@article{2850, abstract = {Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on capturing the measured correlations among pairs of neurons. Here we suggest an alternative, constructing models that are consistent with the distribution of global network activity, i.e. the probability that K out of N cells in the network generate action potentials in the same small time bin. The inverse problem that we need to solve in constructing the model is analytically tractable, and provides a natural 'thermodynamics' for the network in the limit of large N. We analyze the responses of neurons in a small patch of the retina to naturalistic stimuli, and find that the implied thermodynamics is very close to an unusual critical point, in which the entropy (in proper units) is exactly equal to the energy. © 2013 IOP Publishing Ltd and SISSA Medialab srl. }, author = {Tkacik, Gasper and Marre, Olivier and Mora, Thierry and Amodei, Dario and Berry, Michael and Bialek, William}, journal = {Journal of Statistical Mechanics Theory and Experiment}, number = {3}, publisher = {IOP Publishing Ltd.}, title = {{The simplest maximum entropy model for collective behavior in a neural network}}, doi = {10.1088/1742-5468/2013/03/P03011}, volume = {2013}, year = {2013}, } @article{2851, abstract = {The number of possible activity patterns in a population of neurons grows exponentially with the size of the population. Typical experiments explore only a tiny fraction of the large space of possible activity patterns in the case of populations with more than 10 or 20 neurons. It is thus impossible, in this undersampled regime, to estimate the probabilities with which most of the activity patterns occur. As a result, the corresponding entropy - which is a measure of the computational power of the neural population - cannot be estimated directly. We propose a simple scheme for estimating the entropy in the undersampled regime, which bounds its value from both below and above. The lower bound is the usual 'naive' entropy of the experimental frequencies. The upper bound results from a hybrid approximation of the entropy which makes use of the naive estimate, a maximum entropy fit, and a coverage adjustment. We apply our simple scheme to artificial data, in order to check their accuracy; we also compare its performance to those of several previously defined entropy estimators. We then apply it to actual measurements of neural activity in populations with up to 100 cells. Finally, we discuss the similarities and differences between the proposed simple estimation scheme and various earlier methods. © 2013 IOP Publishing Ltd and SISSA Medialab srl.}, author = {Berry, Michael and Tkacik, Gasper and Dubuis, Julien and Marre, Olivier and Da Silveira, Ravá}, journal = {Journal of Statistical Mechanics Theory and Experiment}, number = {3}, publisher = {IOP Publishing Ltd.}, title = {{A simple method for estimating the entropy of neural activity}}, doi = {10.1088/1742-5468/2013/03/P03015}, volume = {2013}, year = {2013}, } @article{2853, abstract = {High relatedness among interacting individuals has generally been considered a precondition for the evolution of altruism. However, kin-selection theory also predicts the evolution of altruism when relatedness is low, as long as the cost of the altruistic act is minor compared with its benefit. Here, we demonstrate evidence for a low-cost altruistic act in bacteria. We investigated Escherichia coli responding to the attack of an obligately lytic phage by committing suicide in order to prevent parasite transmission to nearby relatives. We found that bacterial suicide provides large benefits to survivors at marginal costs to committers. The cost of suicide was low, because infected cells are moribund, rapidly dying upon phage infection, such that no more opportunity for reproduction remains. As a consequence of its marginal cost, host suicide was selectively favoured even when relatedness between committers and survivors approached zero. Altogether, our findings demonstrate that low-cost suicide can evolve with ease, represents an effective host-defence strategy, and seems to be widespread among microbes. Moreover, low-cost suicide might also occur in higher organisms as exemplified by infected social insect workers leaving the colony to die in isolation.}, author = {Refardt, Dominik and Bergmiller, Tobias and Kümmerli, Rolf}, issn = {1471-2954}, journal = {Proceedings of the Royal Society of London Series B Biological Sciences}, number = {1759}, publisher = {The Royal Society}, title = {{Altruism can evolve when relatedness is low: Evidence from bacteria committing suicide upon phage infection}}, doi = {10.1098/rspb.2012.3035}, volume = {280}, year = {2013}, } @article{2854, abstract = {We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective to stay forever in a given set of states, and its dual, the reachability objective to reach a given set of states. First, we present a simple proof of the fact that in concurrent reachability games, for all ε>0, memoryless ε-optimal strategies exist. A memoryless strategy is independent of the history of plays, and an ε-optimal strategy achieves the objective with probability within ε of the value of the game. In contrast to previous proofs of this fact, our proof is more elementary and more combinatorial. Second, we present a strategy-improvement (a.k.a. policy-iteration) algorithm for concurrent games with reachability objectives. Finally, we present a strategy-improvement algorithm for turn-based stochastic games (where each player selects moves in turns) with safety objectives. Our algorithms yield sequences of player-1 strategies which ensure probabilities of winning that converge monotonically (from below) to the value of the game. © 2012 Elsevier Inc.}, author = {Chatterjee, Krishnendu and De Alfaro, Luca and Henzinger, Thomas A}, journal = {Journal of Computer and System Sciences}, number = {5}, pages = {640 -- 657}, publisher = {Elsevier}, title = {{Strategy improvement for concurrent reachability and turn based stochastic safety games}}, doi = {10.1016/j.jcss.2012.12.001}, volume = {79}, year = {2013}, } @article{2855, abstract = {Genomic imprinting leads to preferred expression of either the maternal or paternal alleles of a subset of genes. Imprinting is essential for mammalian development, and its deregulation causes many diseases. However, the functional relevance of imprinting at the cellular level is poorly understood for most imprinted genes. We used mosaic analysis with double markers (MADM) in mice to create uniparental disomies (UPDs) and to visualize imprinting effects with single-cell resolution. Although chromosome 12 UPD did not produce detectable phenotypes, chromosome 7 UPD caused highly significant paternal growth dominance in the liver and lung, but not in the brain or heart. A single gene on chromosome 7, encoding the secreted insulin-like growth factor 2 (IGF2), accounts for most of the paternal dominance effect. Mosaic analyses implied additional imprinted loci on chromosome 7 acting cell autonomously to transmit the IGF2 signal. Our study reveals chromosome- and cell-type specificity of genomic imprinting effects.}, author = {Hippenmeyer, Simon and Johnson, Randy and Luo, Liqun}, journal = {Cell Reports}, number = {3}, pages = {960 -- 967}, publisher = {Cell Press}, title = {{Mosaic analysis with double markers reveals cell type specific paternal growth dominance}}, doi = {10.1016/j.celrep.2013.02.002}, volume = {3}, year = {2013}, } @article{2856, abstract = {G protein–coupled receptors (GPCRs), the largest family of membrane signaling proteins, respond to neurotransmitters, hormones and small environmental molecules. The neuronal function of many GPCRs has been difficult to resolve because of an inability to gate them with subtype specificity, spatial precision, speed and reversibility. To address this, we developed an approach for opto-chemical engineering of native GPCRs. We applied this to the metabotropic glutamate receptors (mGluRs) to generate light-agonized and light-antagonized mGluRs (LimGluRs). The light-agonized LimGluR2, on which we focused, was fast, bistable and supported multiple rounds of on/off switching. Light gated two of the primary neuronal functions of mGluR2: suppression of excitability and inhibition of neurotransmitter release. We found that the light-antagonized tool LimGluR2-block was able to manipulate negative feedback of synaptically released glutamate on transmitter release. We generalized the optical control to two additional family members: mGluR3 and mGluR6. This system worked in rodent brain slices and in zebrafish in vivo, where we found that mGluR2 modulated the threshold for escape behavior. These light-gated mGluRs pave the way for determining the roles of mGluRs in synaptic plasticity, memory and disease.}, author = {Levitz, Joshua and Pantoja, Carlos and Gaub, Benjamin and Janovjak, Harald L and Reiner, Andreas and Hoagland, Adam and Schoppik, David and Kane, Brian and Stawski, Philipp and Schier, Alexander and Trauner, Dirk and Isacoff, Ehud}, journal = {Nature Neuroscience}, pages = {507 -- 516}, publisher = {Nature Publishing Group}, title = {{Optical control of metabotropic glutamate receptors}}, doi = {10.1038/nn.3346}, volume = {16}, year = {2013}, } @article{2857, abstract = {In the vibrant field of optogenetics, optics and genetic targeting are combined to commandeer cellular functions, such as the neuronal action potential, by optically stimulating light-sensitive ion channels expressed in the cell membrane. One broadly applicable manifestation of this approach are covalently attached photochromic tethered ligands (PTLs) that allow activating ligand-gated ion channels with outstanding spatial and temporal resolution. Here, we describe all steps towards the successful development and application of PTL-gated ion channels in cell lines and primary cells. The basis for these experiments forms a combination of molecular modeling, genetic engineering, cell culture, and electrophysiology. The light-gated glutamate receptor (LiGluR), which consists of the PTL-functionalized GluK2 receptor, serves as a model.}, author = {Szobota, Stephanie and Mckenzie, Catherine and Janovjak, Harald L}, journal = {Methods in Molecular Biology}, pages = {417 -- 435}, publisher = {Springer}, title = {{Optical control of ligand-gated ion channels}}, doi = {10.1007/978-1-62703-351-0_32}, volume = {998}, year = {2013}, } @article{2858, abstract = {Tumor growth is caused by the acquisition of driver mutations, which enhance the net reproductive rate of cells. Driver mutations may increase cell division, reduce cell death, or allow cells to overcome density-limiting effects. We study the dynamics of tumor growth as one additional driver mutation is acquired. Our models are based on two-type branching processes that terminate in either tumor disappearance or tumor detection. In our first model, both cell types grow exponentially, with a faster rate for cells carrying the additional driver. We find that the additional driver mutation does not affect the survival probability of the lesion, but can substantially reduce the time to reach the detectable size if the lesion is slow growing. In our second model, cells lacking the additional driver cannot exceed a fixed carrying capacity, due to density limitations. In this case, the time to detection depends strongly on this carrying capacity. Our model provides a quantitative framework for studying tumor dynamics during different stages of progression. We observe that early, small lesions need additional drivers, while late stage metastases are only marginally affected by them. These results help to explain why additional driver mutations are typically not detected in fast-growing metastases.}, author = {Reiter, Johannes and Božić, Ivana and Allen, Benjamin and Chatterjee, Krishnendu and Nowak, Martin}, journal = {Evolutionary Applications}, number = {1}, pages = {34 -- 45}, publisher = {Wiley-Blackwell}, title = {{The effect of one additional driver mutation on tumor progression}}, doi = {10.1111/eva.12020}, volume = {6}, year = {2013}, } @article{2859, abstract = {Given a continuous function f:X-R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of f. In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case X=R3 has ramifications in the fields of medical imaging and scientific visualization.}, author = {Bendich, Paul and Edelsbrunner, Herbert and Morozov, Dmitriy and Patel, Amit}, journal = {Homology, Homotopy and Applications}, number = {1}, pages = {51 -- 72}, publisher = {International Press}, title = {{Homology and robustness of level and interlevel sets}}, doi = {10.4310/HHA.2013.v15.n1.a3}, volume = {15}, year = {2013}, } @article{2860, abstract = {In the hippocampus, cell assemblies forming mnemonic representations of space are thought to arise as a result of changes in functional connections of pyramidal cells. We have found that CA1 interneuron circuits are also reconfigured during goal-oriented spatial learning through modification of inputs from pyramidal cells. As learning progressed, new pyramidal assemblies expressed in theta cycles alternated with previously established ones, and eventually overtook them. The firing patterns of interneurons developed a relationship to new, learning-related assemblies: some interneurons associated their activity with new pyramidal assemblies while some others dissociated from them. These firing associations were explained by changes in the weight of monosynaptic inputs received by interneurons from new pyramidal assemblies, as these predicted the associational changes. Spatial learning thus engages circuit modifications in the hippocampus that incorporate a redistribution of inhibitory activity that might assist in the segregation of competing pyramidal cell assembly patterns in space and time.}, author = {Dupret, David and O'Neill, Joseph and Csicsvari, Jozsef L}, journal = {Neuron}, number = {1}, pages = {166 -- 180}, publisher = {Elsevier}, title = {{Dynamic reconfiguration of hippocampal interneuron circuits during spatial learning}}, doi = {10.1016/j.neuron.2013.01.033}, volume = {78}, year = {2013}, } @article{2861, abstract = {We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory.}, author = {Botella Soler, Vicente and Oteo, José and Ros, Javier and Glendinning, Paul}, journal = {Journal of Physics A: Mathematical and Theoretical}, number = {12}, publisher = {IOP Publishing Ltd.}, title = {{Lyapunov exponent and topological entropy plateaus in piecewise linear maps}}, doi = {10.1088/1751-8113/46/12/125101}, volume = {46}, year = {2013}, } @article{2862, abstract = {Motile cilia perform crucial functions during embryonic development and throughout adult life. Development of organs containing motile cilia involves regulation of cilia formation (ciliogenesis) and formation of a luminal space (lumenogenesis) in which cilia generate fluid flows. Control of ciliogenesis and lumenogenesis is not yet fully understood, and it remains unclear whether these processes are coupled. In the zebrafish embryo, lethal giant larvae 2 (lgl2) is expressed prominently in ciliated organs. Lgl proteins are involved in establishing cell polarity and have been implicated in vesicle trafficking. Here, we identified a role for Lgl2 in development of ciliated epithelia in Kupffer's vesicle, which directs left-right asymmetry of the embryo; the otic vesicles, which give rise to the inner ear; and the pronephric ducts of the kidney. Using Kupffer's vesicle as a model ciliated organ, we found that depletion of Lgl2 disrupted lumen formation and reduced cilia number and length. Immunofluorescence and time-lapse imaging of Kupffer's vesicle morphogenesis in Lgl2-deficient embryos suggested cell adhesion defects and revealed loss of the adherens junction component E-cadherin at lateral membranes. Genetic interaction experiments indicate that Lgl2 interacts with Rab11a to regulate E-cadherin and mediate lumen formation that is uncoupled from cilia formation. These results uncover new roles and interactions for Lgl2 that are crucial for both lumenogenesis and ciliogenesis and indicate that these processes are genetically separable in zebrafish.}, author = {Tay, Hwee and Schulze, Sabrina and Compagnon, Julien and Foley, Fiona and Heisenberg, Carl-Philipp J and Yost, H Joseph and Abdelilah Seyfried, Salim and Amack, Jeffrey}, journal = {Development}, number = {7}, pages = {1550 -- 1559}, publisher = {Company of Biologists}, title = {{Lethal giant larvae 2 regulates development of the ciliated organ Kupffer’s vesicle}}, doi = {10.1242/dev.087130}, volume = {140}, year = {2013}, } @article{2863, abstract = {Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME) model—a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population.}, author = {Granot Atedgi, Einat and Tkacik, Gasper and Segev, Ronen and Schneidman, Elad}, journal = {PLoS Computational Biology}, number = {3}, publisher = {Public Library of Science}, title = {{Stimulus-dependent maximum entropy models of neural population codes}}, doi = {10.1371/journal.pcbi.1002922}, volume = {9}, year = {2013}, } @article{2880, abstract = {Lateral root (LR) formation is initiated when pericycle cells accumulate auxin, thereby acquiring founder cell (FC) status and triggering asymmetric cell divisions, giving rise to a new primordium. How this auxin maximum in pericycle cells builds up and remains focused is not understood. We report that the endodermis plays an active role in the regulation of auxin accumulation and is instructive for FCs to progress during the LR initiation (LRI) phase. We describe the functional importance of a PIN3 (PIN-formed) auxin efflux carrier-dependent hormone reflux pathway between overlaying endodermal and pericycle FCs. Disrupting this reflux pathway causes dramatic defects in the progress of FCs towards the next initiation phase. Our data identify an unexpected regulatory function for the endodermis in LRI as part of the fine-tuning mechanism that appears to act as a check point in LR organogenesis after FCs are specified.}, author = {Marhavy, Peter and Vanstraelen, Marleen and De Rybel, Bert and Zhaojun, Ding and Bennett, Malcolm and Beeckman, Tom and Benková, Eva}, journal = {EMBO Journal}, number = {1}, pages = {149 -- 158}, publisher = {Wiley-Blackwell}, title = {{Auxin reflux between the endodermis and pericycle promotes lateral root initiation}}, doi = {10.1038/emboj.2012.303}, volume = {32}, year = {2013}, } @article{2882, abstract = {Gravitropic bending of plant organs is mediated by an asymmetric signaling of the plant hormone auxin between the upper and lower side of the respective organ. Here, we show that also another plant hormone, gibberellic acid (GA), shows asymmetric action during gravitropic responses. Immunodetection using an antibody against GA and monitoring GA signaling output by downstream degradation of DELLA proteins revealed an asymmetric GA distribution and response with the maximum at the lower side of gravistimulated roots. Genetic or pharmacological manipulation of GA levels or response affects gravity-mediated auxin redistribution and root bending response. The higher GA levels at the lower side of the root correlate with increased amounts of PIN-FORMED2 (PIN2) auxin transporter at the plasma membrane. The observed increase in PIN2 stability is caused by a specific GA effect on trafficking of PIN proteins to lytic vacuoles that presumably occurs downstream of brefeldin A-sensitive endosomes. Our results suggest that asymmetric auxin distribution instructive for gravity-induced differential growth is consolidated by the asymmetric action of GA that stabilizes the PIN-dependent auxin stream along the lower side of gravistimulated roots.}, author = {Löfke, Christian and Zwiewka, Marta and Heilmann, Ingo and Van Montagu, Marc and Teichmann, Thomas and Friml, Jirí}, journal = {PNAS}, number = {9}, pages = {3627 -- 3632}, publisher = {National Academy of Sciences}, title = {{Asymmetric gibberellin signaling regulates vacuolar trafficking of PIN auxin transporters during root gravitropism}}, doi = {10.1073/pnas.1300107110}, volume = {110}, year = {2013}, } @article{2883, abstract = {Plant architecture is influenced by the polar, cell-to-cell transport of auxin that is primarily provided and regulated by plasma membrane efflux catalysts of the PIN-FORMED and B family of ABC transporter (ABCB) classes. The latter were shown to require the functionality of the FK506 binding protein42 TWISTED DWARF1 (TWD1), although underlying mechanisms are unclear. By genetic manipulation of TWD1 expression, we show here that TWD1 affects shootward root auxin reflux and, thus, downstream developmental traits, such as epidermal twisting and gravitropism of the root. Using immunological assays, we demonstrate a predominant lateral, mainly outward-facing, plasma membrane location for TWD1 in the root epidermis characterized by the lateral marker ABC transporter G36/PLEIOTROPIC DRUG-RESISTANCE8/PENETRATION3. At these epidermal plasma membrane domains, TWD1 colocalizes with nonpolar ABCB1. In planta bioluminescence resonance energy transfer analysis was used to verify specific ABC transporter B1 (ABCB1)-TWD1 interaction. Our data support a model in which TWD1 promotes lateral ABCB-mediated auxin efflux via protein-protein interaction at the plasma membrane, minimizing reflux from the root apoplast into the cytoplasm.}, author = {Wang, Bangjun and Bailly, Aurélien and Zwiewk, Marta and Henrichs, Sina and Azzarello, Elisa and Mancuso, Stefano and Maeshima, Masayoshi and Friml, Jirí and Schulz, Alexander and Geisler, Markus}, journal = {Plant Cell}, number = {1}, pages = {202 -- 214}, publisher = {American Society of Plant Biologists}, title = {{Arabidopsis TWISTED DWARF1 functionally interacts with auxin exporter ABCB1 on the root plasma membrane}}, doi = {10.1105/tpc.112.105999}, volume = {25}, year = {2013}, } @article{2884, author = {Maître, Jean-Léon and Berthoumieux, Hélène and Krens, Gabriel and Salbreux, Guillaume and Julicher, Frank and Paluch, Ewa and Heisenberg, Carl-Philipp J}, journal = {Medecine Sciences}, number = {2}, pages = {147 -- 150}, publisher = {Éditions Médicales et Scientifiques}, title = {{Cell adhesion mechanics of zebrafish gastrulation}}, doi = {10.1051/medsci/2013292011}, volume = {29}, year = {2013}, } @proceedings{2885, abstract = {This volume contains the post-proceedings of the 8th Doctoral Workshop on Mathematical and Engineering Methods in Computer Science, MEMICS 2012, held in Znojmo, Czech Republic, in October, 2012. The 13 thoroughly revised papers were carefully selected out of 31 submissions and are presented together with 6 invited papers. The topics covered by the papers include: computer-aided analysis and verification, applications of game theory in computer science, networks and security, modern trends of graph theory in computer science, electronic systems design and testing, and quantum information processing.}, editor = {Kucera, Antonin and Henzinger, Thomas A and Nesetril, Jaroslav and Vojnar, Tomas and Antos, David}, location = {Znojmo, Czech Republic}, pages = {1 -- 228}, publisher = {Springer}, title = {{Mathematical and Engineering Methods in Computer Science}}, doi = {10.1007/978-3-642-36046-6}, volume = {7721}, year = {2013}, } @inproceedings{2886, abstract = {We focus on the realizability problem of Message Sequence Graphs (MSG), i.e. the problem whether a given MSG specification is correctly distributable among parallel components communicating via messages. This fundamental problem of MSG is known to be undecidable. We introduce a well motivated restricted class of MSG, so called controllable-choice MSG, and show that all its models are realizable and moreover it is decidable whether a given MSG model is a member of this class. In more detail, this class of MSG specifications admits a deadlock-free realization by overloading existing messages with additional bounded control data. We also show that the presented class is the largest known subclass of MSG that allows for deadlock-free realization.}, author = {Chmelik, Martin and Řehák, Vojtěch}, location = {Znojmo, Czech Republic}, pages = {118 -- 130}, publisher = {Springer}, title = {{Controllable-choice message sequence graphs}}, doi = {10.1007/978-3-642-36046-6_12}, volume = {7721}, year = {2013}, } @article{2887, abstract = {Root system growth and development is highly plastic and is influenced by the surrounding environment. Roots frequently grow in heterogeneous environments that include interactions from neighboring plants and physical impediments in the rhizosphere. To investigate how planting density and physical objects affect root system growth, we grew rice in a transparent gel system in close proximity with another plant or a physical object. Root systems were imaged and reconstructed in three dimensions. Root-root interaction strength was calculated using quantitative metrics that characterize the extent towhich the reconstructed root systems overlap each other. Surprisingly, we found the overlap of root systems of the same genotype was significantly higher than that of root systems of different genotypes. Root systems of the same genotype tended to grow toward each other but those of different genotypes appeared to avoid each other. Shoot separation experiments excluded the possibility of aerial interactions, suggesting root communication. Staggered plantings indicated that interactions likely occur at root tips in close proximity. Recognition of obstacles also occurred through root tips, but through physical contact in a size-dependent manner. These results indicate that root systems use two different forms of communication to recognize objects and alter root architecture: root-root recognition, possibly mediated through root exudates, and root-object recognition mediated by physical contact at the root tips. This finding suggests that root tips act as local sensors that integrate rhizosphere information into global root architectural changes.}, author = {Fang, Suqin and Clark, Randy and Zheng, Ying and Iyer Pascuzzi, Anjali and Weitz, Joshua and Kochian, Leon and Edelsbrunner, Herbert and Liao, Hong and Benfey, Philip}, journal = {PNAS}, number = {7}, pages = {2670 -- 2675}, publisher = {National Academy of Sciences}, title = {{Genotypic recognition and spatial responses by rice roots}}, doi = {10.1073/pnas.1222821110}, volume = {110}, year = {2013}, }