¿Flujo acústico, la “pequeña invención” de las cianobacterias?

Micro-engineering pumping devices without mechanical parts appeared “way back” in the early 1990’s. The working principle is acoustic streaming. Has Nature “rediscovered” this invention 2.7 Gyr ago? Strands of marine cyanobacteria Synechococcus swim 25 diameters per second without any visible means of propulsion. We show that nanoscale amplitude vibrations on the S-layer (a crystalline shell outside the outer membrane present in motile strands) and frequencies of the order of 0.5-1.5 MHz (achievable by molecular motors), could produce steady streaming slip velocities outside a (Stokes) boundary layer. Inside this boundary layer the flow pattern is rotational (hence biologically advantageous). In addition to this purported “swimming by singing”, we also indicate other possible instantiations of acoustic streaming. Sir James Lighthill has proposed that acoustic streaming occurs in the cochlear dynamics, and new findings on the outer hair cell membranes are suggestive. Other possibilities are membrane vibrations of yeast cells, enhancing its chemistry (beer and bread, keep it up, yeast!), squirming motion of red blood cells along capillaries, and fluid pumping by silicated diatoms.Los mecanismos de bombeo en microingeniería aparecieron al principio de la década de los 90. El principio detrás de esto es el de flujo acústico. ¿Ha descubierto la Naturaleza este invento de hace 2.700 millones de años? Algunas cianobacterias marinas de la especie Synechococcus nadan 25 diámetros por segundo sin ningún medio visible de propulsión. Especulamos en este artículo que vibraciones de amplitud de nanoescala del estrato S (una cáscara cristalina que cubre las membranas exteriores en las cepas móviles) y con frecuencias del orden de 0,5-1,5 MHz (y esto es factible por los motores moleculares), podrían producir velocidades de deslizamiento del fluido, en el exterior de la frontera de la región Stokes. Dentro de esta capa límite (que para nuestra sorpresa resulta ser relativamente ancha) el comportamiento del flujo es rotacional (y en consecuencia, ventajoso desde el punto de vista biológico). Adicionalmente a este supuesto mecanismo que se podria llamar “nadando cantando”, mostramos otros posibles ejemplos biológicos de corrientes acústicas. Sir James Lighthill ha sugerido que el flujo acústico también se da en la cóclea del oído de los mamíferos, y son muy sugerentes los nuevos hallazgos en las células ciliadas externas. Otras posibilidades son flujos acústicos producidos por vibraciones de las membranas en células de levadura, mejorando su química (¡cerveza y pan!), el contoneo de los glóbulos rojos en los tubos capilares y el bombeo de fluido producido por las diatomeas

Stochastic differential equations for evolutionary dynamics with demographic noise and mutations

We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDE). For large, but finite populations this allows to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates, $\mu$, are not too small compared to the inverse population size 1/N. This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For $\mu N\ll1$ this limits the use of SDE's, but in this case there are well established alternative approximations based on time scale separation. We illustrate our approach by a Rock-Scissors-Paper game with mutations, where we demonstrate excellent agreement with simulation based results for sufficiently large populations. In the absence of mutations the excellent agreement extends to small population sizes.Comment: 8 pages, 2 figures, accepted for publication in Physical Review

Cancer phenotype as the outcome of an evolutionary game between normal and malignant cells

There is variability in the cancer phenotype across individuals: two patients with the same tumour may experience different disease life histories, resulting from genetic variation within the tumour and from the interaction between tumour and host. Until now, phenotypic variability has precluded a clear-cut identification of the fundamental characteristics of a given tumour type.Journal ArticleResearch Support, Non-U.S. Gov'tSCOPUS: ar.jinfo:eu-repo/semantics/publishe

Stern-Judging: A Simple, Successful Norm Which Promotes Cooperation under Indirect Reciprocity

We study the evolution of cooperation under indirect reciprocity, believed to constitute the biological basis of morality. We employ an evolutionary game theoretical model of multilevel selection, and show that natural selection and mutation lead to the emergence of a robust and simple social norm, which we call stern-judging. Under stern-judging, helping a good individual or refusing help to a bad individual leads to a good reputation, whereas refusing help to a good individual or helping a bad one leads to a bad reputation. Similarly for tit-for-tat and win-stay-lose-shift, the simplest ubiquitous strategies in direct reciprocity, the lack of ambiguity of stern-judging, where implacable punishment is compensated by prompt forgiving, supports the idea that simplicity is often associated with evolutionary success

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on {\em E. coli} have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with {\em E. coli}. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion

Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy

Pairs of $n\times n$ matrices whose commutator differ from the identity by a matrix of rank $r$ are used to construct bispectral differential operators with $r\times r$ matrix coefficients satisfying the Lax equations of the Matrix KP hierarchy. Moreover, the bispectral involution on these operators has dynamical significance for the spin Calogero particles system whose phase space such pairs represent. In the case $r=1$, this reproduces well-known results of Wilson and others from the 1990's relating (spinless) Calogero-Moser systems to the bispectrality of (scalar) differential operators. This new class of pairs $(L, \Lambda)$ of bispectral matrix differential operators is different than those previously studied in that $L$ acts from the left, but $\Lambda$ from the right on a common $r\times r$ eigenmatrix.Comment: 16 page

Hamiltonian walks on Sierpinski and n-simplex fractals

We study Hamiltonian walks (HWs) on Sierpinski and $n$--simplex fractals. Via numerical analysis of exact recursion relations for the number of HWs we calculate the connectivity constant $\omega$ and find the asymptotic behaviour of the number of HWs. Depending on whether or not the polymer collapse transition is possible on a studied lattice, different scaling relations for the number of HWs are obtained. These relations are in general different from the well-known form characteristic of homogeneous lattices which has thus far been assumed to hold for fractal lattices too.Comment: 22 pages, 6 figures; final versio

Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq equations

We establish a connection between Optimal Transport Theory and classical Convection Theory for geophysical flows. Our starting point is the model designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal Transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized Hydrostatic-Boussinesq equations) to various models involving Optimal Transport (and the related Monge-Ampere equation. This includes the 2D semi-geostrophic equations and some fully non-linear versions of the so-called high-field limit of the Vlasov-Poisson system and of the Keller-Segel for Chemotaxis. Finally, we show how a ``stringy'' generalization of the AHT model can be related to the magnetic relaxation model studied by Arnold and Moffatt to obtain stationary solutions of the Euler equations with prescribed topology

The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations

We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the discrete problem, we are able to derive a corresponding continuous weak formulation for the probability density. Therefore, we obtain a family of partial differential equations (PDE) for the evolution of the probability density, and which will be an approximation of the discrete process in the joint large population, small time-steps and weak selection limit. If the fitness functions are sufficiently regular, we can recast the weak formulation in a more standard formulation, without any boundary conditions, but supplemented by a number of conservation laws. The equations in this family can be purely diffusive, purely hyperbolic or of convection-diffusion type, with frequency dependent convection. The particular outcome will depend on the assumed scalings. The diffusive equations are of the degenerate type; using a duality approach, we also obtain a frequency dependent version of the Kimura equation without any further assumptions. We also show that the convective approximation is related to the replicator dynamics and provide some estimate of how accurate is the convective approximation, with respect to the convective-diffusion approximation. In particular, we show that the mode, but not the expected value, of the probability distribution is modelled by the replicator dynamics. Some numerical simulations that illustrate the results are also presented