@article{1408,
  abstract     = {The concept of well group in a special but important case captures homological properties of the zero set of a continuous map (Formula presented.) on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within (Formula presented.) distance r from f for a given (Formula presented.). The main drawback of the approach is that the computability of well groups was shown only when (Formula presented.) or (Formula presented.). Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of (Formula presented.) by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and (Formula presented.), our approximation of the (Formula presented.)th well group is exact. For the second part, we find examples of maps (Formula presented.) with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status.},
  author       = {Franek, Peter and Krcál, Marek},
  journal      = {Discrete & Computational Geometry},
  number       = {1},
  pages        = {126 -- 164},
  publisher    = {Springer},
  title        = {{On computability and triviality of well groups}},
  doi          = {10.1007/s00454-016-9794-2},
  volume       = {56},
  year         = {2016},
}

@article{1409,
  author       = {Abbott, Richard and Barton, Nicholas H and Good, Jeffrey},
  journal      = {Molecular Ecology},
  number       = {11},
  pages        = {2325 -- 2332},
  publisher    = {Wiley-Blackwell},
  title        = {{Genomics of hybridization and its evolutionary consequences}},
  doi          = {10.1111/mec.13685},
  volume       = {25},
  year         = {2016},
}

@article{1410,
  abstract     = {The pollen grains arise after meiosis of pollen mother cells within the anthers. A series of complex structural changes follows, generating mature pollen grains capable of performing the double fertilization of the female megasporophyte. Several signaling molecules, including hormones and lipids, have been involved in the regulation and appropriate control of pollen development. Phosphatidylinositol 4-phophate 5-kinases (PIP5K), which catalyze the biosynthesis of the phosphoinositide PtdIns(4,5)P2, are important for tip polar growth of root hairs and pollen tubes, embryo development, vegetative plant growth, and responses to the environment. Here, we report a role of PIP5Ks during microgametogenesis. PIP5K1 and PIP5K2 are expressed during early stages of pollen development and their transcriptional activity respond to auxin in pollen grains. Early male gametophytic lethality to certain grade was observed in both pip5k1-/- and pip5k2-/- single mutants. The number of pip5k mutant alleles is directly related to the frequency of aborted pollen grains suggesting the two genes are involved in the same function. Indeed PIP5K1 and PIP5K2 are functionally redundant since homozygous double mutants did not render viable pollen grains. The loss of function of PIP5K1 and PIP5K2results in defects in vacuole morphology in pollen at the later stages and epidermal root cells. Our results show that PIP5K1, PIP5K2 and phosphoinositide signaling are important cues for early developmental stages and vacuole formation during microgametogenesis.},
  author       = {Ugalde, José and Rodríguez Furlán, Cecilia and De Rycke, Riet and Norambuena, Lorena and Friml, Jirí and León, Gabriel and Tejos, Ricardo},
  journal      = {Plant Science},
  pages        = {10 -- 19},
  publisher    = {Elsevier},
  title        = {{Phosphatidylinositol 4-phosphate 5-kinases 1 and 2 are involved in the regulation of vacuole morphology during Arabidopsis thaliana pollen development}},
  doi          = {10.1016/j.plantsci.2016.05.014},
  volume       = {250},
  year         = {2016},
}

@article{1411,
  abstract     = {We consider two systems (α1, …, αm) and (β1, …,βn) of simple curves drawn on a compact two-dimensional surface M with boundary. Each αi and each βj is either an arc meeting the boundary of M at its two endpoints, or a closed curve. The αi are pairwise disjoint except for possibly sharing endpoints, and similarly for the βj. We want to “untangle” the βj from the ai by a self-homeomorphism of M; more precisely, we seek a homeomorphism φ:M→M fixing the boundary of M pointwise such that the total number of crossings of the ai with the φ(βj) is as small as possible. This problem is motivated by an application in the algorithmic theory of embeddings and 3-manifolds. We prove that if M is planar, i.e., a sphere with h ≥ 0 boundary components (“holes”), then O(mn) crossings can be achieved (independently of h), which is asymptotically tight, as an easy lower bound shows. In general, for an arbitrary (orientable or nonorientable) surface M with h holes and of (orientable or nonorientable) genus g ≥ 0, we obtain an O((m + n)4) upper bound, again independent of h and g. The proofs rely, among other things, on a result concerning simultaneous planar drawings of graphs by Erten and Kobourov.},
  author       = {Matoušek, Jiří and Sedgwick, Eric and Tancer, Martin and Wagner, Uli},
  journal      = {Israel Journal of Mathematics},
  number       = {1},
  pages        = {37 -- 79},
  publisher    = {Springer},
  title        = {{Untangling two systems of noncrossing curves}},
  doi          = {10.1007/s11856-016-1294-9},
  volume       = {212},
  year         = {2016},
}

@article{1412,
  abstract     = {Combining high-resolution level set surface tracking with lower resolution physics is an inexpensive method for achieving highly detailed liquid animations. Unfortunately, the inherent resolution mismatch introduces several types of disturbing visual artifacts. We identify the primary sources of these artifacts and present simple, efficient, and practical solutions to address them. First, we propose an unconditionally stable filtering method that selectively removes sub-grid surface artifacts not seen by the fluid physics, while preserving fine detail in dynamic splashing regions. It provides comparable results to recent error-correction techniques at lower cost, without substepping, and with better scaling behavior. Second, we show how a modified narrow-band scheme can ensure accurate free surface boundary conditions in the presence of large resolution mismatches. Our scheme preserves the efficiency of the narrow-band methodology, while eliminating objectionable stairstep artifacts observed in prior work. Third, we demonstrate that the use of linear interpolation of velocity during advection of the high-resolution level set surface is responsible for visible grid-aligned kinks; we therefore advocate higher-order velocity interpolation, and show that it dramatically reduces this artifact. While these three contributions are orthogonal, our results demonstrate that taken together they efficiently address the dominant sources of visual artifacts arising with high-resolution embedded liquid surfaces; the proposed approach offers improved visual quality, a straightforward implementation, and substantially greater scalability than competing methods.},
  author       = {Goldade, Ryan and Batty, Christopher and Wojtan, Christopher J},
  journal      = {Computer Graphics Forum},
  number       = {2},
  pages        = {233 -- 242},
  publisher    = {Wiley-Blackwell},
  title        = {{A practical method for high-resolution embedded liquid surfaces}},
  doi          = {10.1111/cgf.12826},
  volume       = {35},
  year         = {2016},
}

@article{1413,
  abstract     = {This paper generalizes the well-known Diffusion Curves Images (DCI), which are composed of a set of Bezier curves with colors specified on either side. These colors are diffused as Laplace functions over the image domain, which results in smooth color gradients interrupted by the Bezier curves. Our new formulation allows for more color control away from the boundary, providing a similar expressive power as recent Bilaplace image models without introducing associated issues and computational costs. The new model is based on a special Laplace function blending and a new edge blur formulation. We demonstrate that given some user-defined boundary curves over an input raster image, fitting colors and edge blur from the image to the new model and subsequent editing and animation is equally convenient as with DCIs. Numerous examples and comparisons to DCIs are presented.},
  author       = {Jeschke, Stefan},
  journal      = {Computer Graphics Forum},
  number       = {2},
  pages        = {71 -- 79},
  publisher    = {Wiley-Blackwell},
  title        = {{Generalized diffusion curves: An improved vector representation for smooth-shaded images}},
  doi          = {10.1111/cgf.12812},
  volume       = {35},
  year         = {2016},
}

@article{1414,
  abstract     = {In this paper, we present a method to model hyperelasticity that is well suited for representing the nonlinearity of real-world objects, as well as for estimating it from deformation examples. Previous approaches suffer several limitations, such as lack of integrability of elastic forces, failure to enforce energy convexity, lack of robustness of parameter estimation, or difficulty to model cross-modal effects. Our method avoids these problems by relying on a general energy-based definition of elastic properties. The accuracy of the resulting elastic model is maximized by defining an additive model of separable energy terms, which allow progressive parameter estimation. In addition, our method supports efficient modeling of extreme nonlinearities thanks to energy-limiting constraints. We combine our energy-based model with an optimization method to estimate model parameters from force-deformation examples, and we show successful modeling of diverse deformable objects, including cloth, human finger skin, and internal human anatomy in a medical imaging application.},
  author       = {Miguel Villalba, Eder and Miraut, David and Otaduy, Miguel},
  journal      = {Computer Graphics Forum},
  number       = {2},
  pages        = {385 -- 396},
  publisher    = {Wiley-Blackwell},
  title        = {{Modeling and estimation of energy-based hyperelastic objects}},
  doi          = {10.1111/cgf.12840},
  volume       = {35},
  year         = {2016},
}

@article{1415,
  abstract     = {The Fluid Implicit Particle method (FLIP) for liquid simulations uses particles to reduce numerical dissipation and provide important visual cues for events like complex splashes and small-scale features near the liquid surface. Unfortunately, FLIP simulations can be computationally expensive, because they require a dense sampling of particles to fill the entire liquid volume. Furthermore, the vast majority of these FLIP particles contribute nothing to the fluid's visual appearance, especially for larger volumes of liquid. We present a method that only uses FLIP particles within a narrow band of the liquid surface, while efficiently representing the remaining inner volume on a regular grid. We show that a naïve realization of this idea introduces unstable and uncontrollable energy fluctuations, and we propose a novel coupling scheme between FLIP particles and regular grid which overcomes this problem. Our method drastically reduces the particle count and simulation times while yielding results that are nearly indistinguishable from regular FLIP simulations. Our approach is easy to integrate into any existing FLIP implementation.},
  author       = {Ferstl, Florian and Ando, Ryoichi and Wojtan, Christopher J and Westermann, Rüdiger and Thuerey, Nils},
  journal      = {Computer Graphics Forum},
  number       = {2},
  pages        = {225 -- 232},
  publisher    = {Wiley-Blackwell},
  title        = {{Narrow band FLIP for liquid simulations}},
  doi          = {10.1111/cgf.12825},
  volume       = {35},
  year         = {2016},
}

@article{1416,
  abstract     = {Anisotropic dipole-dipole interactions between ultracold dipolar fermions break the symmetry of the Fermi surface and thereby deform it. Here we demonstrate that such a Fermi surface deformation induces a topological phase transition - the so-called Lifshitz transition - in the regime accessible to present-day experiments. We describe the impact of the Lifshitz transition on observable quantities such as the Fermi surface topology, the density-density correlation function, and the excitation spectrum of the system. The Lifshitz transition in ultracold atoms can be controlled by tuning the dipole orientation and, in contrast to the transition studied in crystalline solids, is completely interaction driven.},
  author       = {Van Loon, Erik and Katsnelson, Mikhail and Chomaz, Lauriane and Lemeshko, Mikhail},
  journal      = {Physical Review B - Condensed Matter and Materials Physics},
  number       = {19},
  publisher    = {American Physical Society},
  title        = {{Interaction-driven Lifshitz transition with dipolar fermions in optical lattices}},
  doi          = {10.1103/PhysRevB.93.195145},
  volume       = {93},
  year         = {2016},
}

@article{1417,
  abstract     = {Plant development mediated by the phytohormone auxin depends on tightly controlled cellular auxin levels at its target tissue that are largely established by intercellular and intracellular auxin transport mediated by PIN auxin transporters. Among the eight members of the Arabidopsis PIN family, PIN6 is the least characterized candidate. In this study we generated functional, fluorescent protein-tagged PIN6 proteins and performed comprehensive analysis of their subcellular localization and also performed a detailed functional characterization of PIN6 and its developmental roles. The localization study of PIN6 revealed a dual localization at the plasma membrane (PM) and endoplasmic reticulum (ER). Transport and metabolic profiling assays in cultured cells and Arabidopsis strongly suggest that PIN6 mediates both auxin transport across the PM and intracellular auxin homeostasis, including the regulation of free auxin and auxin conjugates levels. As evidenced by the loss- and gain-of-function analysis, the complex function of PIN6 in auxin transport and homeostasis is required for auxin distribution during lateral and adventitious root organogenesis and for progression of these developmental processes. These results illustrate a unique position of PIN6 within the family of PIN auxin transporters and further add complexity to the developmentally crucial process of auxin transport.},
  author       = {Simon, Sibu and Skůpa, Petr and Viaene, Tom and Zwiewka, Marta and Tejos, Ricardo and Klíma, Petr and Čarná, Mária and Rolčík, Jakub and De Rycke, Riet and Moreno, Ignacio and Dobrev, Petre and Orellana, Ariel and Zažímalová, Eva and Friml, Jirí},
  journal      = {New Phytologist},
  number       = {1},
  pages        = {65 -- 74},
  publisher    = {Wiley-Blackwell},
  title        = {{PIN6 auxin transporter at endoplasmic reticulum and plasma membrane mediates auxin homeostasis and organogenesis in Arabidopsis}},
  doi          = {10.1111/nph.14019},
  volume       = {211},
  year         = {2016},
}

@article{1419,
  abstract     = {We study the superconducting phase of the Hubbard model using the Gutzwiller variational wave function (GWF) and the recently proposed diagrammatic expansion technique (DE-GWF). The DE-GWF method works on the level of the full GWF and in the thermodynamic limit. Here, we consider a finite-size system to study the accuracy of the results as a function of the system size (which is practically unrestricted). We show that the finite-size scaling used, e.g. in the variational Monte Carlo method can lead to significant, uncontrolled errors. The presented research is the first step towards applying the DE-GWF method in studies of inhomogeneous situations, including systems with impurities, defects, inhomogeneous phases, or disorder.},
  author       = {Tomski, Andrzej and Kaczmarczyk, Jan},
  journal      = {Journal of Physics: Condensed Matter},
  number       = {17},
  publisher    = {IOP Publishing Ltd.},
  title        = {{Gutzwiller wave function for finite systems: Superconductivity in the Hubbard model}},
  doi          = {10.1088/0953-8984/28/17/175701},
  volume       = {28},
  year         = {2016},
}

@article{1420,
  abstract     = {Selection, mutation, and random drift affect the dynamics of allele frequencies and consequently of quantitative traits. While the macroscopic dynamics of quantitative traits can be measured, the underlying allele frequencies are typically unobserved. Can we understand how the macroscopic observables evolve without following these microscopic processes? This problem has been studied previously by analogy with statistical mechanics: the allele frequency distribution at each time point is approximated by the stationary form, which maximizes entropy. We explore the limitations of this method when mutation is small (4Nμ < 1) so that populations are typically close to fixation, and we extend the theory in this regime to account for changes in mutation strength. We consider a single diallelic locus either under directional selection or with overdominance and then generalize to multiple unlinked biallelic loci with unequal effects. We find that the maximum-entropy approximation is remarkably accurate, even when mutation and selection change rapidly. },
  author       = {Bod'ová, Katarína and Tkacik, Gasper and Barton, Nicholas H},
  journal      = {Genetics},
  number       = {4},
  pages        = {1523 -- 1548},
  publisher    = {Genetics Society of America},
  title        = {{A general approximation for the dynamics of quantitative traits}},
  doi          = {10.1534/genetics.115.184127},
  volume       = {202},
  year         = {2016},
}

@inproceedings{1421,
  abstract     = {Hybridization methods enable the analysis of hybrid automata with complex, nonlinear dynamics through a sound abstraction process. Complex dynamics are converted to simpler ones with added noise, and then analysis is done using a reachability method for the simpler dynamics. Several such recent approaches advocate that only "dynamic" hybridization techniquesi.e., those where the dynamics are abstracted on-The-fly during a reachability computation are effective. In this paper, we demonstrate this is not the case, and create static hybridization methods that are more scalable than earlier approaches. The main insight in our approach is that quick, numeric simulations can be used to guide the process, eliminating the need for an exponential number of hybridization domains. Transitions between domains are generally timetriggered, avoiding accumulated error from geometric intersections. We enhance our static technique by combining time-Triggered transitions with occasional space-Triggered transitions, and demonstrate the benefits of the combined approach in what we call mixed-Triggered hybridization. Finally, error modes are inserted to confirm that the reachable states stay within the hybridized regions. The developed techniques can scale to higher dimensions than previous static approaches, while enabling the parallelization of the main performance bottleneck for many dynamic hybridization approaches: The nonlinear optimization required for sound dynamics abstraction. We implement our method as a model transformation pass in the HYST tool, and perform reachability analysis and evaluation using an unmodified version of SpaceEx on nonlinear models with up to six dimensions.},
  author       = {Bak, Stanley and Bogomolov, Sergiy and Henzinger, Thomas A and Johnson, Taylor and Prakash, Pradyot},
  location     = {Vienna, Austria},
  pages        = {155 -- 164},
  publisher    = {Springer},
  title        = {{Scalable static hybridization methods for analysis of nonlinear systems}},
  doi          = {10.1145/2883817.2883837},
  year         = {2016},
}

@article{1422,
  abstract     = {We study the time-dependent Bogoliubov–de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg–Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.},
  author       = {Frank, Rupert and Hainzl, Christian and Schlein, Benjamin and Seiringer, Robert},
  journal      = {Letters in Mathematical Physics},
  number       = {7},
  pages        = {913 -- 923},
  publisher    = {Springer},
  title        = {{Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations}},
  doi          = {10.1007/s11005-016-0847-5},
  volume       = {106},
  year         = {2016},
}

@article{1423,
  abstract     = {Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player's previous move, and memory-one strategies, which take into account the own and the co-player's previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation.},
  author       = {Baek, Seung and Jeong, Hyeongchai and Hilbe, Christian and Nowak, Martin},
  journal      = {Scientific Reports},
  publisher    = {Nature Publishing Group},
  title        = {{Comparing reactive and memory-one strategies of direct reciprocity}},
  doi          = {10.1038/srep25676},
  volume       = {6},
  year         = {2016},
}

@article{1426,
  abstract     = {Brood parasites exploit their host in order to increase their own fitness. Typically, this results in an arms race between parasite trickery and host defence. Thus, it is puzzling to observe hosts that accept parasitism without any resistance. The ‘mafia’ hypothesis suggests that these hosts accept parasitism to avoid retaliation. Retaliation has been shown to evolve when the hosts condition their response to mafia parasites, who use depredation as a targeted response to rejection. However, it is unclear if acceptance would also emerge when ‘farming’ parasites are present in the population. Farming parasites use depredation to synchronize the timing with the host, destroying mature clutches to force the host to re-nest. Herein, we develop an evolutionary model to analyse the interaction between depredatory parasites and their hosts. We show that coevolutionary cycles between farmers and mafia can still induce host acceptance of brood parasites. However, this equilibrium is unstable and in the long-run the dynamics of this host–parasite interaction exhibits strong oscillations: when farmers are the majority, accepters conditional to mafia (the host will reject first and only accept after retaliation by the parasite) have a higher fitness than unconditional accepters (the host always accepts parasitism). This leads to an increase in mafia parasites’ fitness and in turn induce an optimal environment for accepter hosts.},
  author       = {Chakra, Maria and Hilbe, Christian and Traulsen, Arne},
  journal      = {Royal Society Open Science},
  number       = {5},
  publisher    = {Royal Society, The},
  title        = {{Coevolutionary interactions between farmers and mafia induce host acceptance of avian brood parasites}},
  doi          = {10.1098/rsos.160036},
  volume       = {3},
  year         = {2016},
}

@article{1427,
  abstract     = {Changes in gene expression are an important mode of evolution; however, the proximate mechanism of these changes is poorly understood. In particular, little is known about the effects of mutations within cis binding sites for transcription factors, or the nature of epistatic interactions between these mutations. Here, we tested the effects of single and double mutants in two cis binding sites involved in the transcriptional regulation of the Escherichia coli araBAD operon, a component of arabinose metabolism, using a synthetic system. This system decouples transcriptional control from any posttranslational effects on fitness, allowing a precise estimate of the effect of single and double mutations, and hence epistasis, on gene expression. We found that epistatic interactions between mutations in the araBAD cis-regulatory element are common, and that the predominant form of epistasis is negative. The magnitude of the interactions depended on whether the mutations are located in the same or in different operator sites. Importantly, these epistatic interactions were dependent on the presence of arabinose, a native inducer of the araBAD operon in vivo, with some interactions changing in sign (e.g., from negative to positive) in its presence. This study thus reveals that mutations in even relatively simple cis-regulatory elements interact in complex ways such that selection on the level of gene expression in one environment might perturb regulation in the other environment in an unpredictable and uncorrelated manner.},
  author       = {Lagator, Mato and Igler, Claudia and Moreno, Anaisa and Guet, Calin C and Bollback, Jonathan P},
  journal      = {Molecular Biology and Evolution},
  number       = {3},
  pages        = {761 -- 769},
  publisher    = {Oxford University Press},
  title        = {{Epistatic interactions in the arabinose cis-regulatory element}},
  doi          = {10.1093/molbev/msv269},
  volume       = {33},
  year         = {2016},
}

@inproceedings{1428,
  abstract     = {We report on a mathematically rigorous analysis of the superfluid properties of a Bose- Einstein condensate in the many-body ground state of a one-dimensional model of interacting bosons in a random potential.},
  author       = {Könenberg, Martin and Moser, Thomas and Seiringer, Robert and Yngvason, Jakob},
  booktitle    = {Journal of Physics: Conference Series},
  location     = {Shanghai, China},
  number       = {1},
  publisher    = {IOP Publishing Ltd.},
  title        = {{Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential}},
  doi          = {10.1088/1742-6596/691/1/012016},
  volume       = {691},
  year         = {2016},
}

@article{1429,
  abstract     = {Solitons are localized waves formed by a balance of focusing and defocusing effects. These nonlinear waves exist in diverse forms of matter yet exhibit similar properties including stability, periodic recurrence and particle-like trajectories. One important property is soliton fission, a process by which an energetic higher-order soliton breaks apart due to dispersive or nonlinear perturbations. Here we demonstrate through both experiment and theory that nonlinear photocarrier generation can induce soliton fission. Using near-field measurements, we directly observe the nonlinear spatial and temporal evolution of optical pulses in situ in a nanophotonic semiconductor waveguide. We develop an analytic formalism describing the free-carrier dispersion (FCD) perturbation and show the experiment exceeds the minimum threshold by an order of magnitude. We confirm these observations with a numerical nonlinear Schrödinger equation model. These results provide a fundamental explanation and physical scaling of optical pulse evolution in free-carrier media and could enable improved supercontinuum sources in gas based and integrated semiconductor waveguides.},
  author       = {Husko, Chad and Wulf, Matthias and Lefrançois, Simon and Combrié, Sylvain and Lehoucq, Gaëlle and De Rossi, Alfredo and Eggleton, Benjamin and Kuipers, Laurens},
  journal      = {Nature Communications},
  publisher    = {Nature Publishing Group},
  title        = {{Free-carrier-induced soliton fission unveiled by in situ measurements in nanophotonic waveguides}},
  doi          = {10.1038/ncomms11332},
  volume       = {7},
  year         = {2016},
}

@article{14302,
  abstract     = {One key goal of DNA nanotechnology is the bottom-up construction of macroscopic crystalline materials. Beyond applications in fields such as photonics or plasmonics, DNA-based crystal matrices could possibly facilitate the diffraction-based structural analysis of guest molecules. Seeman and co-workers reported in 2009 the first designed crystal matrices based on a 38 kDa DNA triangle that was composed of seven chains. The crystal lattice was stabilized, unprecedentedly, by Watson–Crick base pairing. However, 3D crystallization of larger designed DNA objects that include more chains such as DNA origami remains an unsolved problem. Larger objects would offer more degrees of freedom and design options with respect to tailoring lattice geometry and for positioning other objects within a crystal lattice. The greater rigidity of multilayer DNA origami could also positively influence the diffractive properties of crystals composed of such particles. Here, we rationally explore the role of heterogeneity and Watson–Crick interaction strengths in crystal growth using 40 variants of the original DNA triangle as model multichain objects. Crystal growth of the triangle was remarkably robust despite massive chemical, geometrical, and thermodynamical sample heterogeneity that we introduced, but the crystal growth sensitively depended on the sequences of base pairs next to the Watson–Crick sticky ends of the triangle. Our results point to weak lattice interactions and high concentrations as decisive factors for achieving productive crystallization, while sample heterogeneity and impurities played a minor role.},
  author       = {Stahl, Evi and Praetorius, Florian M and de Oliveira Mann, Carina C. and Hopfner, Karl-Peter and Dietz, Hendrik},
  issn         = {1936-086X},
  journal      = {ACS Nano},
  number       = {10},
  pages        = {9156--9164},
  publisher    = {American Chemical Society},
  title        = {{Impact of heterogeneity and lattice bond strength on DNA triangle crystal growth}},
  doi          = {10.1021/acsnano.6b04787},
  volume       = {10},
  year         = {2016},
}