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Small is beautiful, and dry

Thousands of plant and animal species have been observed to have superhydrophobic surfaces that lead to various novel behaviors [1-5]. These observations have inspired attempts to create artificial superhydrophobic surfaces, given such surfaces have multitudinous applications [6-13]. Superhydrophobicity is an enhanced effect of surface roughness and there are known relationships that correlate surface roughness and superhydrophobicity, based on the underlying physics. However, while these recognize the level of roughness they tell us little about the independent effect of its scale. Thus, they are not capable of explaining why naturally occurring such surfaces commonly have micron-submicron sizes. Here we report on the discovery of a new relation, its physical basis and its experimental verification. The results reveal that scaling-down roughness into the micro-submicron range is a unique and elegant strategy to not only achieve superhydrophobicity but also to increase its stability against environmental disturbances. This new relation takes into account the previously overlooked but key fact that the accumulated line energy arising from the numerous solid-water-air intersections that can be distributed in the apparent contact area when air packets are trapped at small scales on the surface can dramatically increase as the roughness scale shrinks. This term can in fact become the dominant contributor to the surface energy and so becomes crucial for accomplishing superhydrophobicity. These findings guide fabrication of stable super water-repellant surfaces.

cond-mat.soft↗

The shade avoidance syndrome: a non-markovian stochastic growth model

Plants at high population density compete for light, showing a series of physiological responses known as the shade avoidance syndrome. These responses are controlled by the synthesis of the hormone auxin, which is regulated by two signals, an environmental one and an internal one. Considering that the auxin signal induces plant growth after a time lag, this work shows that plant growth can be modelled in terms of an energy-like function extremization, provided that the Markov property is not applied. The simulated height distributions are bimodal and right skewed, as in real community of plants. In the case of isolated plants, the theoretical expressions for the growth dynamics and the growth speed excellently fit experimental data for Arabidopsis thaliana. Moreover, the growth dynamics of this model is shown to be consistent with the biomass production function of an independent model. These results suggest that memory effects play a non-negligible role in plant growth processes.

q-bio.OT↗

BAK1 Gene Variation: the doubts remain

Dr. Hatchwell [2010] has proposed that the BAK1 gene variants were likely due to sequencing of a processed gene on chromosome 20. However, in response, Dr. Gottlieb and co-authors [2010] have argued that "some but not all of the sequence changes present in the BAK1 sequence of our abdominal aorta samples are also present in the chromosome 20 BAK1 sequence. However, all the AAA and AA cDNA samples are identical to each other and different from chromosome 20 BAK1 sequence at amino acids 2 and 145". I have been following this discussion because I have independently reached almost the same conclusion as Dr. Hatchwell did [Yamagishi, 2009], and, unfortunately, the response from Dr. Gottlieb and his co-authors seems to me to be unsatisfactory for the reasons listed below

q-bio.GN↗

The filling law: a general framework for leaf shape diversity and its consequences on folded leaves

Leaves are packed in a bud in different ways, being flat, enrolled, or folded, but always filling the whole bud volume. This « filling law » has many consequences, in particular on the shape of growing folded leaves. This is shown here for different types of folding and packing. The folded volume is always part of an ellipsoid, with the veins on the outside rounded face, and the lamina margin on an adaxial plane or axis. The veins on the abaxial side protect the more fragile lamina. The first general consequence of the folds is the presence of symmetries on the leaf shape, but also quantitative relationships between lobes and sinus sizes. For particular geometries, the leaf lamina can be limited by lateral veins, creating spoon-like lobes, or transverse cuts, creating asymmetrical wavy perimeters. A change in the packing between cultivars induces the corresponding change in the leaf shape. Each particular case shows how pervasive are the geometrical consequences of the filling law.

q-bio.TO↗

Influence of spatially modified tissue on atrial fibrillation patterns: Insight from solutions of the FitzHugh-Nagumo equations

We study the interplay between traveling action potentials and spatial inhomogeneities in the FitzHugh-Nagumo model to investigate possible mechanisms for the occurrence of fibrillatory states in the atria of the heart. Different dynamical patterns such as ectopic foci, localized and meandering spiral waves are found depending on the characteristics of the inhomogeneities. Their appearance in dependence of the size and strength of the inhomogeneities is quantified by phase diagrams. Furthermore it is shown that regularly paced waves in a region R, that is connected by a small bridge connection to another region L with perturbing waves emanating from an additional pacemaker, can be strongly disturbed, so that a fibrillatory state emerges in region R after a transient time interval. This finding supports conjectures that fibrillatory states in the right atrium can be induced by self-excitatory pacemakers in the left atrium.

physics.bio-ph↗

Growth-Algorithm Model of Leaf Shape

The innumerable shapes of plant leaves present a challenge to the explanatory power of biophysical theory. A model is needed that can produce these shapes with a small set of parameters. This paper presents a simple model of leaf shape based on a growth algorithm, which governs the growth rate of leaf tissue in two dimensions and hence the outline of the leaf. The growth of leaf lobes is governed by the position of leaf veins. This model gives an approximation to a wide variety of higher plant leaf shapes. The variation of leaf shapes found in closely related plants is discussed in terms of variability in the growth algorithms. The model can be extended to more complex leaf types.

q-bio.TO↗

Modelling the spatial organization of cell proliferation in the developing central nervous system

How far is neuroepithelial cell proliferation in the developing central nervous system a deterministic process? Or, to put it in a more precise way, how accurately can it be described by a deterministic mathematical model? To provide tracks to answer this question, a deterministic system of transport and diffusion partial differential equations, both physiologically and spatially structured, is introduced as a model to describe the spatially organized process of cell proliferation during the development of the central nervous system. As an initial step towards dealing with the three-dimensional case, a unidimensional version of the model is presented. Numerical analysis and numerical tests are performed. In this work we also achieve a first experimental validation of the proposed model, by using cell proliferation data recorded from histological sections obtained during the development of the optic tectum in the chick embryo.

math.AP↗

Mobilisation readiness state and the frequency structure of heart rate variability

A number of studies showed association of mental status with heart rate variability. This work discovered a feature of frequency structure of heart rate variability that is associated with mental readiness. In three independent groups of 64, 39, and 19 volunteers by the factor analysis of heart rate periodograms, it has been discovered that there are at least two other heart rate oscillation phenomena apart from the well known low frequency oscillations and respiratory arrhythmia. They have periods of 3 and 4 heart beats. Association of amplitude of 3-beats oscillation with level of mental readiness was shown due to further observation in two independent groups of 12 and 7. Moreover, possibility of assessment of mental readiness by the mathematical model based on heart rate periodogram was suggested.

q-bio.TO↗

Frequency Structure of Heart Rate Variability

Factor structure of heart rate periodogram has been detected with factor analysis. The results showed that there are at least four periodical phenomena of HRV. Two of them have not been discovered and physiologically explained yet. Their frequency ranges are 0.21 to 0.31 1/beat with the peak at 0.26 1/beat and 0.25 to 0.5 1/beat with the peak 0.35 1/beat. Despite of differences of the peak frequencies the frequency rages of the factors are overlapped. Therefore, power of spectral density within any frequency range could not be a measure of a modulating physiological mechanism activity.

q-bio.TO↗

A Hierarchical Probability Model of Colon Cancer

We consider a model of fixed size $N = 2^l$ in which there are $l$ generations of daughter cells and a stem cell. In each generation $i$ there are $2^{i-1}$ daughter cells. At each integral time unit the cells split so that the stem cell splits into a stem cell and generation 1 daughter cell and the generation $i$ daughter cells become two cells of generation $i+1$. The last generation is removed from the population. The stem cell gets first and second mutations at rates $u_1$ and $u_2$ and the daughter cells get first and second mutations at rates $v_1$ and $v_2$. We find the distribution for the time it takes to get two mutations as $N$ goes to infinity and the mutation rates go to 0. We also find the distribution for the location of the mutations. Several outcomes are possible depending on how fast the rates go to 0. The model considered has been proposed by Komarova (2007) as a model for colon cancer.

math.PR↗

Quantitative predictions on auxin-induced polar distribution of PIN proteins during vein formation in leaves

The dynamic patterning of the plant hormone auxin and its efflux facilitator the PIN protein are the key regulator for the spatial and temporal organization of plant development. In particular auxin induces the polar localization of its own efflux facilitator. Due to this positive feedback auxin flow is directed and patterns of auxin and PIN arise. During the earliest stage of vein initiation in leaves auxin accumulates in a single cell in a rim of epidermal cells from which it flows into the ground meristem tissue of the leaf blade. There the localized auxin supply yields the successive polarization of PIN distribution along a strand of cells. We model the auxin and PIN dynamics within cells with a minimal canalization model. Solving the model analytically we uncover an excitable polarization front that triggers a polar distribution of PIN proteins in cells. As polarization fronts may extend to opposing directions from their initiation site we suggest a possible resolution to the puzzling occurrence of bipolar cells, such we offer an explanation for the development of closed, looped veins. Employing non-linear analysis we identify the role of the contributing microscopic processes during polarization. Furthermore, we deduce quantitative predictions on polarization fronts establishing a route to determine the up to now largely unknown kinetic rates of auxin and PIN dynamics.

q-bio.TO↗

Myocardial Contractions and the Ventricular Pressure--Volume Relationship

We present a reduced-order heart model with the aim of introducing a novel point of view in the interpretation of the pressure-volume loops. The novelty of the approach is based on the definition of active contraction as opposed to that of active stress. The consequences of the assumption are discussed with reference to a specific pressure-volume loop characteristic of a normal human patient.

q-bio.TO↗

Growth-induced mass flows in fungal networks

Cord-forming fungi form extensive networks that continuously adapt to maintain an efficient transport system. As osmotically driven water uptake is often distal from the tips, and aqueous fluids are incompressible, we propose that growth induces mass flows across the mycelium, whether or not there are intrahyphal concentration gradients. We imaged the temporal evolution of networks formed by Phanerochaete velutina, and at each stage calculated the unique set of currents that account for the observed changes in cord volume, while minimising the work required to overcome viscous drag. Predicted speeds were in reasonable agreement with experimental data, and the pressure gradients needed to produce these flows are small. Furthermore, cords that were predicted to carry fast-moving or large currents were significantly more likely to increase in size than cords with slow-moving or small currents. The incompressibility of the fluids within fungi means there is a rapid global response to local fluid movements. Hence velocity of fluid flow is a local signal that conveys quasi-global information about the role of a cord within the mycelium. We suggest that fluid incompressibility and the coupling of growth and mass flow are critical physical features that enable the development of efficient, adaptive, biological transport networks.

q-bio.TO↗

Understanding thermoregulatory transitions during haemorrhage by piecewise regression

Transition points are common in physiological processes. However the transition between normothermia and hypothermia during haemorrhagic shock has rarely been systematically quantified from intensive time series data. We estimated the critical transition point (CTP) and provided confidence intervals for core body temperature response to acute severe haemorrhage in a conscious rat model. Estimates were obtained by traditional piecewise linear regression (broken stick model) and compared to those from the more novel bent cable regression. Bent cable regression relaxes the assumption of an abrupt point transition, and thus allows the capture of a potentially gradual transition phase; the broken stick is a special case of the bent cable model. We calculated two types of confidence intervals, assuming either independent or autoregressive structure for the residuals. In spite of the severity of the haemorrhage, median temperature change was minor (0.8 C; IQR 0.57-1.31 C) and only four of 38 rats were clinically hypothermic (core temperature < 35 C). However, a transition could be estimated for 23 rats. Bent cable fits were superior when the transition appeared to be gradual rather than abrupt. In all cases, assuming independence gave incorrect uncertainty estimates of CTP. For 15 animals, neither model could be fitted because of irregular temperature profiles that did not conform to the assumption of a single transition. Arbitrary imposition of broken stick fits on a gradual transition profile and assuming independent rather than autocorrelated error may result in misleading estimates of CTP. Identification of the onset of irreversible shock will require further quantification of appropriate time-dependent physiological variables and their behaviour during haemorrhage.

stat.AP↗

Spreading speeds and traveling waves for a model of epidermal wound healing

In this paper, we shall establish the spreading speed and existence of traveling waves for a non-cooperative system arising from epidermal wound healing and characterize the spreading speed as the slowest speed of a family of non-constant traveling wave solutions. Our results on the spreading speed and traveling waves can also be applied to a large class of non-cooperative reaction-diffusion systems.

q-bio.QM↗

Toward A Quantitative Understanding of Gas Exchange in the Lung

In this work we present a mathematical framework that quantifies the gas-exchange processes in the lung. The theory is based on the solution of the one-dimensional diffusion equation on a simplified model of lung septum. Gases dissolved into different compartments of the lung are all treated separately with physiologically important parameters. The model can be applied in magnetic resonance of hyperpolarized xenon for quantification of lung parameters such as surface-to-volume ratio and the air-blood barrier thickness. In general this model provides a description of a broad range of biological exchange processes that are driven by diffusion.

q-bio.QM↗

Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis

Angiogenesis is a key process in the tumoral growth which allows the cancerous tissue to impact on its vasculature in order to improve the nutrient's supply and the metastatic process. In this paper, we introduce a model for the density of metastasis which takes into account for this feature. It is a two dimensional structured equation with a vanishing velocity field and a source term on the boundary. We present here the mathematical analysis of the model, namely the well-posedness of the equation and the asymptotic behavior of the solutions, whose natural regularity led us to investigate some basic properties of the space $\Wd(\Om)=\{V\in L^1;\;÷(GV)\in L^1\}$, where $G$ is the velocity field of the equation.

math.AP↗

A closed-form solution of the three-dimensional contact problem for biphasic cartilage layers

A three-dimensional unilateral contact problem for articular cartilage layers is considered in the framework of the biphasic cartilage model. The articular cartilages bonded to subchondral bones are modeled as biphasic materials consisting of a solid phase and a fluid phase. It is assumed that the subchondral bones are rigid and shaped like elliptic paraboloids. The obtained analytical solution is valid over long time periods and can be used for increasing loading conditions.

physics.bio-ph↗