TY - JOUR AB - Lateral root (LR) formation is an example of a plant post-embryonic organogenesis event. LRs are issued from non-dividing cells entering consecutive steps of formative divisions, proliferation and elongation. The chromatin remodeling protein PICKLE (PKL) negatively regulates auxin-mediated LR formation through a mechanism that is not yet known. Here we show that PKL interacts with RETINOBLASTOMA-RELATED 1 (RBR1) to repress the LATERAL ORGAN BOUNDARIES-DOMAIN 16 (LBD16) promoter activity. Since LBD16 function is required for the formative division of LR founder cells, repression mediated by the PKL–RBR1 complex negatively regulates formative division and LR formation. Inhibition of LR formation by PKL–RBR1 is counteracted by auxin, indicating that, in addition to auxin-mediated transcriptional responses, the fine-tuned process of LR formation is also controlled at the chromatin level in an auxin-signaling dependent manner. AU - Ötvös, Krisztina AU - Miskolczi, Pál AU - Marhavý, Peter AU - Cruz-Ramírez, Alfredo AU - Benková, Eva AU - Robert, Stéphanie AU - Bakó, László ID - 9332 IS - 8 JF - International Journal of Molecular Sciences SN - 1661-6596 TI - Pickle recruits retinoblastoma related 1 to control lateral root formation in arabidopsis VL - 22 ER - TY - JOUR AB - We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα, where φ0 is the electron ground state of the Pekar energy functional and ξα the associated coherent state of the phonons, can be approximated by a global phase for times small compared to α2. In the present note we prove that a similar approximation holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons that is generated by an operator proportional to α−2 and quadratic in creation and annihilation operators. Our result implies that the electron ground state remains close to its initial state for times of order α2, while the phonon fluctuations around the coherent state ξα can be described by a time-dependent Bogoliubov transformation. AU - Mitrouskas, David Johannes ID - 9333 JF - Letters in Mathematical Physics SN - 03779017 TI - A note on the Fröhlich dynamics in the strong coupling limit VL - 111 ER - TY - JOUR AB - Various degenerate diffusion equations exhibit a waiting time phenomenon: depending on the “flatness” of the compactly supported initial datum at the boundary of the support, the support of the solution may not expand for a certain amount of time. We show that this phenomenon is captured by particular Lagrangian discretizations of the porous medium and the thin film equations, and we obtain sufficient criteria for the occurrence of waiting times that are consistent with the known ones for the original PDEs. For the spatially discrete solution, the waiting time phenomenon refers to a deviation of the edge of support from its original position by a quantity comparable to the mesh width, over a mesh-independent time interval. Our proof is based on estimates on the fluid velocity in Lagrangian coordinates. Combining weighted entropy estimates with an iteration technique à la Stampacchia leads to upper bounds on free boundary propagation. Numerical simulations show that the phenomenon is already clearly visible for relatively coarse discretizations. AU - Fischer, Julian L AU - Matthes, Daniel ID - 9335 IS - 1 JF - SIAM Journal on Numerical Analysis SN - 0036-1429 TI - The waiting time phenomenon in spatially discretized porous medium and thin film equations VL - 59 ER - TY - JOUR AB - The way in which interactions between mechanics and biochemistry lead to the emergence of complex cell and tissue organization is an old question that has recently attracted renewed interest from biologists, physicists, mathematicians and computer scientists. Rapid advances in optical physics, microscopy and computational image analysis have greatly enhanced our ability to observe and quantify spatiotemporal patterns of signalling, force generation, deformation, and flow in living cells and tissues. Powerful new tools for genetic, biophysical and optogenetic manipulation are allowing us to perturb the underlying machinery that generates these patterns in increasingly sophisticated ways. Rapid advances in theory and computing have made it possible to construct predictive models that describe how cell and tissue organization and dynamics emerge from the local coupling of biochemistry and mechanics. Together, these advances have opened up a wealth of new opportunities to explore how mechanochemical patterning shapes organismal development. In this roadmap, we present a series of forward-looking case studies on mechanochemical patterning in development, written by scientists working at the interface between the physical and biological sciences, and covering a wide range of spatial and temporal scales, organisms, and modes of development. Together, these contributions highlight the many ways in which the dynamic coupling of mechanics and biochemistry shapes biological dynamics: from mechanoenzymes that sense force to tune their activity and motor output, to collectives of cells in tissues that flow and redistribute biochemical signals during development. AU - Lenne, Pierre François AU - Munro, Edwin AU - Heemskerk, Idse AU - Warmflash, Aryeh AU - Bocanegra, Laura AU - Kishi, Kasumi AU - Kicheva, Anna AU - Long, Yuchen AU - Fruleux, Antoine AU - Boudaoud, Arezki AU - Saunders, Timothy E. AU - Caldarelli, Paolo AU - Michaut, Arthur AU - Gros, Jerome AU - Maroudas-Sacks, Yonit AU - Keren, Kinneret AU - Hannezo, Edouard B AU - Gartner, Zev J. AU - Stormo, Benjamin AU - Gladfelter, Amy AU - Rodrigues, Alan AU - Shyer, Amy AU - Minc, Nicolas AU - Maître, Jean Léon AU - Di Talia, Stefano AU - Khamaisi, Bassma AU - Sprinzak, David AU - Tlili, Sham ID - 9349 IS - 4 JF - Physical biology TI - Roadmap for the multiscale coupling of biochemical and mechanical signals during development VL - 18 ER - TY - JOUR AB - Polaritons with directional in-plane propagation and ultralow losses in van der Waals (vdW) crystals promise unprecedented manipulation of light at the nanoscale. However, these polaritons present a crucial limitation: their directional propagation is intrinsically determined by the crystal structure of the host material, imposing forbidden directions of propagation. Here, we demonstrate that directional polaritons (in-plane hyperbolic phonon polaritons) in a vdW crystal (α-phase molybdenum trioxide) can be directed along forbidden directions by inducing an optical topological transition, which emerges when the slab is placed on a substrate with a given negative permittivity (4H–silicon carbide). By visualizing the transition in real space, we observe exotic polaritonic states between mutually orthogonal hyperbolic regimes, which unveil the topological origin of the transition: a gap opening in the dispersion. This work provides insights into optical topological transitions in vdW crystals, which introduce a route to direct light at the nanoscale. AU - Duan, J. AU - Álvarez-Pérez, G. AU - Voronin, K. V. AU - Prieto Gonzalez, Ivan AU - Taboada-Gutiérrez, J. AU - Volkov, V. S. AU - Martín-Sánchez, J. AU - Nikitin, A. Y. AU - Alonso-González, P. ID - 9334 IS - 14 JF - Science Advances TI - Enabling propagation of anisotropic polaritons along forbidden directions via a topological transition VL - 7 ER - TY - JOUR AB - We consider the many-body quantum evolution of a factorized initial data, in the mean-field regime. We show that fluctuations around the limiting Hartree dynamics satisfy large deviation estimates that are consistent with central limit theorems that have been established in the last years. AU - Kirkpatrick, Kay AU - Rademacher, Simone Anna Elvira AU - Schlein, Benjamin ID - 9351 JF - Annales Henri Poincare SN - 1424-0637 TI - A large deviation principle in many-body quantum dynamics VL - 22 ER - TY - JOUR AB - Mentorship is experience and/or knowledge‐based guidance. Mentors support, sponsor and advocate for mentees. Having one or more mentors when you seek advice can significantly influence and improve your research endeavours, well‐being and career development. Positive mentee–mentor relationships are vital for maintaining work–life balance and success in careers. Early‐career researchers (ECRs), in particular, can benefit from mentorship to navigate challenges in academic and nonacademic life and careers. Yet, strategies for selecting mentors and maintaining interactions with them are often underdiscussed within research environments. In this Words of Advice, we provide recommendations for ECRs to seek and manage mentorship interactions. Our article draws from our experiences as ECRs and published work, to provide suggestions for mentees to proactively promote beneficial mentorship interactions. The recommended practices highlight the importance of identifying mentorship needs, planning and selecting multiple and diverse mentors, setting goals, and maintaining constructive, and mutually beneficial working relationships with mentors. AU - Sarabipour, Sarvenaz AU - Hainer, Sarah J. AU - Arslan, Feyza N AU - De Winde, Charlotte M. AU - Furlong, Emily AU - Bielczyk, Natalia AU - Jadavji, Nafisa M. AU - Shah, Aparna P. AU - Davla, Sejal ID - 9336 JF - FEBS Journal SN - 1742-464X TI - Building and sustaining mentor interactions as a mentee ER - TY - JOUR AB - Intercellular adhesion is the key to multicellularity, and its malfunction plays an important role in various developmental and disease-related processes. Although it has been intensively studied by both biologists and physicists, a commonly accepted definition of cell-cell adhesion is still being debated. Cell-cell adhesion has been described at the molecular scale as a function of adhesion receptors controlling binding affinity, at the cellular scale as resistance to detachment forces or modulation of surface tension, and at the tissue scale as a regulator of cellular rearrangements and morphogenesis. In this review, we aim to summarize and discuss recent advances in the molecular, cellular, and theoretical description of cell-cell adhesion, ranging from biomimetic models to the complexity of cells and tissues in an organismal context. In particular, we will focus on cadherin-mediated cell-cell adhesion and the role of adhesion signaling and mechanosensation therein, two processes central for understanding the biological and physical basis of cell-cell adhesion. AU - Arslan, Feyza N AU - Eckert, Julia AU - Schmidt, Thomas AU - Heisenberg, Carl-Philipp J ID - 9350 JF - Biophysical Journal SN - 0006-3495 TI - Holding it together: when cadherin meets cadherin VL - 120 ER - TY - JOUR AB - We consider the stochastic quantization of a quartic double-well energy functional in the semiclassical regime and derive optimal asymptotics for the exponentially small splitting of the ground state energy. Our result provides an infinite-dimensional version of some sharp tunneling estimates known in finite dimensions for semiclassical Witten Laplacians in degree zero. From a stochastic point of view it proves that the L2 spectral gap of the stochastic one-dimensional Allen-Cahn equation in finite volume satisfies a Kramers-type formula in the limit of vanishing noise. We work with finite-dimensional lattice approximations and establish semiclassical estimates which are uniform in the dimension. Our key estimate shows that the constant separating the two exponentially small eigenvalues from the rest of the spectrum can be taken independently of the dimension. AU - Brooks, Morris AU - Di Gesù, Giacomo ID - 9348 IS - 3 JF - Journal of Functional Analysis SN - 0022-1236 TI - Sharp tunneling estimates for a double-well model in infinite dimension VL - 281 ER - TY - JOUR AB - This paper provides an a priori error analysis of a localized orthogonal decomposition method for the numerical stochastic homogenization of a model random diffusion problem. If the uniformly elliptic and bounded random coefficient field of the model problem is stationary and satisfies a quantitative decorrelation assumption in the form of the spectral gap inequality, then the expected $L^2$ error of the method can be estimated, up to logarithmic factors, by $H+(\varepsilon/H)^{d/2}$, $\varepsilon$ being the small correlation length of the random coefficient and $H$ the width of the coarse finite element mesh that determines the spatial resolution. The proof bridges recent results of numerical homogenization and quantitative stochastic homogenization. AU - Fischer, Julian L AU - Gallistl, Dietmar AU - Peterseim, Dietmar ID - 9352 IS - 2 JF - SIAM Journal on Numerical Analysis SN - 0036-1429 TI - A priori error analysis of a numerical stochastic homogenization method VL - 59 ER - TY - JOUR AB - Optogenetics has been harnessed to shed new mechanistic light on current and future therapeutic strategies. This has been to date achieved by the regulation of ion flow and electrical signals in neuronal cells and neural circuits that are known to be affected by disease. In contrast, the optogenetic delivery of trophic biochemical signals, which support cell survival and are implicated in degenerative disorders, has never been demonstrated in an animal model of disease. Here, we reengineered the human and Drosophila melanogaster REarranged during Transfection (hRET and dRET) receptors to be activated by light, creating one-component optogenetic tools termed Opto-hRET and Opto-dRET. Upon blue light stimulation, these receptors robustly induced the MAPK/ERK proliferative signaling pathway in cultured cells. In PINK1B9 flies that exhibit loss of PTEN-induced putative kinase 1 (PINK1), a kinase associated with familial Parkinson’s disease (PD), light activation of Opto-dRET suppressed mitochondrial defects, tissue degeneration and behavioral deficits. In human cells with PINK1 loss-of-function, mitochondrial fragmentation was rescued using Opto-dRET via the PI3K/NF-кB pathway. Our results demonstrate that a light-activated receptor can ameliorate disease hallmarks in a genetic model of PD. The optogenetic delivery of trophic signals is cell type-specific and reversible and thus has the potential to inspire novel strategies towards a spatio-temporal regulation of tissue repair. AU - Inglés Prieto, Álvaro AU - Furthmann, Nikolas AU - Crossman, Samuel H. AU - Tichy, Alexandra Madelaine AU - Hoyer, Nina AU - Petersen, Meike AU - Zheden, Vanessa AU - Bicher, Julia AU - Gschaider-Reichhart, Eva AU - György, Attila AU - Siekhaus, Daria E AU - Soba, Peter AU - Winklhofer, Konstanze F. AU - Janovjak, Harald L ID - 9363 IS - 4 JF - PLoS genetics TI - Optogenetic delivery of trophic signals in a genetic model of Parkinson's disease VL - 17 ER - TY - JOUR AB - Shigella are pathogens originating within the Escherichia lineage but frequently classified as a separate genus. Shigella genomes contain numerous insertion sequences (ISs) that lead to pseudogenisation of affected genes and an increase of non-homologous recombination. Here, we study 414 genomes of E. coli and Shigella strains to assess the contribution of genomic rearrangements to Shigella evolution. We found that Shigella experienced exceptionally high rates of intragenomic rearrangements and had a decreased rate of homologous recombination compared to pathogenic and non-pathogenic E. coli. The high rearrangement rate resulted in independent disruption of syntenic regions and parallel rearrangements in different Shigella lineages. Specifically, we identified two types of chromosomally encoded E3 ubiquitin-protein ligases acquired independently by all Shigella strains that also showed a high level of sequence conservation in the promoter and further in the 5′-intergenic region. In the only available enteroinvasive E. coli (EIEC) strain, which is a pathogenic E. coli with a phenotype intermediate between Shigella and non-pathogenic E. coli, we found a rate of genome rearrangements comparable to those in other E. coli and no functional copies of the two Shigella-specific E3 ubiquitin ligases. These data indicate that the accumulation of ISs influenced many aspects of genome evolution and played an important role in the evolution of intracellular pathogens. Our research demonstrates the power of comparative genomics-based on synteny block composition and an important role of non-coding regions in the evolution of genomic islands. AU - Seferbekova, Zaira AU - Zabelkin, Alexey AU - Yakovleva, Yulia AU - Afasizhev, Robert AU - Dranenko, Natalia O. AU - Alexeev, Nikita AU - Gelfand, Mikhail S. AU - Bochkareva, Olga ID - 9380 JF - Frontiers in Microbiology TI - High rates of genome rearrangements and pathogenicity of Shigella spp VL - 12 ER - TY - JOUR AB - We prove that the factorization homologies of a scheme with coefficients in truncated polynomial algebras compute the cohomologies of its generalized configuration spaces. Using Koszul duality between commutative algebras and Lie algebras, we obtain new expressions for the cohomologies of the latter. As a consequence, we obtain a uniform and conceptual approach for treating homological stability, homological densities, and arithmetic densities of generalized configuration spaces. Our results categorify, generalize, and in fact provide a conceptual understanding of the coincidences appearing in the work of Farb--Wolfson--Wood. Our computation of the stable homological densities also yields rational homotopy types, answering a question posed by Vakil--Wood. Our approach hinges on the study of homological stability of cohomological Chevalley complexes, which is of independent interest. AU - Ho, Quoc P ID - 9359 IS - 2 JF - Geometry & Topology KW - Generalized configuration spaces KW - homological stability KW - homological densities KW - chiral algebras KW - chiral homology KW - factorization algebras KW - Koszul duality KW - Ran space SN - 1364-0380 TI - Homological stability and densities of generalized configuration spaces VL - 25 ER - TY - JOUR AB - The multimeric matrix (M) protein of clinically relevant paramyxoviruses orchestrates assembly and budding activity of viral particles at the plasma membrane (PM). We identified within the canine distemper virus (CDV) M protein two microdomains, potentially assuming α-helix structures, which are essential for membrane budding activity. Remarkably, while two rationally designed microdomain M mutants (E89R, microdomain 1 and L239D, microdomain 2) preserved proper folding, dimerization, interaction with the nucleocapsid protein, localization at and deformation of the PM, the virus-like particle formation, as well as production of infectious virions (as monitored using a membrane budding-complementation system), were, in sharp contrast, strongly impaired. Of major importance, raster image correlation spectroscopy (RICS) revealed that both microdomains contributed to finely tune M protein mobility specifically at the PM. Collectively, our data highlighted the cornerstone membrane budding-priming activity of two spatially discrete M microdomains, potentially by coordinating the assembly of productive higher oligomers at the PM. AU - Gast, Matthieu AU - Kadzioch, Nicole P. AU - Milius, Doreen AU - Origgi, Francesco AU - Plattet, Philippe ID - 9361 IS - 2 JF - mSphere TI - Oligomerization and cell egress controlled by two microdomains of canine distemper virus matrix protein VL - 6 ER - TY - JOUR AB - This paper presents a method for designing planar multistable compliant structures. Given a sequence of desired stable states and the corresponding poses of the structure, we identify the topology and geometric realization of a mechanism—consisting of bars and joints—that is able to physically reproduce the desired multistable behavior. In order to solve this problem efficiently, we build on insights from minimally rigid graph theory to identify simple but effective topologies for the mechanism. We then optimize its geometric parameters, such as joint positions and bar lengths, to obtain correct transitions between the given poses. Simultaneously, we ensure adequate stability of each pose based on an effective approximate error metric related to the elastic energy Hessian of the bars in the mechanism. As demonstrated by our results, we obtain functional multistable mechanisms of manageable complexity that can be fabricated using 3D printing. Further, we evaluated the effectiveness of our method on a large number of examples in the simulation and fabricated several physical prototypes. AU - Zhang, Ran AU - Auzinger, Thomas AU - Bickel, Bernd ID - 9376 IS - 5 JF - ACM Transactions on Graphics KW - multistability KW - mechanism KW - computational design KW - rigidity SN - 0730-0301 TI - Computational design of planar multistable compliant structures VL - 40 ER - TY - JOUR AB - Genetic variation segregates as linked sets of variants, or haplotypes. Haplotypes and linkage are central to genetics and underpin virtually all genetic and selection analysis. And yet, genomic data often lack haplotype information, due to constraints in sequencing technologies. Here we present “haplotagging”, a simple, low-cost linked-read sequencing technique that allows sequencing of hundreds of individuals while retaining linkage information. We apply haplotagging to construct megabase-size haplotypes for over 600 individual butterflies (Heliconius erato and H. melpomene), which form overlapping hybrid zones across an elevational gradient in Ecuador. Haplotagging identifies loci controlling distinctive high- and lowland wing color patterns. Divergent haplotypes are found at the same major loci in both species, while chromosome rearrangements show no parallelism. Remarkably, in both species the geographic clines for the major wing pattern loci are displaced by 18 km, leading to the rise of a novel hybrid morph in the centre of the hybrid zone. We propose that shared warning signalling (Müllerian mimicry) may couple the cline shifts seen in both species, and facilitate the parallel co-emergence of a novel hybrid morph in both co-mimetic species. Our results show the power of efficient haplotyping methods when combined with large-scale sequencing data from natural populations. AU - Meier, Joana I. AU - Salazar, Patricio A. AU - Kučka, Marek AU - Davies, Robert William AU - Dréau, Andreea AU - Aldás, Ismael AU - Power, Olivia Box AU - Nadeau, Nicola J. AU - Bridle, Jon R. AU - Rolian, Campbell AU - Barton, Nicholas H AU - McMillan, W. Owen AU - Jiggins, Chris D. AU - Chan, Yingguang Frank ID - 9375 IS - 25 JF - PNAS TI - Haplotype tagging reveals parallel formation of hybrid races in two butterfly species VL - 118 ER - TY - JOUR AB - Chromosomal inversions have long been recognized for their role in local adaptation. By suppressing recombination in heterozygous individuals, they can maintain coadapted gene complexes and protect them from homogenizing effects of gene flow. However, to fully understand their importance for local adaptation we need to know their influence on phenotypes under divergent selection. For this, the marine snail Littorina saxatilis provides an ideal study system. Divergent ecotypes adapted to wave action and crab predation occur in close proximity on intertidal shores with gene flow between them. Here, we used F2 individuals obtained from crosses between the ecotypes to test for associations between genomic regions and traits distinguishing the Crab‐/Wave‐adapted ecotypes including size, shape, shell thickness, and behavior. We show that most of these traits are influenced by two previously detected inversion regions that are divergent between ecotypes. We thus gain a better understanding of one important underlying mechanism responsible for the rapid and repeated formation of ecotypes: divergent selection acting on inversions. We also found that some inversions contributed to more than one trait suggesting that they may contain several loci involved in adaptation, consistent with the hypothesis that suppression of recombination within inversions facilitates differentiation in the presence of gene flow. AU - Koch, Eva L. AU - Morales, Hernán E. AU - Larsson, Jenny AU - Westram, Anja M AU - Faria, Rui AU - Lemmon, Alan R. AU - Lemmon, E. Moriarty AU - Johannesson, Kerstin AU - Butlin, Roger K. ID - 9394 IS - 3 JF - Evolution Letters TI - Genetic variation for adaptive traits is associated with polymorphic inversions in Littorina saxatilis VL - 5 ER - TY - JOUR AB - A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium. AU - Kleshnina, Maria AU - Streipert, Sabrina S. AU - Filar, Jerzy A. AU - Chatterjee, Krishnendu ID - 9381 IS - 4 JF - PLoS Computational Biology SN - 1553734X TI - Mistakes can stabilise the dynamics of rock-paper-scissors games VL - 17 ER - TY - JOUR AB - Humans conceptualize the diversity of life by classifying individuals into types we call ‘species’1. The species we recognize influence political and financial decisions and guide our understanding of how units of diversity evolve and interact. Although the idea of species may seem intuitive, a debate about the best way to define them has raged even before Darwin2. So much energy has been devoted to the so-called ‘species problem’ that no amount of discourse will ever likely solve it2,3. Dozens of species concepts are currently recognized3, but we lack a concrete understanding of how much researchers actually disagree and the factors that cause them to think differently1,2. To address this, we used a survey to quantify the species problem for the first time. The results indicate that the disagreement is extensive: two randomly chosen respondents will most likely disagree on the nature of species. The probability of disagreement is not predicted by researcher experience or broad study system, but tended to be lower among researchers with similar focus, training and who study the same organism. Should we see this diversity of perspectives as a problem? We argue that we should not. AU - Stankowski, Sean AU - Ravinet, Mark ID - 9392 IS - 9 JF - Current Biology SN - 09609822 TI - Quantifying the use of species concepts VL - 31 ER - TY - JOUR AB - We report the complete analysis of a deterministic model of deleterious mutations and negative selection against them at two haploid loci without recombination. As long as mutation is a weaker force than selection, mutant alleles remain rare at the only stable equilibrium, and otherwise, a variety of dynamics are possible. If the mutation-free genotype is absent, generally the only stable equilibrium is the one that corresponds to fixation of the mutant allele at the locus where it is less deleterious. This result suggests that fixation of a deleterious allele that follows a click of the Muller’s ratchet is governed by natural selection, instead of random drift. AU - Khudiakova, Kseniia AU - Neretina, Tatiana Yu. AU - Kondrashov, Alexey S. ID - 9387 JF - Journal of Theoretical Biology KW - General Biochemistry KW - Genetics and Molecular Biology KW - Modelling and Simulation KW - Statistics and Probability KW - General Immunology and Microbiology KW - Applied Mathematics KW - General Agricultural and Biological Sciences KW - General Medicine SN - 0022-5193 TI - Two linked loci under mutation-selection balance and Muller’s ratchet VL - 524 ER -