TY - JOUR AB - As a function of packing fraction at zero temperature and applied stress, an amorphous packing of spheres exhibits a jamming transition where the system is sensitive to boundary conditions even in the thermodynamic limit. Upon further compression, the system should become insensitive to boundary conditions provided it is sufficiently large. Here we explore the linear response to a large class of boundary perturbations in 2 and 3 dimensions. We consider each finite packing with periodic-boundary conditions as the basis of an infinite square or cubic lattice and study properties of vibrational modes at arbitrary wave vector. We find that the stability of such modes can be understood in terms of a competition between plane waves and the anomalous vibrational modes associated with the jamming transition; infinitesimal boundary perturbations become irrelevant for systems that are larger than a length scale that characterizes the transverse excitations. This previously identified length diverges at the jamming transition. AU - Schoenholz, Samuel S. AU - Goodrich, Carl Peter AU - Kogan, Oleg AU - Liu, Andrea J. AU - Nagel, Sidney R. ID - 7775 IS - 46 JF - Soft Matter SN - 1744-683X TI - Stability of jammed packings II: The transverse length scale VL - 9 ER - TY - JOUR AB - In 2005, Wyart et al. [Europhys. Lett., 2005, 72, 486] showed that the low frequency vibrational properties of jammed amorphous sphere packings can be understood in terms of a length scale, called l*, that diverges as the system becomes marginally unstable. Despite the tremendous success of this theory, it has been difficult to connect the counting argument that defines l* to other length scales that diverge near the jamming transition. We present an alternate derivation of l* based on the onset of rigidity. This phenomenological approach reveals the physical mechanism underlying the length scale and is relevant to a range of systems for which the original argument breaks down. It also allows us to present the first direct numerical measurement of l*. AU - Goodrich, Carl Peter AU - Ellenbroek, Wouter G. AU - Liu, Andrea J. ID - 7774 IS - 46 JF - Soft Matter SN - 1744-683X TI - Stability of jammed packings I: The rigidity length scale VL - 9 ER - TY - JOUR AB - While the plasticity of excitatory synaptic connections in the brain has been widely studied, the plasticity of inhibitory connections is much less understood. Here, we present recent experimental and theoretical findings concerning the rules of spike timing-dependent inhibitory plasticity and their putative network function. This is a summary of a workshop at the COSYNE conference 2012. AU - Vogels, Tim P AU - Froemke, R. C. AU - Doyon, N. AU - Gilson, M. AU - Haas, J. S. AU - Liu, R. AU - Maffei, A. AU - Miller, P. AU - Wierenga, C. J. AU - Woodin, M. A. AU - Zenke, F. AU - Sprekeler, H. ID - 8030 JF - Frontiers in Neural Circuits TI - Inhibitory synaptic plasticity: Spike timing-dependence and putative network function VL - 7 ER - TY - JOUR AB - Cell migration is commonly accompanied by protrusion of membrane ruffles and lamellipodia. In two-dimensional migration, protrusion of these thin sheets of cytoplasm is considered relevant to both exploration of new space and initiation of nascent adhesion to the substratum. Lamellipodium formation can be potently stimulated by Rho GTPases of the Rac subfamily, but alsoby RhoG or Cdc42. Here we describe viable fibroblast cell lines geneticallydeficient for Rac1 that lack detectable levels of Rac2 and Rac3. Rac-deficient cells were devoid of apparent lamellipodia, but these structures were restored by expression of either Rac subfamily member, but not by Cdc42 or RhoG. Cells deficient in Rac showed strong reduction in wound closure and random cell migration and a notable loss of sensitivity to a chemotactic gradient. Despite these defects, Rac-deficient cells were able to spread, formed filopodia and established focal adhesions. Spreading in these cells was achieved by the extension of filopodia followed by the advancement of cytoplasmic veils between them. The number and size of focal adhesions as well as their intensity were largely unaffected by genetic removal of Rac1. However, Rac deficiency increased the mobility of different components in focal adhesions, potentially explaining how Rac - although not essential - can contribute to focal adhesion assembly. Together, our data demonstrate that Rac signaling is essential for lamellipodium protrusion and for efficient cell migration, but not for spreading or filopodium formation. Our findings also suggest that Rac GTPases are crucial to the establishment or maintenance of polarity in chemotactic migration. AU - Steffen, Anika AU - Ladwein, Markus AU - Georgi Dimchev AU - Hein, Anke AU - Schwenkmezger, Lisa AU - Arens, Stefan AU - Ladwein, Kathrin I AU - Holleboom, J. Margit AU - Florian Schur AU - Small, John V AU - Schwarz, Janett AU - Gerhard, Ralf AU - Faix, Jan AU - Stradal, Theresia E AU - Brakebusch, Cord H AU - Rottner, Klemens ID - 811 IS - 20 JF - Journal of Cell Science TI - Rac function is crucial for cell migration but is not required for spreading and focal adhesion formation VL - 126 ER - TY - JOUR AB - Lamellipodia are sheet-like protrusions formed during migration or phagocytosis and comprise a network of actin filaments. Filament formation in this network is initiated by nucleation/branching through the actin-related protein 2/3 (Arp2/3) complex downstream of its activator, suppressor of cAMP receptor/WASP-family verprolin homologous (Scar/WAVE), but the relative relevance of Arp2/3-mediated branching versus actin filament elongation is unknown. Here we use instantaneous interference with Arp2/3 complex function in live fibroblasts with established lamellipodia. This allows direct examination of both the fate of elongating filaments upon instantaneous suppression of Arp2/3 complex activity and the consequences of this treatment on the dynamics of other lamellipodial regulators. We show that Arp2/3 complex is an essential organizer of treadmilling actin filament arrays but has little effect on the net rate of actin filament turnover at the cell periphery. In addition, Arp2/3 complex serves as key upstream factor for the recruitment of modulators of lamellipodia formation such as capping protein or cofilin. Arp2/3 complex is thus decisive for filament organization and geometry within the network not only by generating branches and novel filament ends, but also by directing capping or severing activities to the lamellipodium. Arp2/3 complex is also crucial to lamellipodia-based migration of keratocytes. AU - Koestler, Stefan A AU - Steffen, Anika AU - Maria Nemethova AU - Winterhoff, Moritz AU - Luo, Ningning AU - Holleboom, J. Margit AU - Krupp, Jessica AU - Jacob, Sonja AU - Vinzenz, Marlene AU - Florian Schur AU - Schlüter, Kai AU - Gunning, Peter W AU - Winkler, Christoph AU - Schmeiser, Christian AU - Faix, Jan AU - Stradal, Theresia E AU - Small, John V AU - Rottner, Klemens ID - 812 IS - 18 JF - Molecular Biology of the Cell TI - Arp2/3 complex is essential for actin network treadmilling as well as for targeting of capping protein and cofilin VL - 24 ER - TY - JOUR AB - Cryo-electron tomography combined with image processing by sub-tomogram averaging is unique in its power to resolve the structures of proteins and macromolecular complexes in situ. Limitations of the method, including the low signal to noise ratio within individual images from cryo-tomographic datasets and difficulties in determining the defocus at which the data was collected, mean that to date the very best structures obtained by sub-tomogram averaging are limited to a resolution of approximately 15. Å. Here, by optimizing data collection and defocus determination steps, we have determined the structure of assembled Mason-Pfizer monkey virus Gag protein using sub-tomogram averaging to a resolution of 8.5. Å. At this resolution alpha-helices can be directly and clearly visualized. These data demonstrate for the first time that high-resolution structural information can be obtained from cryo-electron tomograms using sub-tomogram averaging. Sub-tomogram averaging has the potential to allow detailed studies of unsolved and biologically relevant structures under biologically relevant conditions. AU - Florian Schur AU - Hagen, Wim J AU - De Marco, Alex AU - Briggs, John A ID - 810 IS - 3 JF - Journal of Structural Biology TI - Determination of protein structure at 8.5Å resolution using cryo-electron tomography and sub-tomogram averaging VL - 184 ER - TY - JOUR AB - Background: Monoclonal antibodies (mAb), such as trastuzumab are a valuable addition to breast cancer therapy. Data obtained from neoadjuvant settings revealed that antibody-dependent cell-mediated cytotoxicity (ADCC) is a major mechanism of action for the mAb trastuzumab. Conflicting results still call into question whether disease progression, prolonged treatment or concomitant chemotherapy influences ADCC and related immunological phenomena. Methods: We analyzed the activity of ADCC and antibody-dependent cell-mediated phagocytosis (ADCP) of peripheral blood mononuclear cells (PBMCs) from human epidermal growth factor receptor 2 (HER2/neu) positive breast cancer patients receiving trastuzumab therapy either in an adjuvant (n = 13) or metastatic (n = 15) setting as well as from trastuzumab treatment-naive (t-naive) HER2/neu negative patients (n = 15). PBMCs from healthy volunteers (n = 24) were used as controls. ADCC and ADCP activity was correlated with the expression of antibody binding Fc-gamma receptor (FcγR)I (CD64), FcγRII (CD32) and FcγRIII (CD16) on CD14+ (monocytes) and CD56+ (NK) cells, as well as the expression of CD107a+ (LAMP-1) on CD56+ cells and the total amount of CD4+CD25+FOXP3+ (Treg) cells. In metastatic patients, markers were correlated with progression-free survival (PFS). Results: ADCC activity was significantly down regulated in metastatic, adjuvant and t-naive patient cohorts as compared to healthy controls. Reduced ADCC activity was inversely correlated with the expression of CD107a on CD56+ cells in adjuvant patients. ADCC and ADCP activity of the patient cohorts were similar, regardless of treatment duration or additional chemotherapy. PFS in metastatic patients inversely correlated with the number of peripheral Treg cells. Conclusion: The reduction of ADCC in patients as compared to healthy controls calls for adjuvant strategies, such as immune-enhancing agents, to improve the activity of trastuzumab. However, efficacy of trastuzumab-specific ADCC and ADCP appears not to be affected by treatment duration, disease progression or concomitant chemotherapy. This finding supports the application of trastuzumab at any stage of the disease. AU - Petricevic, Branka AU - Laengle, Johannes AU - Singer, Josef AU - Sachet, Monika AU - Fazekas, Judit AU - Steger, Guenther AU - Bartsch, Rupert AU - Jensen-Jarolim, Erika AU - Bergmann, Michael ID - 8245 JF - Journal of Translational Medicine SN - 1479-5876 TI - Trastuzumab mediates antibody-dependent cell-mediated cytotoxicity and phagocytosis to the same extent in both adjuvant and metastatic HER2/neu breast cancer patients VL - 11 ER - TY - JOUR AB - As sessile organisms, plants have to be able to adapt to a continuously changing environment. Plants that perceive some of these changes as stress signals activate signaling pathways to modulate their development and to enable them to survive. The complex responses to environmental cues are to a large extent mediated by plant hormones that together orchestrate the final plant response. The phytohormone cytokinin is involved in many plant developmental processes. Recently, it has been established that cytokinin plays an important role in stress responses, but does not act alone. Indeed, the hormonal control of plant development and stress adaptation is the outcome of a complex network of multiple synergistic and antagonistic interactions between various hormones. Here, we review the recent findings on the cytokinin function as part of this hormonal network. We focus on the importance of the crosstalk between cytokinin and other hormones, such as abscisic acid, jasmonate, salicylic acid, ethylene, and auxin in the modulation of plant development and stress adaptation. Finally, the impact of the current research in the biotechnological industry will be discussed. AU - O'Brien, José AU - Benková, Eva ID - 827 JF - Frontiers in Plant Science TI - Cytokinin cross talking during biotic and abiotic stress responses VL - 4 ER - TY - JOUR AB - The plant root system is essential for providing anchorage to the soil, supplying minerals and water, and synthesizing metabolites. It is a dynamic organ modulated by external cues such as environmental signals, water and nutrients availability, salinity and others. Lateral roots (LRs) are initiated from the primary root post-embryonically, after which they progress through discrete developmental stages which can be independently controlled, providing a high level of plasticity during root system formation. Within this review, main contributions are presented, from the classical forward genetic screens to the more recent high-throughput approaches, combined with computer model predictions, dissecting how LRs and thereby root system architecture is established and developed. AU - Cuesta, Candela AU - Wabnik, Krzysztof T AU - Benková, Eva ID - 828 JF - Frontiers in Plant Science TI - Systems approaches to study root architecture dynamics VL - 4 ER - TY - JOUR AB - Upon hormonal signaling, ovules develop as lateral organs from the placenta. Ovule numbers ultimately determine the number of seeds that develop, and thereby contribute to the final seed yield in crop plants. We demonstrate here that CUP-SHAPED COTYLEDON 1 (CUC1), CUC2 and AINTEGUMENTA (ANT) have additive effects on ovule primordia formation. We show that expression of the CUC1 and CUC2 genes is required to redundantly regulate expression of PINFORMED1 (PIN1), which in turn is required for ovule primordia formation. Furthermore, our results suggest that the auxin response factor MONOPTEROS (MP/ARF5) may directly bind ANT, CUC1 and CUC2 and promote their transcription. Based on our findings, we propose an integrative model to describe the molecular mechanisms of the early stages of ovule development. AU - Galbiati, Francesca AU - Sinha Roy, Dola AU - Simonini, Sara AU - Cucinotta, Mara AU - Ceccato, Luca AU - Cuesta, Candela AU - Šimášková, Mária AU - Benková, Eva AU - Kamiuchi, Yuri AU - Aida, Mitsuhiro AU - Weijers, Dolf AU - Simon, Rüdiger AU - Masiero, Simona AU - Colombo, Lucia ID - 830 IS - 3 JF - The Plant journal for cell and molecular biology TI - An integrative model of the control of ovule primordia formation VL - 76 ER - TY - JOUR AB - In Arabidopsis, lateral roots originate from pericycle cells deep within the primary root. New lateral root primordia (LRP) have to emerge through several overlaying tissues. Here, we report that auxin produced in new LRP is transported towards the outer tissues where it triggers cell separation by inducing both the auxin influx carrier LAX3 and cell-wall enzymes. LAX3 is expressed in just two cell files overlaying new LRP. To understand how this striking pattern of LAX3 expression is regulated, we developed a mathematical model that captures the network regulating its expression and auxin transport within realistic three-dimensional cell and tissue geometries. Our model revealed that, for the LAX3 spatial expression to be robust to natural variations in root tissue geometry, an efflux carrier is required--later identified to be PIN3. To prevent LAX3 from being transiently expressed in multiple cell files, PIN3 and LAX3 must be induced consecutively, which we later demonstrated to be the case. Our study exemplifies how mathematical models can be used to direct experiments to elucidate complex developmental processes. AU - Péret, Benjamin AU - Middleton, Alistair M AU - French, Andrew P AU - Larrieu, Antoine AU - Bishopp, Anthony AU - Njo, Maria AU - Wells, Darren M AU - Porco, Silvana AU - Mellor, Nathan AU - Band, Leah R AU - Casimiro, Ilda AU - Kleine-Vehn, Jürgen AU - Vanneste, Steffen AU - Sairanen, Ilkka AU - Mallet, Romain AU - Sandberg, Göran AU - Ljung, Karin AU - Beeckman, Tom AU - Eva Benková AU - Jirí Friml AU - Kramer, Eric AU - King, John R AU - De Smet, Ive AU - Pridmore, Tony AU - Owen, Markus AU - Bennett, Malcolm J ID - 831 JF - Molecular Systems Biology TI - Sequential induction of auxin efflux and influx carriers regulates lateral root emergence VL - 9 ER - TY - JOUR AB - Solid-state NMR provides insight into protein motion over time scales ranging from picoseconds to seconds. While in solution state the methodology to measure protein dynamics is well established, there is currently no such consensus protocol for measuring dynamics in solids. In this article, we perform a detailed investigation of measurement protocols for fast motions, i.e. motions ranging from picoseconds to a few microseconds, which is the range covered by dipolar coupling and relaxation experiments. We perform a detailed theoretical investigation how dipolar couplings and relaxation data can provide information about amplitudes and time scales of local motion. We show that the measurement of dipolar couplings is crucial for obtaining accurate motional parameters, while systematic errors are found when only relaxation data are used. Based on this realization, we investigate how the REDOR experiment can provide such data in a very accurate manner. We identify that with accurate rf calibration, and explicit consideration of rf field inhomogeneities, one can obtain highly accurate absolute order parameters. We then perform joint model-free analyses of 6 relaxation data sets and dipolar couplings, based on previously existing, as well as new data sets on microcrystalline ubiquitin. We show that nanosecond motion can be detected primarily in loop regions, and compare solid-state data to solution-state relaxation and RDC analyses. The protocols investigated here will serve as a useful basis towards the establishment of a routine protocol for the characterization of ps–μs motions in proteins by solid-state NMR. AU - Haller, Jens D. AU - Schanda, Paul ID - 8461 IS - 3 JF - Journal of Biomolecular NMR KW - Spectroscopy KW - Biochemistry SN - 0925-2738 TI - Amplitudes and time scales of picosecond-to-microsecond motion in proteins studied by solid-state NMR: a critical evaluation of experimental approaches and application to crystalline ubiquitin VL - 57 ER - TY - JOUR AB - The transition of proteins from their soluble functional state to amyloid fibrils and aggregates is associated with the onset of several human diseases. Protein aggregation often requires some structural reshaping and the subsequent formation of intermolecular contacts. Therefore, the study of the conformation of excited protein states and their ability to form oligomers is of primary importance for understanding the molecular basis of amyloid fibril formation. Here, we investigated the oligomerization processes that occur along the folding of the amyloidogenic human protein β2-microglobulin. The combination of real-time two-dimensional NMR data with real-time small-angle X-ray scattering measurements allowed us to derive thermodynamic and kinetic information on protein oligomerization of different conformational states populated along the folding pathways. In particular, we could demonstrate that a long-lived folding intermediate (I-state) has a higher propensity to oligomerize compared to the native state. Our data agree well with a simple five-state kinetic model that involves only monomeric and dimeric species. The dimers have an elongated shape with the dimerization interface located at the apical side of β2-microglobulin close to Pro32, the residue that has a trans conformation in the I-state and a cis conformation in the native (N) state. Our experimental data suggest that partial unfolding in the apical half of the protein close to Pro32 leads to an excited state conformation with enhanced propensity for oligomerization. This excited state becomes more populated in the transient I-state due to the destabilization of the native conformation by the trans-Pro32 configuration. AU - Rennella, E. AU - Cutuil, T. AU - Schanda, Paul AU - Ayala, I. AU - Gabel, F. AU - Forge, V. AU - Corazza, A. AU - Esposito, G. AU - Brutscher, B. ID - 8462 IS - 15 JF - Journal of Molecular Biology KW - Molecular Biology SN - 0022-2836 TI - Oligomeric states along the folding pathways of β2-microglobulin: Kinetics, thermodynamics, and structure VL - 425 ER - TY - JOUR AB - Understanding fitness landscapes, a conceptual depiction of the genotype-to-phenotype relationship, is crucial to many areas of biology. Two aspects of fitness landscapes are the focus of contemporary studies of molecular evolution. First, the local shape of the fitness landscape defined by the contribution of individual alleles to fitness that is independent of all genetic interactions. Second, the global, multidimensional fitness landscape shape determined by how interactions between alleles at different loci change each other’s fitness impact, or epistasis. In explaining the high amino-acid usage (u), we focused on the global shape of the fitness landscape, ignoring the perturbations at individual sites. AU - Breen, Michael S AU - Kemena, Carsten AU - Vlasov, Peter K AU - Notredame, Cédric AU - Fyodor Kondrashov ID - 899 IS - 7451 JF - Nature TI - Breen et al. reply VL - 497 ER - TY - JOUR AB - The coalescence of nano-crystals during sintering is often found to result in interesting crystalline structures such as multi-fold twins, and yet the plasticity mechanism accompanying their formation is unclear. In this work, the sintering behavior of two unsupported copper nanoparticles initially at room temperature is investigated by molecular dynamics simulations under the constant-energy ensemble. The results reveal that once the two nanoparticles are brought into contact, they often go through drastic structural changes with the inter-particle grain boundary quickly eliminated, and single- and multi-fold twinning occurs frequently in the coalesced product. Whereas the formation of single twins is found to be via the more usual mechanism of emission of Shockley partials on {1 1 1} planes, the formation of fivefold twins, however, takes place via a novel dislocation-free mechanism involving a series of shear and rigid-body rotation processes caused by elastic waves with amplitudes not corresponding to any allowable Burgers vector in the fcc lattice. Such a lattice-wave, dislocation-free twinning mechanism has never been reported before. AU - Cheng, Bingqing AU - Ngan, Alfonso H.W. ID - 9674 JF - International Journal of Plasticity SN - 0749-6419 TI - The crystal structures of sintered copper nanoparticles: A molecular dynamics study VL - 47 ER - TY - JOUR AB - Despite its relevance to a range of technological applications including nanocrystalline material fabrication, the sintering mechanisms of nanoparticles have not been well understood. It has been recognized that extrapolation from understanding of macro-particle sintering is unreliable for the nano-particle size regime. In this work, the sintering behaviour of copper nanoparticles under periodic boundary conditions at different temperatures and pressures was investigated by Molecular Dynamics simulations. It was found that smaller particle sizes, higher temperature and higher external pressure facilitate densification. Through a comparison with a two-sphere model, the governing mechanisms for many nanoparticles sintered at low temperature (T⩽900K) were identified to be a variety of plasticity processes including dislocation, twinning and even amorphization at the contact neck regions, due to the presence of high stresses. AU - Cheng, Bingqing AU - Ngan, Alfonso H.W. ID - 9676 JF - Computational Materials Science SN - 0927-0256 TI - The sintering and densification behaviour of many copper nanoparticles: A molecular dynamics study VL - 74 ER - TY - JOUR AB - We study the stability of the normal state in a mesoscopic NSN junction biased by a constant voltage V with respect to the formation of the superconducting order. Using the linearized time-dependent Ginzburg-Landau equation, we obtain the temperature dependence of the instability line, V inst(T), where nucleation of superconductivity takes place. For sufficiently low biases, a stationary symmetric superconducting state emerges below the instability line. For higher biases, the normal phase is destroyed by the formation of a nonstationary bimodal state with two superconducting nuclei localized near the opposite terminals. The low-temperature and large-voltage behavior of the instability line is highly sensitive to the details of the inelastic relaxation mechanism in the wire. Therefore, experimental studies of Vinst(T) in NSN junctions may be used as an effective tool to access the parameters of the inelastic relaxation in the normal state. AU - Maksym Serbyn AU - Skvortsov, Mikhail A ID - 971 IS - 2 JF - Physical Review B - Condensed Matter and Materials Physics TI - Onset of superconductivity in a voltage-biased normal-superconducting-normal microbridge VL - 87 ER - TY - JOUR AB - In topological crystalline insulators (TCIs), topology and crystal symmetry intertwine to create surface states with distinct characteristics. The breaking of crystal symmetry in TCIs is predicted to impart mass to the massless Dirac fermions. Here, we report high-resolution scanning tunneling microscopy studies of a TCI, Pb1-xSnxSe that reveal the coexistence of zero-mass Dirac fermions protected by crystal symmetry with massive Dirac fermions consistent with crystal symmetry breaking. In addition, we show two distinct regimes of the Fermi surface topology separated by a Van-Hove singularity at the Lifshitz transition point. Our work paves the way for engineering the Dirac band gap and realizing interaction-driven topological quantum phenomena in TCIs. AU - Okada, Yoshinori AU - Serbyn, Maksym AU - Lin, Hsin AU - Walkup, Daniel AU - Zhou, Wenwen AU - Dhital, Chetan AU - Neupane, Madhab AU - Xu, Suyang AU - Wang, Yungjui AU - Sankar, Raman AU - Chou, Fangcheng AU - Bansil, Arun AU - Hasan, Md AU - Wilson, Stephen AU - Fu, Liang AU - Madhavan, Vidya ID - 972 IS - 6153 JF - Science TI - Observation of dirac node formation and mass acquisition in a topological crystalline insulator VL - 341 ER - TY - JOUR AB - Recent numerical work by Bardarson, Pollmann, and Moore revealed a slow, logarithmic in time, growth of the entanglement entropy for initial product states in a putative many-body localized phase. We show that this surprising phenomenon results from the dephasing due to exponentially small interaction-induced corrections to the eigenenergies of different states. For weak interactions, we find that the entanglement entropy grows as ξln (Vt/), where V is the interaction strength, and ξ is the single-particle localization length. The saturated value of the entanglement entropy at long times is determined by the participation ratios of the initial state over the eigenstates of the subsystem. Our work shows that the logarithmic entanglement growth is a universal phenomenon characteristic of the many-body localized phase in any number of spatial dimensions, and reveals a broad hierarchy of dephasing time scales present in such a phase. AU - Maksym Serbyn AU - Papić, Zlatko AU - Abanin, Dmitry A ID - 975 IS - 26 JF - Physical Review Letters TI - Universal slow growth of entanglement in interacting strongly disordered systems VL - 110 ER - TY - GEN AB - Cooperative behavior, where one individual incurs a cost to help another, is a wide spread phenomenon. Here we study direct reciprocity in the context of the alternating Prisoner's Dilemma. We consider all strategies that can be implemented by one and two-state automata. We calculate the payoff matrix of all pairwise encounters in the presence of noise. We explore deterministic selection dynamics with and without mutation. Using different error rates and payoff values, we observe convergence to a small number of distinct equilibria. Two of them are uncooperative strict Nash equilibria representing always-defect (ALLD) and Grim. The third equilibrium is mixed and represents a cooperative alliance of several strategies, dominated by a strategy which we call Forgiver. Forgiver cooperates whenever the opponent has cooperated; it defects once when the opponent has defected, but subsequently Forgiver attempts to re-establish cooperation even if the opponent has defected again. Forgiver is not an evolutionarily stable strategy, but the alliance, which it rules, is asymptotically stable. For a wide range of parameter values the most commonly observed outcome is convergence to the mixed equilibrium, dominated by Forgiver. Our results show that although forgiving might incur a short-term loss it can lead to a long-term gain. Forgiveness facilitates stable cooperation in the presence of exploitation and noise. AU - Zagorsky, Benjamin AU - Reiter, Johannes AU - Chatterjee, Krishnendu AU - Nowak, Martin ID - 9749 TI - Forgiver triumphs in alternating prisoner's dilemma ER -