Enquiry into the topology of plasma membrane localized PIN auxin transport components - Nodzyński, Tomasz; Vanneste, Steffen; Zwiewka, Marta; Pernisová, Markéta; Hejátko, Jan; Friml, Jirí (Molecular Plant)
Auxin directs plant ontogenesis via differential accumulation within tissues depending largely on the activity of PIN proteins that mediate auxin efflux from cells and its directional cell-to-cell transport. Regardless of the developmental importance of PINs, the structure of these transporters is poorly characterized. Here, we present experimental data concerning protein topology of plasma membrane-localized PINs. Utilizing approaches based on pH-dependent quenching of fluorescent reporters combined with immunolocalization techniques, we mapped the membrane topology of PINs and further cross-validated our results using available topology modeling software. We delineated the topology of PIN1 with two transmembrane (TM) bundles of five α-helices linked by a large intracellular loop and a C-terminus positioned outside the cytoplasm. Using constraints derived from our experimental data, we also provide an updated position of helical regions generating a verisimilitude model of PIN1. Since the canonical long PINs show a high degree of conservation in TM domains and auxin transport capacity has been demonstrated for Arabidopsis representatives of this group, this empirically enhanced topological model of PIN1 will be an important starting point for further studies on PIN structure–function relationships. In addition, we have established protocols that can be used to probe the topology of other plasma membrane proteins in plants. © 2016 The Authors

Auxin flow mediated competition between axillary buds to restore apical dominance - Balla, Jozef; Medved'Ová, Zuzana; Kalousek, Petr; Matiješčuková, Natálie; Friml, Jirí; Reinöhl, Vilém; Procházka, Stanislav (Scientific Reports)
Apical dominance is one of the fundamental developmental phenomena in plant biology, which determines the overall architecture of aerial plant parts. Here we show apex decapitation activated competition for dominance in adjacent upper and lower axillary buds. A two-nodal-bud pea (Pisum sativum L.) was used as a model system to monitor and assess auxin flow, auxin transport channels, and dormancy and initiation status of axillary buds. Auxin flow was manipulated by lateral stem wounds or chemically by auxin efflux inhibitors 2,3,5-triiodobenzoic acid (TIBA), 1-N-naphtylphtalamic acid (NPA), or protein synthesis inhibitor cycloheximide (CHX) treatments, which served to interfere with axillary bud competition. Redirecting auxin flow to different points influenced which bud formed the outgrowing and dominant shoot. The obtained results proved that competition between upper and lower axillary buds as secondary auxin sources is based on the same auxin canalization principle that operates between the shoot apex and axillary bud. © The Author(s) 2016.

Adaptive moment closure for parameter inference of biochemical reaction networks - Schilling, Christian; Bogomolov, Sergiy; Henzinger, Thomas A; Podelski, Andreas; Ruess, Jakob (Biosystems)
Continuous-time Markov chain (CTMC) models have become a central tool for understanding the dynamics of complex reaction networks and the importance of stochasticity in the underlying biochemical processes. When such models are employed to answer questions in applications, in order to ensure that the model provides a sufficiently accurate representation of the real system, it is of vital importance that the model parameters are inferred from real measured data. This, however, is often a formidable task and all of the existing methods fail in one case or the other, usually because the underlying CTMC model is high-dimensional and computationally difficult to analyze. The parameter inference methods that tend to scale best in the dimension of the CTMC are based on so-called moment closure approximations. However, there exists a large number of different moment closure approximations and it is typically hard to say a priori which of the approximations is the most suitable for the inference procedure. Here, we propose a moment-based parameter inference method that automatically chooses the most appropriate moment closure method. Accordingly, contrary to existing methods, the user is not required to be experienced in moment closure techniques. In addition to that, our method adaptively changes the approximation during the parameter inference to ensure that always the best approximation is used, even in cases where different approximations are best in different regions of the parameter space. © 2016 Elsevier Ireland Ltd

A study of rigorous ODE integrators for multi scale set oriented computations - Miyaji, Tomoyuki; Pilarczyk, Pawel; Gameiro, Marcio; Kokubu, Hiroshi; Mischaikow, Konstantin (Applied Numerical Mathematics)
We study the usefulness of two most prominent publicly available rigorous ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable of handling entire sets of initial conditions and provide tight rigorous outer enclosures of the images under a time-T map. We conduct extensive benchmark computations using the well-known Lorenz system, and compare the computation time against the final accuracy achieved. We also discuss the effect of a few technical parameters, such as the order of the numerical integration method, the value of T, and the phase space resolution. We conclude that COSY may provide more precise results due to its ability of avoiding the variable dependency problem. However, the overall cost of computations conducted using CAPD is typically lower, especially when intervals of parameters are involved. Moreover, access to COSY is limited (registration required) and the rigorous ODE integrators are not publicly available, while CAPD is an open source free software project. Therefore, we recommend the latter integrator for this kind of computations. Nevertheless, proper choice of the various integration parameters turns out to be of even greater importance than the choice of the integrator itself. © 2016 IMACS. Published by Elsevier B.V. All rights reserved.

A Radical Break Restraining Neutrophil Migration - Renkawitz, Jörg; Sixt, Michael K (Developmental Cell)
When neutrophils infiltrate a site of inflammation, they have to stop at the right place to exert their effector function. In this issue of Developmental Cell, Wang et al. (2016) show that neutrophils sense reactive oxygen species via the TRPM2 channel to arrest migration at their target site. © 2016 Elsevier Inc.

A noncanonical auxin sensing mechanism is required for organ morphogenesis in arabidopsis - Simonini, Sara; Deb, Joyita; Moubayidin, Laila; Stephenson, Pauline; Valluru, Manoj; Freire Rios, Alejandra; Sorefan, Karim; Weijers, Dolf; Friml, Jirí; Östergaard, Lars (Genes and Development)
Tissue patterning in multicellular organisms is the output of precise spatio–temporal regulation of gene expression coupled with changes in hormone dynamics. In plants, the hormone auxin regulates growth and development at every stage of a plant’s life cycle. Auxin signaling occurs through binding of the auxin molecule to a TIR1/AFB F-box ubiquitin ligase, allowing interaction with Aux/IAA transcriptional repressor proteins. These are subsequently ubiquitinated and degraded via the 26S proteasome, leading to derepression of auxin response factors (ARFs). How auxin is able to elicit such a diverse range of developmental responses through a single signaling module has not yet been resolved. Here we present an alternative auxin-sensing mechanism in which the ARF ARF3/ETTIN controls gene expression through interactions with process-specific transcription factors. This noncanonical hormonesensing mechanism exhibits strong preference for the naturally occurring auxin indole 3-acetic acid (IAA) and is important for coordinating growth and patterning in diverse developmental contexts such as gynoecium morphogenesis, lateral root emergence, ovule development, and primary branch formation. Disrupting this IAA-sensing ability induces morphological aberrations with consequences for plant fitness. Therefore, our findings introduce a novel transcription factor-based mechanism of hormone perception in plants. © 2016 Simonini et al.

A model of differential growth guided apical hook formation in plants - Žádníková, Petra; Wabnik, Krzysztof T; Abuzeineh, Anas; Gallemí, Marçal; Van Der Straeten, Dominique; Smith, Richard; Inze, Dirk; Friml, Jirí; Prusinkiewicz, Przemysław; Benková, Eva (Plant Cell)
Differential cell growth enables flexible organ bending in the presence of environmental signals such as light or gravity. A prominent example of the developmental processes based on differential cell growth is the formation of the apical hook that protects the fragile shoot apical meristem when it breaks through the soil during germination. Here, we combined in silico and in vivo approaches to identify a minimal mechanism producing auxin gradient-guided differential growth during the establishment of the apical hook in the model plant Arabidopsis thaliana. Computer simulation models based on experimental data demonstrate that asymmetric expression of the PIN-FORMED auxin efflux carrier at the concave (inner) versus convex (outer) side of the hook suffices to establish an auxin maximum in the epidermis at the concave side of the apical hook. Furthermore, we propose a mechanism that translates this maximum into differential growth, and thus curvature, of the apical hook. Through a combination of experimental and in silico computational approaches, we have identified the individual contributions of differential cell elongation and proliferation to defining the apical hook and reveal the role of auxin-ethylene crosstalk in balancing these two processes. © 2016 American Society of Plant Biologists. All rights reserved.

A microfluidic device for measuring cell migration towards substrate bound and soluble chemokine gradients - Schwarz, Jan; Bierbaum, Veronika; Merrin, Jack; Frank, Tino; Hauschild, Robert; Bollenbach, Mark Tobias; Tay, Savaş; Sixt, Michael K; Mehling, Matthias (Scientific Reports)
Cellular locomotion is a central hallmark of eukaryotic life. It is governed by cell-extrinsic molecular factors, which can either emerge in the soluble phase or as immobilized, often adhesive ligands. To encode for direction, every cue must be present as a spatial or temporal gradient. Here, we developed a microfluidic chamber that allows measurement of cell migration in combined response to surface immobilized and soluble molecular gradients. As a proof of principle we study the response of dendritic cells to their major guidance cues, chemokines. The majority of data on chemokine gradient sensing is based on in vitro studies employing soluble gradients. Despite evidence suggesting that in vivo chemokines are often immobilized to sugar residues, limited information is available how cells respond to immobilized chemokines. We tracked migration of dendritic cells towards immobilized gradients of the chemokine CCL21 and varying superimposed soluble gradients of CCL19. Differential migratory patterns illustrate the potential of our setup to quantitatively study the competitive response to both types of gradients. Beyond chemokines our approach is broadly applicable to alternative systems of chemo- and haptotaxis such as cells migrating along gradients of adhesion receptor ligands vs. any soluble cue.

Facets of the r-stable (n, k)-hypersimplex - Hibi, Takayugi; Liam Solus (Annals of Combinatorics)
Let k, n, and r be positive integers with k < n and r≤⌊nk⌋. We determine the facets of the r-stable n, k-hypersimplex. As a result, it turns out that the r-stable n, k-hypersimplex has exactly 2n facets for every r<⌊nk⌋. We then utilize the equations of the facets to study when the r-stable hypersimplex is Gorenstein. For every k > 0 we identify an infinite collection of Gorenstein r-stable hypersimplices, consequently expanding the collection of r-stable hypersimplices known to have unimodal Ehrhart δ-vectors.

Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population - Lee, Ji; Schnelli, Kevin (Annals of Applied Probability)
We consider sample covariance matrices of the form Q = ( σ1/2X)(σ1/2X)∗, where the sample X is an M ×N random matrix whose entries are real independent random variables with variance 1/N and whereσ is an M × M positive-definite deterministic matrix. We analyze the asymptotic fluctuations of the largest rescaled eigenvalue of Q when both M and N tend to infinity with N/M →d ϵ (0,∞). For a large class of populations σ in the sub-critical regime, we show that the distribution of the largest rescaled eigenvalue of Q is given by the type-1 Tracy-Widom distribution under the additional assumptions that (1) either the entries of X are i.i.d. Gaussians or (2) that σ is diagonal and that the entries of X have a sub-exponential decay.

Shedding light on the grey zone of speciation along a continuum of genomic divergence - Roux, Camille; Fraisse, Christelle; Romiguier, Jonathan; Anciaux, Youann; Galtier, Nicolas; Bierne, Nicolas (PLoS Biology)
Speciation results from the progressive accumulation of mutations that decrease the probability of mating between parental populations or reduce the fitness of hybrids—the so-called species barriers. The speciation genomic literature, however, is mainly a collection of case studies, each with its own approach and specificities, such that a global view of the gradual process of evolution from one to two species is currently lacking. Of primary importance is the prevalence of gene flow between diverging entities, which is central in most species concepts and has been widely discussed in recent years. Here, we explore the continuum of speciation thanks to a comparative analysis of genomic data from 61 pairs of populations/species of animals with variable levels of divergence. Gene flow between diverging gene pools is assessed under an approximate Bayesian computation (ABC) framework. We show that the intermediate "grey zone" of speciation, in which taxonomy is often controversial, spans from 0.5% to 2% of net synonymous divergence, irrespective of species life history traits or ecology. Thanks to appropriate modeling of among-locus variation in genetic drift and introgression rate, we clarify the status of the majority of ambiguous cases and uncover a number of cryptic species. Our analysis also reveals the high incidence in animals of semi-isolated species (when some but not all loci are affected by barriers to gene flow) and highlights the intrinsic difficulty, both statistical and conceptual, of delineating species in the grey zone of speciation.

Hanani-Tutte for radial planarity II - Fulek, Radoslav; Pelsmajer, Michael; Schaefer, Marcus
A drawing of a graph G is radial if the vertices of G are placed on concentric circles C1, … , Ck with common center c, and edges are drawn radially: every edge intersects every circle centered at c at most once. G is radial planar if it has a radial embedding, that is, a crossing-free radial drawing. If the vertices of G are ordered or partitioned into ordered levels (as they are for leveled graphs), we require that the assignment of vertices to circles corresponds to the given ordering or leveling. A pair of edges e and f in a graph is independent if e and f do not share a vertex. We show that a graph G is radial planar if G has a radial drawing in which every two independent edges cross an even number of times; the radial embedding has the same leveling as the radial drawing. In other words, we establish the strong Hanani-Tutte theorem for radial planarity. This characterization yields a very simple algorithm for radial planarity testing.

C-planarity of embedded cyclic c-graphs - Fulek, Radoslav
We show that c-planarity is solvable in quadratic time for flat clustered graphs with three clusters if the combinatorial embedding of the underlying graph is fixed. In simpler graph-theoretical terms our result can be viewed as follows. Given a graph G with the vertex set partitioned into three parts embedded on a 2-sphere, our algorithm decides if we can augment G by adding edges without creating an edge-crossing so that in the resulting spherical graph the vertices of each part induce a connected sub-graph. We proceed by a reduction to the problem of testing the existence of a perfect matching in planar bipartite graphs. We formulate our result in a slightly more general setting of cyclic clustered graphs, i.e., the simple graph obtained by contracting each cluster, where we disregard loops and multi-edges, is a cycle.

A symbolic SAT based algorithm for almost sure reachability with small strategies in POMDPs - Chatterjee, Krishnendu; Chmelik, Martin; Davies, Jessica (Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence)
POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIMEcomplete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach. © 2016, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.

Beyond the hypercube evolutionary accessibility of fitness landscapes with realistic mutational networks - Zagórski, Marcin P; Burda, Zdzisław; Wacław, Bartłomiej (PLoS Computational Biology)
Evolutionary pathways describe trajectories of biological evolution in the space of different variants of organisms (genotypes). The probability of existence and the number of evolutionary pathways that lead from a given genotype to a better-adapted genotype are important measures of accessibility of local fitness optima and the reproducibility of evolution. Both quantities have been studied in simple mathematical models where genotypes are represented as binary sequences of two types of basic units, and the network of permitted mutations between the genotypes is a hypercube graph. However, it is unclear how these results translate to the biologically relevant case in which genotypes are represented by sequences of more than two units, for example four nucleotides (DNA) or 20 amino acids (proteins), and the mutational graph is not the hypercube. Here we investigate accessibility of the best-adapted genotype in the general case of K > 2 units. Using computer generated and experimental fitness landscapes we show that accessibility of the global fitness maximum increases with K and can be much higher than for binary sequences. The increase in accessibility comes from the increase in the number of indirect trajectories exploited by evolution for higher K. As one of the consequences, the fraction of genotypes that are accessible increases by three orders of magnitude when the number of units K increases from 2 to 16 for landscapes of size N ∼ 106genotypes. This suggests that evolution can follow many different trajectories on such landscapes and the reconstruction of evolutionary pathways from experimental data might be an extremely difficult task.

Modular parameter identification of biomolecular networks - Lang, Moritz; Stelling, Jörg (SIAM Journal on Scientific Computing)
The increasing complexity of dynamic models in systems and synthetic biology poses computational challenges especially for the identification of model parameters. While modularization of the corresponding optimization problems could help reduce the “curse of dimensionality,” abundant feedback and crosstalk mechanisms prohibit a simple decomposition of most biomolecular networks into subnetworks, or modules. Drawing on ideas from network modularization and multiple-shooting optimization, we present here a modular parameter identification approach that explicitly allows for such interdependencies. Interfaces between our modules are given by the experimentally measured molecular species. This definition allows deriving good (initial) estimates for the inter-module communication directly from the experimental data. Given these estimates, the states and parameter sensitivities of different modules can be integrated independently. To achieve consistency between modules, we iteratively adjust the estimates for inter-module communication while optimizing the parameters. After convergence to an optimal parameter set---but not during earlier iterations---the intermodule communication as well as the individual modules\' state dynamics agree with the dynamics of the nonmodularized network. Our modular parameter identification approach allows for easy parallelization; it can reduce the computational complexity for larger networks and decrease the probability to converge to suboptimal local minima. We demonstrate the algorithm\'s performance in parameter estimation for two biomolecular networks, a synthetic genetic oscillator and a mammalian signaling pathway.

Understanding regulatory networks requires more than computing a multitude of graph statistics: Comment on "Drivers of structural features in gene regulatory networks: From biophysical constraints to biological function" by O. C. Martin et al. - Tkacik, Gasper (Physics of Life Reviews)

Nonequilibrium description of de novo biogenesis and transport through Golgi-like cisternae - Sachdeva, Himani; Barma, Mustansir; Rao, Madan (Scientific Reports)
A central issue in cell biology is the physico-chemical basis of organelle biogenesis in intracellular trafficking pathways, its most impressive manifestation being the biogenesis of Golgi cisternae. At a basic level, such morphologically and chemically distinct compartments should arise from an interplay between the molecular transport and chemical maturation. Here, we formulate analytically tractable, minimalist models, that incorporate this interplay between transport and chemical progression in physical space, and explore the conditions for de novo biogenesis of distinct cisternae. We propose new quantitative measures that can discriminate between the various models of transport in a qualitative manner-this includes measures of the dynamics in steady state and the dynamical response to perturbations of the kind amenable to live-cell imaging.

A closer look at multiple-forking: Leveraging (in)dependence for a tighter bound - Kamath Hosdurg, Chethan; Chatterjee, Sanjit (Algorithmica)
Boldyreva, Palacio and Warinschi introduced a multiple forking game as an extension of general forking. The notion of (multiple) forking is a useful abstraction from the actual simulation of cryptographic scheme to the adversary in a security reduction, and is achieved through the intermediary of a so-called wrapper algorithm. Multiple forking has turned out to be a useful tool in the security argument of several cryptographic protocols. However, a reduction employing multiple forking incurs a significant degradation of (Formula presented.) , where (Formula presented.) denotes the upper bound on the underlying random oracle calls and (Formula presented.) , the number of forkings. In this work we take a closer look at the reasons for the degradation with a tighter security bound in mind. We nail down the exact set of conditions for success in the multiple forking game. A careful analysis of the cryptographic schemes and corresponding security reduction employing multiple forking leads to the formulation of ‘dependence’ and ‘independence’ conditions pertaining to the output of the wrapper in different rounds. Based on the (in)dependence conditions we propose a general framework of multiple forking and a General Multiple Forking Lemma. Leveraging (in)dependence to the full allows us to improve the degradation factor in the multiple forking game by a factor of (Formula presented.). By implication, the cost of a single forking involving two random oracles (augmented forking) matches that involving a single random oracle (elementary forking). Finally, we study the effect of these observations on the concrete security of existing schemes employing multiple forking. We conclude that by careful design of the protocol (and the wrapper in the security reduction) it is possible to harness our observations to the full extent.

Pseudoentropy: Lower-bounds for chain rules and transformations - Pietrzak, Krzysztof Z; Maciej, Skorski
Computational notions of entropy have recently found many applications, including leakage-resilient cryptography, deterministic encryption or memory delegation. The two main types of results which make computational notions so useful are (1) Chain rules, which quantify by how much the computational entropy of a variable decreases if conditioned on some other variable (2) Transformations, which quantify to which extend one type of entropy implies another. Such chain rules and transformations typically lose a significant amount in quality of the entropy, and are the reason why applying these results one gets rather weak quantitative security bounds. In this paper we for the first time prove lower bounds in this context, showing that existing results for transformations are, unfortunately, basically optimal for non-adaptive black-box reductions (and it’s hard to imagine how non black-box reductions or adaptivity could be useful here.) A variable X has k bits of HILL entropy of quality (ϵ,s) if there exists a variable Y with k bits min-entropy which cannot be distinguished from X with advantage ϵ by distinguishing circuits of size s. A weaker notion is Metric entropy, where we switch quantifiers, and only require that for every distinguisher of size s, such a Y exists. We first describe our result concerning transformations. By definition, HILL implies Metric without any loss in quality. Metric entropy often comes up in applications, but must be transformed to HILL for meaningful security guarantees. The best known result states that if a variable X has k bits of Metric entropy of quality (ϵ,s) , then it has k bits of HILL with quality (2ϵ,s⋅ϵ2). We show that this loss of a factor Ω(ϵ−2) in circuit size is necessary. In fact, we show the stronger result that this loss is already necessary when transforming so called deterministic real valued Metric entropy to randomised boolean Metric (both these variants of Metric entropy are implied by HILL without loss in quality). The chain rule for HILL entropy states that if X has k bits of HILL entropy of quality (ϵ,s) , then for any variable Z of length m, X conditioned on Z has k−m bits of HILL entropy with quality (ϵ,s⋅ϵ2/2m). We show that a loss of Ω(2m/ϵ) in circuit size necessary here. Note that this still leaves a gap of ϵ between the known bound and our lower bound.