Quantifying the contribution of actin networks to the elastic strength of fibroblasts

The structural models created to understand the cytoskeletal mechanics of cells in suspension are described here. Suspended cells can be deformed by well-defined surface stresses in an Optical Stretcher [Guck, J., Ananthakrishnan, R., Mahmood, H., Moon, T.J., Cunningham, C.C., K?s, J., 2001. The optical stretcher: a novel laser tool to micromanipulate cells. Biophys. J. 81(2), 767-784], a two-beam optical trap designed for the contact-free deformation of cells. Suspended cells have a well-defined cytoskeleton, displaying a radially symmetric actin cortical network underlying the cell membrane with no actin stress fibers, and microtubules and intermediate filaments in the interior. Based on experimental data using suspended fibroblasts, we create two structural models: a thick shell actin cortex model that describes cell deformation for a localized stress distribution on these cells and a three-layered model that considers the entire cytoskeleton when a broad stress distribution is applied. Applying the models to data, we obtain a (actin) cortical shear moduli G of approximately 220 Pa for normal fibroblasts and approximately 185 Pa for malignantly transformed fibroblasts. Additionally, modeling the cortex as a transiently crosslinked isotropic actin network, we show that actin and its crosslinkers must be co-localized into a tight shell to achieve these cortical strengths. The similar moduli values and cortical actin and crosslinker densities but different deformabilities of the normal and cancerous cells suggest that a cell's structural strength is not solely determined by cytoskeletal composition but equally importantly by (actin) cytoskeletal architecture via differing cortical thicknesses. We also find that although the interior structural elements (microtubules, nucleus) contribute to the deformed cell's exact shape via their loose coupling to the cortex, it is the outer actin cortical shell (and its thickness) that mainly determines the cell's structural response.     

Rheology of airway smooth muscle cells is associated with cytoskeletal contractile stress.

Recently reported data from mechanical measurements of cultured airway smooth muscle cells show that stiffness of the cytoskeletal matrix is determined by the extent of static contractile stress borne by the cytoskeleton (Wang N, Toli?-N?rrelykke IM, Chen J, Mijailovich SM, Butler JP, Fredberg JJ, and Stamenovi? D. Am J Physiol Cell Physiol 282, C606-C616, 2002). On the other hand, rheological measurements on these cells show that cytoskeletal stiffness changes with frequency of imposed mechanical loading according to a power law (Fabry B, Maksym GN, Butler JP, Glogauer M, Navajas DF, and Fredberg JJ. Phys Rev Lett 87: 148102, 2001). In this study, we examine the possibility that these two empirical observations might be interrelated. We combine previously reported data for contractile stress of human airway smooth muscle cells with new data describing rheological properties of these cells and derive quantitative, mathematically tractable, and experimentally verifiable empirical relationships between contractile stress and indexes of cell rheology. These findings reveal an intriguing role of the contractile stress: although it maintains structural stability of the cell under applied mechanical loads, it may also regulate rheological properties of the cytoskeleton, which are essential for other cell functions.     

T lymphocyte-triggering factor of african trypanosomes is associated with the flagellar fraction of the cytoskeleton and represents a new family of proteins that are present in several divergent eukaryotes

The trypanosome cytoskeleton consists almost entirely of microtubule-based structures. Although alpha- and beta-tubulin from Trypanosoma brucei have been well characterized, much less is known about other cytoskeleton-associated proteins in trypanosomes. Using biochemical fractionation, we demonstrate here that T lymphocyte-triggering factor (TLTF) from T. brucei is a component of the detergent-resistant and Ca(2+)-resistant fraction of the parasite cytoskeleton. This fraction contains the flagellar apparatus and a subset of cytoskeletal protein complexes that together function in cell motility, cytokinesis, and organelle inheritance. We also show that TLTF-related genes are present in several highly divergent eukaryotic organisms. Although the function of the corresponding proteins is not known, the mammalian TLTF-like gene (GAS11; growth arrest-specific gene 11) is up-regulated in growth-arrested cells and is a candidate tumor suppressor (Whitmore, S. A., Settasatian, C., Crawford, J., Lower, K. M., McCallum, B., Seshadri, R., Cornelisse, C. J., Moerland, E. W., Cleton-Jansen, A. M., Tipping, A. J., Mathew, C. G., Savnio, M., Savoia, A., Verlander, P., Auerbach, A. D., Van Berkel, C., Pronk, J. C., Doggett, N. A., and Callen, D. F. (1998) Genomics 52, 325-331), suggestive of a role in coordinating cytoskeleton activities. Consistent with this possibility, we show that the human GAS11 protein contains a 144-amino acid domain that co-localizes with microtubules when fused to the green fluorescent protein and expressed in mammalian cells. These findings suggest that TLTF represents a newly defined protein family, whose members contribute to cytoskeleton function in species as diverse as protozoa and mammals.     

The statistical analysis of the in vitro chromosome aberration assay using Chinese hamster ovary cells

The purpose of the in vitro chromosome aberration assay (ABS) is to determine whether the test compound is a clastogen, i.e. induces structural changes in chromosomes. Details of this assay can be found in Galloway et al. [S.M. Galloway, M. Aardema, M. Ishidate Jr, J.L. Ivett, D.J. Kirkland, M. Takeshi, P. Mosesso, T. Sofuni, Mutation Res. 312 (1994) 241-261]. The standard design consists of a negative control and at least three positive dose groups. At each dose, a sample, say 200, of metaphase cells is examined microscopically and cells exhibiting at least one type of chromosome aberration are identified. Using Chinese hamster ovary cells, Margolin et al. [B.H. Margolin, M.A. Resnick, J.Y. Rimpo, P. Archer, S.M. Galloway, A.D. Bloom, E. Zeiger, Environ. Mutagen. 8 (1986) 183-204] and Richardson et al. [C. Richardson, D.A. Williams, J.A. Allen, G. Amphlett, D.O. Chanter, B. Phillips, Analysis of data from in vitro cytogenetic assays, in: D.J. Kirkland (Ed.), Statistical Evaluation of Mutagenicity Test Data, Cambridge University Press, Cambridge, 1989, pp. 141-154] demonstrated that a binomial sampling model could be used to describe the proportion of cells with chromosome aberrations.Statisticians and toxicologists have also suggested evaluation criteria for the dose response pattern of ABS. Margolin et al. [B.H. Margolin, M.A. Resnick, J.Y. Rimpo, P. Archer, S.M. Galloway, A.D. Bloom, E. Zeiger, Environ. Mutagen. 8 (1986) 183-204] suggested one use the Cochran-Armitage trend test. Sofuni et al. [T. Sofuni, A. Matsuoka, M. Sawada, M. Ishidate Jr, E. Zeiger, M.D. Shelby, Mutation Res. 241 (1990) 175-213] considered the dose response to be (strong) positive if it had two significant doses out of three dose groups and decided it was weakly positive if it had only one significant dose and there was a significant trend. The criterion of Galloway et al. for a positive response was a clear dose-related increase in cells with structural aberrations in one experiment or a reproducible single positive dose [S.M. Galloway, M. Aardema, M. Ishidate Jr, J.L. Ivett, D.J. Kirkland, M. Takeshi, P. Mosesso, T. Sofuni, Mutation Res. 312 (1994) 241-261].We formulate the above three procedures in terms of a Cochran-Armitage trend test and a Dunnett type test. We then compare the performance of these three procedures in terms of a Monte Carlo simulation study. We then develop a software program from the chosen procedure for its ease of use by statisticians and toxicologists.     

Rheological behavior of living cells is timescale-dependent

The dynamic mechanical behavior of living cells has been proposed to result from timescale-invariant processes governed by the soft glass rheology theory derived from soft matter physics. But this theory is based on experimental measurements over timescales that are shorter than those most relevant for cell growth and function. Here we report results measured over a wider range of timescales which demonstrate that rheological behaviors of living cells are not timescale-invariant. These findings demonstrate that although soft glass rheology appears to accurately predict certain cell mechanical behaviors, it is not a unified model of cell rheology under biologically relevant conditions and thus, alternative mechanisms need to be considered.     

Cyclin D1 down-regulation is essential for DBC2's tumor suppressor function

The expression of tumor suppressor gene DBC2 causes certain breast cancer cells to stop growing [M. Hamaguchi, J.L. Meth, C. Von Klitzing, W. Wei, D. Esposito, L. Rodgers, T. Walsh, P. Welcsh, M.C. King, M.H. Wigler, DBC2, a candidate for a tumor suppressor gene involved in breast cancer, Proc. Natl. Acad. Sci. USA 99 (2002) 13647-13652]. Recently, DBC2 was found to participate in diverse cellular functions such as protein transport, cytoskeleton regulation, apoptosis, and cell cycle control [V. Siripurapu, J.L. Meth, N. Kobayashi, M. Hamaguchi, DBC2 significantly influences cell cycle, apoptosis, cytoskeleton, and membrane trafficking pathways. J. Mol. Biol. 346 (2005) 83-89]. Its tumor suppression mechanism, however, remains unclear. In this paper, we demonstrate that DBC2 suppresses breast cancer proliferation through down-regulation of Cyclin D1 (CCND1). Additionally, the constitutional overexpression of CCND1 prevented the negative impact of DBC2 expression on their growth. Under a CCND1 promoter, the expression of CCNE1 exhibited the same protective effect. Our results indicate that the down-regulation of CCND1 is an essential step for DBC2's growth suppression of cancer cells. We believe that this discovery contributes to a better understanding of DBC2's tumor suppressor function.     

A fitness based analysis of Daisyworld

The Gaia hypothesis [Lovelock, J., Margulis, L., 1974. Atmospheric homeostasis: the Gaia hypothesis. Tellus 26, 1], that the earth functions as a self-regulating system, has never sat particularly comfortably with ideas in mainstream biology [Anon, 2002. In pursuit of arrogant simplicities. Nature 416, 247]. A lack of any clear role for evolution in the model has led to claims of teleology-that self-regulation emerges because it is pre-ordained to do so [Doolittle, W.F., 1981. Is nature really motherly? CoEvol. Q. 58-63; Dawkins, R., 1979. The Extended Phenotype. Oxford University Press, Oxford]. The Daisyworld parable [Watson, A.J., Lovelock, J.E., 1983. Biological homeostasis of the global environment--the parable of Daisyworld. Tellus B 35, 284], a simple mathematical illustration of Gaia, went some way to addressing these critiques but, despite recent success in incorporating natural selection [Stocker, S.,1995. Regarding mutations in Daisyworld models. J. Theor. Biol. 175, 495; Lenton, T.M., 1998. Gaia and natural selection. Nature 394, 439; Lenton, T.M., Lovelock, J.E., 2001. Daisyworld revisited: quantifying biological effects on planetary self-regulation. Tellus B 53, 288; Wood, A.J., Ackland, G.J., Lenton, T.M., 2006. Mutation of albedo and growth response leads to oscillations in a spatial Daisyworld. J. Theor. Biol. 242, 188], it remains a widely held view that the ideas are inconsistent with biological principles. We show that standard methodology from quantitative genetics can be used to predict the stationary states and dynamic behaviour of Daisyworlds. The system regulates its temperature due to the low-level evolutionary dynamics of competition between the thermally coupled daisies, no higher level principle is invoked. A reconciliation of Gaia with evolutionary theory may allow further development of evolutionary arguments for the existence of global self-regulatory systems.     

Simulations of the erythrocyte cytoskeleton at large deformation. II. Micropipette aspiration.

Coarse-grained molecular models of the erythrocyte membrane's spectrin cytoskeleton are presented in Monte Carlo simulations of whole cells in micropipette aspiration. The nonlinear chain elasticity and sterics revealed in more microscopic cytoskeleton models (developed in a companion paper; Boey et al., 1998. Biophys. J. 75:1573-1583) are faithfully represented here by two- and three-body effective potentials. The number of degrees of freedom of the system are thereby reduced to a range that is computationally tractable. Three effective models for the triangulated cytoskeleton are developed: two models in which the cytoskeleton is stress-free and does or does not have internal attractive interactions, and a third model in which the cytoskeleton is prestressed in situ. These are employed in direct, finite-temperature simulations of erythrocyte deformation in a micropipette. All three models show reasonable agreement with aspiration measurements made on flaccid human erythrocytes, but the prestressed model alone yields optimal agreement with fluorescence imaging experiments. Ensemble-averaging of nonaxisymmetrical, deformed structures exhibiting anisotropic strain are thus shown to provide an answer to the basic question of how a triangulated mesh such as that of the red cell cytoskeleton deforms in experiment.     

An Equilibrium Model for the Mg(2+)-Linked Self-Assembly of FtsZ in the Presence of GTP or a GTP Analogue

The concerted formation of a narrow distribution of oligomeric FtsZ species in the presence of GTP or a GTP analogue under close to physiological conditions (neutral pH and 0.5 M K(+)) has been characterized recently by various biophysical methods [Monterroso, B., et al. (2012) Biochemistry51, 4541-4550]. An equilibrium model may semiquantitatively account for the results of this study; in the model, FtsZ self-associates in a noncooperative fashion to form linear fibrils, that upon increasing to a certain size exhibit an increasing tendency to form closed cyclic fibrils, as previously suggested [González, J. M., et al. (2005) Proc. Natl. Acad. Sci. U.S.A.102, 1895-1900]. The closed cyclic fibrils are formed when the natural curvature and flexibility of a linear oligomer bring the ends of a linear fiber sufficiently close to overcome the entropic barrier to loop closure. The size distribution of cyclic oligomers is thus a reflection of the tendency toward curvature of linear fibrils of FtsZ under the conditions used in these experiments.     

Prestress and Adhesion Site Dynamics Control Cell Sensitivity to Extracellular Stiffness

This study aims at improving the understanding of mechanisms responsible for cell sensitivity to extracellular environment. We explain how substrate mechanical properties can modulate the force regulation of cell sensitive elements primarily adhesion sites. We present a theoretical and experimental comparison between two radically different approaches of the force regulation of adhesion sites that depends on their either stationary or dynamic behavior. The most classical stationary model fails to predict cell sensitivity to substrate stiffness whereas the dynamic model predicts extracellular stiffness dependence. This is due to a time dependent reaction force in response to actomyosin traction force exerted on cell sensitive elements. We purposely used two cellular models, i.e., alveolar epithelial cells and alveolar macrophages exhibiting respectively stationary and dynamic adhesion sites, and compared their sensitivity to theoretical predictions. Mechanical and structural results show that alveolar epithelial cells exhibit significant prestress supported by evident stress fibers and lacks sensitivity to substrate stiffness. On the other hand, alveolar macrophages exhibit low prestress and exhibit sensitivity to substrate stiffness. Altogether, theory and experiments consistently show that adhesion site dynamics and cytoskeleton prestress control cell sensitivity to extracellular environment with an optimal sensitivity expected in the intermediate range.     

A hydraulic-photosynthetic model based on extended HLH and its application to Coast redwood (Sequoia sempervirens)

Although recent investigations [Ryan, M.G., Yoder, B.J., 1997. Hydraulic limits to tree height and tree growth. Bioscience 47, 235-242; Koch, G.W., Sillett, S.C.,Jennings, G.M.,Davis, S.D., 2004. The limits to tree height. Nature 428, 851-854; Niklas, K.J., Spatz, H., 2004. Growth and hydraulic (not mechanical) constraints govern the scaling of tree height and mass. Proc. Natl Acad. Sci. 101, 15661-15663; Ryan, M.G., Phillips, N., Bond, B.J., 2006. Hydraulic limitation hypothesis revisited. Plant Cell Environ. 29, 367-381; Niklas, K.J., 2007. Maximum plant height and the biophysical factors that limit it. Tree Physiol. 27, 433-440; Burgess, S.S.O., Dawson, T.E., 2007. Predicting the limits to tree height using statistical regressions of leaf traits. New Phytol. 174, 626-636] suggested that the hydraulic limitation hypothesis (HLH) is the most plausible theory to explain the biophysical limits to maximum tree height and the decline in tree growth rate with age, the analysis is largely qualitative or based on statistical regression. Here we present an integrated biophysical model based on the principle that trees develop physiological compensations (e.g. the declined leaf water potential and the tapering of conduits with heights [West, G.B., Brown, J.H., Enquist, B.J., 1999. A general model for the structure and allometry of plant vascular systems. Nature 400, 664-667]) to resist the increasing water stress with height, the classical HLH and the biochemical limitations on photosynthesis [von Caemmerer, S., 2000. Biochemical Models of Leaf Photosynthesis. CSIRO Publishing, Australia]. The model has been applied to the tallest trees in the world (viz. Coast redwood (Sequoia sempervirens)). Xylem water potential, leaf carbon isotope composition, leaf mass to area ratio at different heights derived from the model show good agreements with the experimental measurements of Koch et al. [2004. The limits to tree height. Nature 428, 851-854]. The model also well explains the universal trend of declining growth rate with age.     

Desmoplakin: an unexpected regulator of microtubule organization in the epidermis

Despite their importance in cell shape and polarity generation, the organization of microtubules in differentiated cells and tissues remains relatively unexplored in mammals. We generated transgenic mice in which the epidermis expresses a fluorescently labeled microtubule-binding protein and show that in epidermis and in cultured keratinocytes, microtubules stereotypically reorganize as they differentiate. In basal cells, microtubules form a cytoplasmic network emanating from an apical centrosome. In suprabasal cells, microtubules concentrate at cell-cell junctions. The centrosome retains its ability to nucleate microtubules in differentiated cells, but no longer anchors them. During epidermal differentiation, ninein, which is a centrosomal protein required for microtubule anchoring (Dammermann, A., and A. Merdes. 2002. J. Cell Biol. 159:255-266; Delgehyr, N., J. Sillibourne, and M. Bornens. 2005. J. Cell Sci. 118:1565-1575; Mogensen, M.M., A. Malik, M. Piel, V. Bouckson-Castaing, and M. Bornens. 2000. J. Cell Sci. 113:3013-3023), is lost from the centrosome and is recruited to desmosomes by desmoplakin (DP). Loss of DP prevents accumulation of cortical microtubules in vivo and in vitro. Our work uncovers a differentiation-specific rearrangement of the microtubule cytoskeleton in epidermis, and defines an essential role for DP in the process.     

Robust strategies for automated AFM force curve analysis-II: adhesion-influenced indentation of soft, elastic materials

In the first of this two-part discourse on the extraction of elastic properties from atomic force microscopy (AFM) data, a scheme for automating the analysis of force-distance curves was introduced and experimentally validated for the Hertzian (i.e., linearly elastic and noninteractive probe-sample pairs) indentation of soft, inhomogeneous materials. In the presence of probe-sample adhesive interactions, which are common especially during retraction of the rigid tip from soft materials, the Hertzian models are no longer adequate. A number of theories (e.g., Johnson-Kendall-Roberts and Derjaguin-Muller-Toporov), covering the full range of sample compliance relative to adhesive force and tip radius, are available for analysis of such data. We incorporated Pietrement and Troyon's approximation (2000, "General Equations Describing Elastic Indentation Depth and Normal Contact Stiffness Versus Load," J. Colloid Interface Sci., 226(1), pp. 166-171) of the Maugis-Dugdale model into the automated procedure. The scheme developed for the processing of Hertzian data was extended to allow for adhesive contact by applying the Pietrement-Troyon equation. Retraction force-displacement data from the indentation of polyvinyl alcohol gels were processed using the customized software. Many of the retraction curves exhibited strong adhesive interactions that were absent in extension. We compared the values of Young's modulus extracted from the retraction data to the values obtained from the extension data and from macroscopic uniaxial compression tests. Application of adhesive contact models and the automated scheme to the retraction curves yielded average values of Young's modulus close to those obtained with Hertzian models for the extension curves. The Pietrement-Troyon equation provided a good fit to the data as indicated by small values of the mean-square error. The Maugis-Dugdale theory is capable of accurately modeling adhesive contact between a rigid spherical indenter and a soft, elastic sample. Pietrement and Troyon's empirical equation greatly simplifies the theory and renders it compatible with the general automation strategies that we developed for Hertzian analysis. Our comprehensive algorithm for automated extraction of Young's moduli from AFM indentation data has been expanded to recognize the presence of either adhesive or Hertzian behavior and apply the appropriate contact model.     

Sustainable systems as organisms?

Schrödinger [Schrödinger, E., 1944. What is Life? Cambridge University Press, Cambridge] marvelled at how the organism is able to use metabolic energy to maintain and even increase its organisation, which could not be understood in terms of classical statistical thermodynamics. Ho [Ho, M.W., 1993. The Rainbow and the Worm, The Physics of Organisms, World Scientific, Singapore; Ho, M.W., 1998a. The Rainbow and the Worm, The Physics of Organisms, 2nd (enlarged) ed., reprinted 1999, 2001, 2003 (available online from ISIS website www.i- sis.org.uk)] outlined a novel “thermodynamics of organised complexity” based on a nested dynamical structure that enables the organism to maintain its organisation and simultaneously achieve non-equilibrium and equilibrium energy transfer at maximum efficiency. This thermodynamic model of the organism is reminiscent of the dynamical structure of steady state ecosystems identified by Ulanowicz [Ulanowicz, R.E., 1983. Identifying the structure of cycling in ecosystems. Math. Biosci. 65, 210–237; Ulanowicz, R.E., 2003. Some steps towards a central theory of ecosystem dynamics. Comput. Biol. Chem. 27, 523–530].The healthy organism excels in maintaining its organisation and keeping away from thermodynamic equilibrium – death by another name – and in reproducing and providing for future generations. In those respects, it is the ideal sustainable system. We propose therefore to explore the common features between organisms and ecosystems, to see how far we can analyse sustainable systems in agriculture, ecology and economics as organisms, and to extract indicators of the system's health or sustainability.We find that looking at sustainable systems as organisms provides fresh insights on sustainability, and offers diagnostic criteria for sustainability that reflect the system's health.In the case of ecosystems, those diagnostic criteria of health translate into properties such as biodiversity and productivity, the richness of cycles, the efficiency of energy use and minimum dissipation. In the case of economic systems, they translate into space-time differentiation or organised heterogeneity, local autonomy and sufficiency at appropriate levels, reciprocity and equality of exchange, and most of all, balancing the exploitation of natural resources – real input into the system – against the ability of the ecosystem to regenerate itself.     

On the biomechanics of stem cell niche formation in the gut - modelling growing organoids

In?vitro culture of intestinal tissue has been attempted for decades. Only recently did Sato et?al. [Sato, T., Vries, R. G., Snippert, H. J., van de Wetering, M., Barker, N., Stange, D. E., van Es, J. H., Abo, A., Kujala, P., Peters, P. J., et?al. (2009) Nature459, 262-265] succeed in establishing long-term intestinal culture, demonstrating that cells expressing the Lgr5 gene can give rise to organoids with crypt-like domains similar to those found in?vivo. In these cultures, Paneth cells provide essential signals supporting stem cell function. We have recently developed an individual cell-based computational model of the intestinal tissue [Buske, P., Galle, J., Barker, N., Aust, G., Clevers, H. & Loeffler, M. (2011) PLoS Comput Biol7, e1001045]. The model is capable of quantitatively reproducing a comprehensive set of experimental data on intestinal cell organization. Here, we present a significant extension of this model that allows simulation of intestinal organoid formation in?silico. For this purpose, we introduce a flexible basal membrane that assigns a bending modulus to the organoid surface. This membrane may be re-organized by cells attached to it depending on their differentiation status. Accordingly, the morphology of the epithelium is self-organized. We hypothesize that local tissue curvature is a key regulatory factor in stem cell organization in the intestinal tissue by controlling Paneth cell specification. In simulation studies, our model closely resembles the spatio-temporal organization of intestinal organoids. According to our results, proliferation-induced shape fluctuations are sufficient to induce crypt-like domains, and spontaneous tissue curvature induced by Paneth cells can control cell number ratios. Thus, stem cell expansion in an organoid depends sensitively on its biomechanics. We suggest a number of experiments that will enable new insights into mechano-transduction in the intestine, and suggest model extensions in the field of gland formation.     

A coalescent dual process in a Moran model with genic selection

A coalescent dual process for a multi-type Moran model with genic selection is derived using a generator approach. This leads to an expansion of the transition functions in the Moran model and the Wright–Fisher diffusion process limit in terms of the transition functions for the coalescent dual. A graphical representation of the Moran model (in the spirit of Harris) identifies the dual as a strong dual process following typed lines backwards in time. An application is made to the harmonic measure problem of finding the joint probability distribution of the time to the first loss of an allele from the population and the distribution of the surviving alleles at the time of loss. Our dual process mirrors the Ancestral Selection Graph of [Krone, S. M., Neuhauser, C., 1997. Ancestral processes with selection. Theoret. Popul. Biol. 51, 210–237; Neuhauser, C., Krone, S. M., 1997. The genealogy of samples in models with selection. Genetics 145, 519–534], which allows one to reconstruct the genealogy of a random sample from a population subject to genic selection. In our setting, we follow [Stephens, M., Donnelly, P., 2002. Ancestral inference in population genetics models with selection. Aust. N. Z. J. Stat. 45, 395–430] in assuming that the types of individuals in the sample are known. There are also close links to [Fearnhead, P., 2002. The common ancestor at a nonneutral locus. J. Appl. Probab. 39, 38–54]. However, our methods and applications are quite different. This work can also be thought of as extending a dual process construction in a Wright–Fisher diffusion in [Barbour, A.D., Ethier, S.N., Griffiths, R.C., 2000. A transition function expansion for a diffusion model with selection. Ann. Appl. Probab. 10, 123–162]. The application to the harmonic measure problem extends a construction provided in the setting of a neutral diffusion process model in [Ethier, S.N., Griffiths, R.C., 1991. Harmonic measure for random genetic drift. In: Pinsky, M.A. (Ed.), Diffusion Processes and Related Problems in Analysis, vol. 1. In: Progress in Probability Series, vol. 22, Birkhäuser, Boston, pp. 73–81].     

Event-driven simulation of cerebellar granule cells

Around half of the neurons of a human brain are granule cells (approximately 10(11)granule neurons) [Kandel, E.R., Schwartz, J.H., Jessell, T.M., 2000. Principles of Neural Science. McGraw-Hill Professional Publishing, New York]. In order to study in detail the functional role of the intrinsic features of this cell we have developed a pre-compiled behavioural model based on the simplified granule-cell model of Bezzi et al. [Bezzi, M., Nieus, T., Arleo, A., D'Angelo, E., Coenen, O.J.-M.D., 2004. Information transfer at the mossy fiber-granule cell synapse of the cerebellum. 34th Annual Meeting. Society for Neuroscience, San Diego, CA, USA]. We can use an efficient event-driven simulation scheme based on lookup tables (EDLUT) [Ros, E., Carrillo, R.R., Ortigosa, E.M., Barbour, B., Ags, R., 2006. Event-driven simulation scheme for spiking neural networks using lookup tables to characterize neuronal dynamics. Neural Computation 18 (12), 2959-2993]. For this purpose it is necessary to compile into tables the data obtained through a massive numerical calculation of the simplified cell model. This allows network simulations requiring minimal numerical calculation. There are three major features that are considered functionally relevant in the simplified granule cell model: bursting, subthreshold oscillations and resonance. In this work we describe how the cell model is compiled into tables keeping these key properties of the neuron model.     

Evolutionary dynamics of finite populations in games with polymorphic fitness equilibria

The hawk-dove (HD) game, as defined by Maynard Smith [1982. Evolution and the Theory of Games. Cambridge University Press, Cambridge], allows for a polymorphic fitness equilibrium (PFE) to exist between its two pure strategies; this polymorphism is the attractor of the standard replicator dynamics [Taylor, P.D., Jonker, L., 1978. Evolutionarily stable strategies and game dynamics. Math. Biosci. 40, 145-156; Hofbauer, J., Sigmund, K., 1998. Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge] operating on an infinite population of pure-strategists. Here, we consider stochastic replicator dynamics, operating on a finite population of pure-strategists playing games similar to HD; in particular, we examine the transient behavior of the system, before it enters an absorbing state due to sampling error. Though stochastic replication prevents the population from fixing onto the PFE, selection always favors the under-represented strategy. Thus, we may naively expect that the mean population state (of the pre-absorption transient) will correspond to the PFE. The empirical results of Fogel et al. [1997. On the instability of evolutionary stable states. BioSystems 44, 135-152] show that the mean population state, in fact, deviates from the PFE with statistical significance. We provide theoretical results that explain their observations. We show that such deviation away from the PFE occurs when the selection pressures that surround the fitness-equilibrium point are asymmetric. Further, we analyze a Markov model to prove that a finite population will generate a distribution over population states that equilibrates selection-pressure asymmetry; the mean of this distribution is generally not the fitness-equilibrium state.