Generation of RNA pseudoknot structures with topological genus filtration

In this paper we present a sampling framework for RNA structures of fixed topological genus. We introduce a novel, linear time, uniform sampling algorithm for RNA structures of fixed topological genus g  , for arbitrary g>0$g>0$. Furthermore we develop a linear time sampling algorithm for RNA structures of fixed topological genus g   that are weighted by a simplified, loop-based energy functional. For this process the partition function of the energy functional has to be computed once, which has O(n²)$O(n^2)$ time complexity.     

Projected US distributions of transgenic and wildtype zebra danios, Danio rerio, based on temperature tolerance data

A genetically modified version of the south Asian, zebra danio, Danio rerio, a common aquarium fish, has become the first transgenic pet sold in the USA. Mean chronic lethal maxima of wildtype (39.8 °C, n=16$n=16$) and transgenic (39.3 °C, n=10$n=10$) zebra danios initially acclimated to 30 °C were statistically (but not dramatically) different as were mean chronic lethal minima of wildtype (5.3 °C, n=16$n=16$) and transgenic (5.6 °C, n=20$n=20$) zebra danios initially acclimated to 20 °C. These temperature tolerance values were used to estimate potential geographic distributions of the two varieties in the USA. Distributions of these D. rerio varieties in the USA should not be limited by their upper temperature tolerances, and low-temperature tolerance data suggest that both varieties are capable of overwintering in some southern and western US waters.     

Ultrashort echo imaging of cyclically loaded rabbit patellar tendon

Tendinopathy affects individuals who perform repetitive joint motion. Magnetic resonance imaging (MRI) is frequently used to qualitatively assess tendon health, but quantitative evaluation of inherent MRI properties of loaded tendon has been limited. This study evaluated the effect of cyclic loading on _T2^?${T_2}^{?}$ values of fresh and frozen rabbit patellar tendons using ultra short echo (UTE) MRI. Eight fresh and 8 frozen rabbit lower extremities had MR scans acquired for tendon _T2^?${T_2}^{?}$ evaluation. The tendons were then manually cyclically loaded for 100 cycles to 45 N at approximately 1 Hz. The MR scanning was repeated to reassess the _T2^?${T_2}^{?}$ values. Analyses were performed to detect differences of tendon _T2^?${T_2}^{?}$ values between fresh and frozen samples prior to and after loading, and to detect changes of tendon _T2^?${T_2}^{?}$ values between the unloaded and loaded configurations. No difference of _T2^?${T_2}^{?}$ was found between the fresh and frozen samples prior to or after loading, p=0.8 and p  =0.1, respectively. The tendons had significantly shorter _T2^?${T_2}^{?}$ values, p  =0.023, and reduced _T2^?${T_2}^{?}$ variability, p  =0.04, after cyclic loading. Histologic evaluation confirmed no induced tendon damage from loading. Shorter _T2^?${T_2}^{?}$, from stronger spin–spin interactions, may be attributed to greater tissue organization from uncrimping of collagen fibrils and lateral contraction of the tendon during loading. Cyclic tensile loading of tissue reduces patellar tendon _T2^?${T_2}^{?}$ values and may provide a quantitative metric to assess tissue organization.     

Effects of lycopene supplementation on antioxidant status,oxidative stress,performance and carcass characteristics in heat-stressed Japanese quail

Lycopene, a carotenoid present predominantly in tomatoes, is one of the most efficient antioxidants. This experiment was conducted to evaluate the effects of dietary lycopene supplementation on performance, carcass characteristics, biomarkers of oxidative stress (malondialdehyde (MDA) and homocysteine), and concentrations of vitamins C, E, A, cholesterol, triglyceride, and glucose in Japanese quails (Coturnix coturnix Japonica) exposed to high-ambient temperature of 34 °C. Two hundred and forty Japanese quails (10 day-old) were randomly assigned to eight treatment groups consisting of 10 replicates of three birds. The birds were kept at a temperature-controlled room at 22 °C (Thermoneutral, TN groups) or 34 °C (for 12 h/day; 09.00 am–05.00 pm; Heat stress, HS groups). Birds were fed either a basal (control) diet (TN and HS) or the basal diet supplemented with 50, 100 or 200 mg of lycopene/kg of diet. Lycopene supplementation linearly increased feed intake (P=0.05$P=0.05$), live weight gain (P=0.01$P=0.01$), feed efficiency (P=0.01$P=0.01$) and cold carcass weight (P=0.01$P=0.01$) and yield (P=0.05$P=0.05$) under heat stress conditions but did not show the same effect at thermoneutral conditions (P>0.05$P>0.05$). The interaction Serum vitamin C, E, and A (P=0.01$P=0.01$) concentrations increased linearly in birds reared at high temperature while non-significant changes occurred at TN groups. Homocysteine level in serum and malondialdehyde (MDA) levels in serum, liver, and heart (P=0.001$P=0.001$) linearly decreased in all birds of both TN and HS groups as dietary lycopene supplementation increased. Heat stress-induced increase in serum cholesterol (P=0.01$P=0.01$), triglycerides (P=0.05$P=0.05$) and glucose (P=0.01$P=0.01$) concentrations were linearly reversed by lycopene supplementation. Supplementation of lycopene increased the HDL concentration whereas, the VLDL and LDL concentrations reduced with lycopene supplementation (P=0.01$P=0.01$, linear), particularly at a dietary concentration of 200 mg/kg. Lycopene could not be detected in control birds while a linear increase was observed in the sera of lycopene supplemented birds The results of the study indicate that lycopene supplementation attenuated the increase in oxidative stress and depletion in antioxidants caused by heat stress in Japanese quails.     

Rectal,telemetry pill and tympanic membrane thermometry during exercise heat stress

We compared the accuracy of an ingestible telemetry pill method of core temperature (T_c) measurement and an infrared tympanic membrane thermometer to values from a rectal thermistor during exercise-induced heat stress. Ten well-trained subjects completed four exercise trials consisting of 40 min constant-load exercise at 63% of maximum work rate followed by a 16.1 km time trial at 30 °C and 70% relative humidity. Temperature at rest was not different between the three methods of T_c measurement (T_re: 37.2±0.3 °C; T_p: 37.2±0.2 °C; T_ty: 37.1±0.3 °C; P=0.40$P=0.40$). Temperature rose continuously during the exercise period (ΔT_re: 2.2±0.5 °C; ΔT_p: 2.2±0.5 °C; ΔT_ty: 1.9±0.5 ±°C and there were no differences between T_re and T_p measurements at any time throughout exercise (P=0.32$P=0.32$). While there were no differences between T_re and T_ty after 10 min (P=0.11$P=0.11$) and 20 min (P=0.06$P=0.06$) of exercise, T_ty was lower than T_re after 30 min of exercise (P<0.01$P<0.01$) and remained significantly lower throughout the remainder of the exercise period. These results demonstrate that the telemetry pill system provides a valid measurement of trunk temperature during rest and exercise-induced thermal strain. T_ty was significantly lower than T_re when temperature exceeded 37.5 °C. However, whether these differences are due to selective brain cooling or imperfections in the tympanic membrane thermometer methodology remains to be determined.     

The Wall-stress Footprint of Blood Cells Flowing in Microvessels

It is well known that mechanotransduction of hemodynamic forces mediates cellular processes, particularly those that lead to vascular development and maintenance. Both the strength and space-time character of these forces have been shown to affect remodeling and morphogenesis. However, the role of blood cells in the process remains unclear. We investigate the possibility that in the smallest vessels blood’s cellular character of itself will lead to forces fundamentally different than the time-averaged forces usually considered, with fluctuations that may significantly exceed their mean values. This is quantitated through the use of a detailed simulation model of microvessel flow in two principal configurations: a diameter D=6.5$D=6.5$μ  m tube—a model for small capillaries through which red blood cells flow in single-file—and a D=12$D=12$μm tube—a model for a nascent vein or artery through which the cells flow in a confined yet chaotic fashion. Results in both cases show strong sensitivity to the mean flow speed U  . Peak stresses exceed their means by greater than a factor of 10 when U/D?10$U/D\mathrm{?}10$ s⁻¹, which corresponds to the inverse relaxation time of a healthy red blood cell. This effect is more significant for smaller D cases. At faster flow rates, including those more commonly observed under normal, nominally static physiological conditions, the peak fluctuations are more comparable with the mean shear stress. Implications for mechanotransduction of hemodynamic forces are discussed.     

Yule-generated trees constrained by node imbalance

The Yule   process generates a class of binary trees which is fundamental to population genetic models and other applications in evolutionary biology. In this paper, we introduce a family of sub-classes of ranked trees, called Ω-trees, which are characterized by imbalance of internal nodes. The degree of imbalance is defined by an integer 0≤ω$0\le \omega$. For caterpillars  , the extreme case of unbalanced trees, ω=0$\omega =0$. Under models of neutral evolution, for instance the Yule model, trees with small ω are unlikely to occur by chance. Indeed, imbalance can be a signature of permanent selection pressure, such as observable in the genealogies of certain pathogens. From a mathematical point of view it is interesting to observe that the space of Ω-trees maintains several statistical invariants although it is drastically reduced in size compared to the space of unconstrained Yule trees. Using generating functions, we study here some basic combinatorial properties of Ω-trees. We focus on the distribution of the number of subtrees with two leaves. We show that expectation and variance of this distribution match those for unconstrained trees already for very small values of ω.     

Epidemic dynamics on semi-directed complex networks

In this paper an SIS model for epidemic spreading on semi-directed networks is established, which can be used to examine and compare the impact of undirected and directed contacts on disease spread. The model is analyzed for the case of uncorrelated semi-directed networks, and the basic reproduction number _R0$R_0$ is obtained analytically. We verify that the _R0$R_0$ contains the outbreak threshold on undirected networks and directed networks as special cases. It is proved that if _R0<1$R_0<1$ then the disease-free equilibrium is globally asymptotically stable, otherwise the disease-free equilibrium is unstable and the unique endemic equilibrium exists, which is globally asymptotically stable. Finally the numerical simulations holds for these analytical results are given.     

On the Treewidths of Graphs of Bounded Degree

In this paper, we develop a new technique to study the treewidth of graphs with bounded degree. We show that the treewidth of a graph G = (V, E) with maximum vertex degree d is at most (1−Ce−4.06d)|V| for sufficiently large d, where C is a constant.     

Dominance of Deleterious Alleles Controls the Response to a Population Bottleneck

Population bottlenecks followed by re-expansions have been common throughout history of many populations. The response of alleles under selection to such demographic perturbations has been a subject of great interest in population genetics. On the basis of theoretical analysis and computer simulations, we suggest that this response qualitatively depends on dominance. The number of dominant or additive deleterious alleles per haploid genome is expected to be slightly increased following the bottleneck and re-expansion. In contrast, the number of completely or partially recessive alleles should be sharply reduced. Changes of population size expose differences between recessive and additive selection, potentially providing insight into the prevalence of dominance in natural populations. Specifically, we use a simple statistic, BR≡∑xipop1/∑xjpop2, where x _i represents the derived allele frequency, to compare the number of mutations in different populations, and detail its functional dependence on the strength of selection and the intensity of the population bottleneck. We also provide empirical evidence showing that gene sets associated with autosomal recessive disease in humans may have a B _R indicative of recessive selection. Together, these theoretical predictions and empirical observations show that complex demographic history may facilitate rather than impede inference of parameters of natural selection.     

Fast Label-Free Cytoskeletal Network Imaging in Living Mammalian Cells

We present a full-field technique that allows label-free cytoskeletal network imaging inside living cells. This noninvasive technique allows monitoring of the cytoskeleton dynamics as well as interactions between the latter and organelles on any timescale. It is based on high-resolution quantitative phase imaging (modified Quadriwave lateral shearing interferometry) and can be directly implemented using any optical microscope without modification. We demonstrate the capability of our setup on fixed and living Chinese hamster ovary cells, showing the cytoskeleton dynamics in lamellipodia during protrusion and mitochondria displacement along the cytoskeletal network. In addition, using the quantitative function of the technique, along with simulation tools, we determined the refractive index of a single tubulin microtubule to be n_tubu=2.36±0.6$n_{tubu}=2.36\pm 0.6$ at λ=527$\lambda =527$ nm.     

Quantitative Analysis of Three-Dimensional Fluorescence Localization Microscopy Data

Identifying the three-dimensional molecular organization of subcellular organelles in intact cells has been challenging to date. Here we present an analysis approach for three-dimensional localization microscopy that can not only identify subcellular objects below the diffraction limit but also quantify their shape and volume. This approach is particularly useful to map the topography of the plasma membrane and measure protein distribution within an undulating membrane.Single molecule localization microscopy (SMLM) (1–3) is a superresolution fluorescence microscopy technique that produces coordinate data for single molecule localizations with a precision of tens of nanometers in live and fixed cells. These methods have mainly been performed with total internal reflectance fluorescence microscopy and therefore have generated two-dimensional molecular coordinates. Such two-dimensional data sets have revealed nanosized clusters of membrane proteins at the cell surface (4–7). This was achieved with analysis routines based on pair-correlation analysis (8), Ripley’s K function (9), and related techniques. While three-dimensional localization microscopy techniques such as biplane imaging (10), astigmatic spot analysis (11), and depth-encoding point-spread functions (12) have now been developed, quantitative analysis approaches of three-dimensional coordinate patterns have not.Here, we describe an approach based on Getis and Franklin''s local point pattern analysis to quantitatively analyze three-dimensional subcellular structures and map plasma membrane topography. The latter can also be used to account for topography-induced clustering of membrane proteins in an undulating membrane. To illustrate the approach, we generated three-dimensional SMLM data of the membrane dye DiI and the protein Linker for Activation of T cells (LAT) fused to the photoswitchable fluorescent protein mEos2 in T cells. It has been previously shown that LAT resides within the plasma membrane as well as membrane-proximal vesicles (5,13). The data were acquired using the biplane SMLM technique and highly inclined and laminated optical sheet illumination (14). Three-dimensional molecular coordinates were calculated by fitting a three-dimensional theoretical point-spread-function to the acquired data.As previously described for two-dimensional SMLM data analysis (5), Ripley’s K-function is calculated according to Eq. 1 where V is the analyzed volume, n is the total number of points, and r is the radius of a sphere (a circle for the two-dimensional case) centered on each point. The value K(r) is thus a measure of how many points are encircled within a sphere of radius r:K(r)=V∑i=1n∑j=1n(δij/n2);δij=1ifd(pointi,pointj)<r,0else.(1)For completely spatially random (CSR) data, K(r) scales with the volume of the sphere. We therefore linearize the K-function such that it scales with radius (the L-function) using:L(r)=(3K(r)4π)1/3.(2)The value of L(r)−r is then zero for the CSR case. Values of L(r)−r above zero indicate clustering at the length scale, r.Next we used the related Getis and Franklin''s local point pattern analysis to generate a clustering value (L(r) at r = 50 nm; L(50)) for each point, j, based on the local three-dimensional molecular density. This was calculated using:Lj(50)=((3V4π)∑i=1n(δijn))1/3;δij=1ifd(pointi,pointj)<50,0else.(3)These values can then be interpolated such that every voxel in a volume is assigned a cluster value based on the number of encircled points, relative to the expected CSR case. This allows construction of isosurfaces where all points on the surface have an identical L(50) value. A high threshold imparts a strict criterion for cluster detection compared to a lower one, and this allows users to, for example, determine the efficiency of sequestration into clusters by quantifying the cluster number and size as a function of the threshold.To illustrate the identification of subcellular structures, Lat-mEos2 was imaged by three-dimensional SMLM in activated T cells at the immunological synapse (Fig. 1 A). Three-dimensional projections of isosurfaces (for L(50) = 200) clearly identified intracellular LAT vesicles at varying depths within the synapse (Fig. 1, B and C). Cluster statistics were extracted from this data set to quantify the distribution of clusters in the z direction as well as the volume and sphericity of the LAT objects themselves (Fig. 1, D–F).Open in a separate windowFigure 1Identification of subcellular objects in three dimensions by isosurface rendering of molecular distribution. (A) Schematic of a T cell synapse formed against an activating coverslip where subsynaptic LAT vesicles (red dots) can be imaged with three-dimensional SMLM. (B and C) Isosurfaces, shown in x,z view (B) and as projection (C), identify T cell vesicles as LAT objects with L(50) > 200 (Eq. 3). (D–F) Distribution of LAT objects in z direction (D), volume (E), and sphericity (F) of LAT objects in T cells.Membrane undulations can cause clustering artifacts when the distribution of membrane proteins is recorded as a two-dimensional projection (15) (Fig. 2 A), as is the case in two-dimensional SMLM under total internal reflectance fluorescence illumination. To illustrate a solution to this problem, we obtained three-dimensional SMLM data sets of the membrane dye DiI (16) in resting T cells adhered onto nonactivating coverslips. With appropriately short labeling times to prevent dye internalization, it can be assumed that all DiI molecules reside in the plasma membrane. In this case, as is the case for plasma membrane proteins, neither two-dimensional nor three-dimensional analysis is appropriate, as it is a priori known the points must be derived from a two-dimensional membrane folded in three-dimensional space. To correct for membrane undulations, the plasma membrane topography must first be mapped so that molecular coordinates of membrane molecules can be appropriately corrected in two-dimensional projections. The position of the plasma membrane in three dimensions, i.e., the membrane topography, was determined by averaging the z position of all DiI molecules within a 100-nm radius in x-y at each point. The averaged z-position of DiI molecules was then displayed as a map, which exhibits a smooth, undulating profile (Fig. 2 B). The selection of this radius determines the accuracy of the assigned z position but also causes smoothing of the membrane profile.Open in a separate windowFigure 2Mapping of membrane topography and correction of molecular distributions in undulating membranes. (A) Two-dimensional projections can cause cluster artifacts, for example in membrane ruffles. Molecules (red rectangles) in the upper image are equally spaced along the membrane but appear as clusters in two-dimensional projections in areas with high gradient. (B) Three-dimensional membrane topography of a 2 × 2 μm plasma membrane area of a resting T cell obtained from averaged z positions of DiI molecules. Note that membrane undulation is ∼100 nm. (C) Map of membrane gradient, corresponding to the topography map shown in panel B, with an area of high gradient highlighted (dashed red box). (D) Correction of the circle radii in the Getis and Franklin cluster map calculations to account for projection artifacts. (E and F) Cluster map of data shown in panel C before (E) and after (F) correction for membrane gradient. Boxes in panels C, E, and F highlight the regions with high membrane gradient.Next, the gradient at the position of each DiI molecule was determined and interpolated into a gradient map (Fig. 2 C). Here, blue represents horizontal, i.e., flat membrane areas, whereas red regions indicate areas of high gradient. The information from the gradient map was then used to ensure that the two-dimensional circles in the Getis and Franklin cluster map calculations each correspond to an identical area of membrane, hence accounting for two-dimensional projection artifacts. To do this, the size of the circle (r) used to calculate the L value for each molecule was modified using Eq. 4, where c is calculated for the surface, S, using Eq. 5:r(corr)=r(uncorr)(1+c2)1/4,(4)c=((∂S∂x)2+(∂S∂y)2)1/2.(5)This operation is shown schematically in Fig. 2. The comparison of Getis and Franklin cluster maps before (Fig. 2 E) and after (Fig. 2 F) correction for the gradient shows that cluster values for DiI molecules were substantially reduced by up to 5–10% at sites where the plasma membrane had a high gradient (area highlighted in red box), and where the two-dimensional projection of three-dimensional structures caused an overestimation of clustering.In conclusion, we demonstrated that three-dimensional superresolution localization microscopy data can be used to identify and quantify subcellular structures. The approach has the distinct advantage that subcellular structures are solely identified by the distribution of the fluorescent marker so that no a priori knowledge of the structure is necessary. How precisely the subcellular structures are identified only depends on how efficiently the fluorescent maker is recruited to the structure, and hence does not depend on the resolution limits of optical microscopy. We applied the methods to two very different structures in T cells: small intracellular vesicles and the undulating plasma membrane. Importantly, the topography of plasma membrane can also be used to correct clustering artifacts in two-dimensional projections, which may be useful for distribution analysis within membranes.     

The limitations,dangers, and benefits of simple methods for testing identifiability

In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading) have commented on our paper in which we proposed a simple scaling method to test structural identifiability. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries. We agree with the limitations raised by these authors but, also, we emphasize that the method is still valuable for its applicability to a wide variety of models, its simplicity, and even as a tool to introduce the problem of identifiability to investigators with little training in mathematics.

In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading [1]) have commented on our paper in which we proposed a simple scaling method to test structural identifiability [2]. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries (we indeed indicated but not investigated the importance of generalizing the method to other symmetries). Thus, we agree that our simple method provides a necessary but not sufficient condition for identifiability, and we appreciate their careful analysis and constructive criticism.We nevertheless think that the simple method remains useful because it is so simple. Even for investigators with little training in mathematics, the method provides a necessary condition for structural identifiability that can be derived in a few minutes with pen and paper. Similarly, we have found its pedagogic strength by teaching the method to our own graduate students and colleagues. More advanced methods (such as STRIKE-GOLDD [3,4], COMBOS [5], or SIAN [6]) are typically intimidating for researchers with a background in Biology or Bioinformatics. This simple method can help those practitioners to familiarize themselves with the identifiability problem and better understand their models.Finally, it is worth noting that if scaling invariance is the only symmetry (as it was in all the cases we analyzed), our SIM remains valuable (albeit uncontrolled), and surprisingly effective for a wide variety of problems (as the extensive list collected in the Supplementary Material our paper [2]). We guess that the SIM especially fails when applied to linear models (as more potential rotations of the variables leave the system invariant), and in non-linear scenarios where some parameters are identical. For instance, the FitzHugh-Nagumo model raised by Villaverde and Massonis, x˙1(t)=c(x1(t)−x13(t)3−x2(t)+d),x˙2(t)=1c(x1(t)+a−b·x2(t)),y(t)=x1(t), could have been written as x˙1(t)=λ1x1(t)−λ2x13(t)3−λ3x2(t)+d,x˙2(t)=λ4x1(t)+a−b·x2(t),y(t)=x1(t) where λ₁ = λ₂ = λ₃ = 1/λ₄ = c. One of the reasons why our method fails, in this case, might be these additional symmetries introduced in this more elaborate notation of the model.Hence, it is worth understanding generic conditions under which the SIM method is expected to be fragile, possibly using STRIKE-GOLDD to test large families of nonlinear models.As a final remark, we appreciate that Villaverde and Massonis have shared their source code, so researchers might have a gold standard to test identifiability.