approximately constant across different tissue types, in contrast to the gene expression probabilities which are, for many genes, markedly different. Many genes are only observed in a small fraction of cells. An investigation of correlation between genes activities shows that this is primarily due to temporal intermittency of transcription, rather than some genes being expressed in specialised cell types. Both the probability of activation and the peak transcription rate have a very wide ranges of values, with a probability density function well approximated by a power law. Taken together, our results indicate that the peak rate of transcription is a persistent property of a gene, and that differences in gene expression are modulated by temporal intermittency of the transcription

Molecular methods for the genetic identification of salmonid prey from Pacific harbor seal (Phoca vitulina richardsi) scat

Twenty-six stocks of Pacific salmon and trout (Oncorhynchus spp.), representing evolutionary significant units (ESU), are listed as threatened or endangered under the Endangered Species Act (ESA) and six more stocks are currently being evaluated for listing. The ecological and economic consequences of these listings are large; therefore considerable effort has been made to understand and respond to these declining populations. Until recently, Pacific harbor seals (Phoca vitulina richardsi) on the west coast increased an average of 5% to 7% per year as a result of the Marine Mammal Protection Act of 1972 (Brown and Kohlman2). Pacific salmon are seasonally important prey for harbor seals (Roffe and Mate, 1984; Olesiuk, 1993); therefore quantifying and understanding the interaction between these two protected species is important for Morphobiologically sound management strategies. Because some Pacific salmonid species in a given area may be threatened or endangered, while others are relatively abundant, it is important to distinguish the species of salmonid upon which the harbor seals are preying. This study takes the first step in understanding these interactions by using molecular genetic tools for species-level identification of salmonid skeletal remains recovered from Pacific harbor seal scats

Optimal Filling of Shapes

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuristic for finding solutions of maximal discs. We consider the properties of ideal distributions of N discs as N approaches infinity. We note an analogy with energy landscapes.Comment: 5 page

Kinematics of the swimming of Spiroplasma

\emph{Spiroplasma} swimming is studied with a simple model based on resistive-force theory. Specifically, we consider a bacterium shaped in the form of a helix that propagates traveling-wave distortions which flip the handedness of the helical cell body. We treat cell length, pitch angle, kink velocity, and distance between kinks as parameters and calculate the swimming velocity that arises due to the distortions. We find that, for a fixed pitch angle, scaling collapses the swimming velocity (and the swimming efficiency) to a universal curve that depends only on the ratio of the distance between kinks to the cell length. Simultaneously optimizing the swimming efficiency with respect to inter-kink length and pitch angle, we find that the optimal pitch angle is 35.5$^\circ$ and the optimal inter-kink length ratio is 0.338, values in good agreement with experimental observations.Comment: 4 pages, 5 figure