Influenza exits the cell without an ESCRT.

Many enveloped viruses depend on the membrane remodeling machinery of their host cells to complete their life cycle. In this issue, Rossman et al. (2010) now demonstrate that influenza virus possesses its own device for releasing nascent virus particles from the plasma membrane, the M2 proton-selective ion channel, which can substitute for the host cell's ESCRT pathway.

Photosynthetic quantum efficiency in south-eastern Amazonian trees may be already affected by climate change.

Tropical forests are experiencing unprecedented high-temperature conditions due to climate change that could limit their photosynthetic functions. We studied the high-temperature sensitivity of photosynthesis in a rainforest site in southern Amazonia, where some of the highest temperatures and most rapid warming in the Tropics have been recorded. The quantum yield (Fv /Fm ) of photosystem II was measured in seven dominant tree species using leaf discs exposed to varying levels of heat stress. T50 was calculated as the temperature at which Fv /Fm was half the maximum value. T5 is defined as the breakpoint temperature, at which Fv /Fm decline was initiated. Leaf thermotolerance in the rapidly warming southern Amazonia was the highest recorded for forest tree species globally. T50 and T5 varied between species, with one mid-storey species, Amaioua guianensis, exhibiting particularly high T50 and T5 values. While the T50 values of the species sampled were several degrees above the maximum air temperatures experienced in southern Amazonia, the T5 values of several species are now exceeded under present-day maximum air temperatures.

SERINC3 and SERINC5 restrict HIV-1 infectivity and are counteracted by Nef.

HIV-1 Nef and the unrelated mouse leukaemia virus glycosylated Gag (glycoGag) strongly enhance the infectivity of HIV-1 virions produced in certain cell types in a clathrin-dependent manner. Here we show that Nef and glycoGag prevent the incorporation of the multipass transmembrane proteins serine incorporator 3 (SERINC3) and SERINC5 into HIV-1 virions to an extent that correlates with infectivity enhancement. Silencing of both SERINC3 and SERINC5 precisely phenocopied the effects of Nef and glycoGag on HIV-1 infectivity. The infectivity of nef-deficient virions increased more than 100-fold when produced in double-knockout human CD4(+) T cells that lack both SERINC3 and SERINC5, and re-expression experiments confirmed that the absence of SERINC3 and SERINC5 accounted for the infectivity enhancement. Furthermore, SERINC3 and SERINC5 together restricted HIV-1 replication, and this restriction was evaded by Nef. SERINC3 and SERINC5 are highly expressed in primary human HIV-1 target cells, and inhibiting their downregulation by Nef is a potential strategy to combat HIV/AIDS.

Analytic Form of the Full Two-Loop Five-Gluon All-Plus Helicity Amplitude.

We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms, and rational functions.

Filler flocculation in polymers - a simplified model derived from thermodynamics and game theory.

The performance of elastomeric materials, i.e. in car tires, is substantially determined by the used reinforcing filler system. In particular, the flocculation tendency of filler particles to form clusters and even network-like structures significantly determines the mechanical properties of these elastomer materials and enhances especially their energy dissipation under periodic mechanical deformations. In a simplified thermodynamic model, inspired by a segregation model from game theory, we describe fundamental mechanisms of filler structure formation. As the final goal of this paper we want to demonstrate how similar structures in society, nature or materials like rubbers emerge when supposing obvious cardinal mechanisms of structure formation in complex systems.

Rubber contact mechanics: adhesion, friction and leakage of seals.

We study the adhesion, friction and leak rate of seals for four different elastomers: Acrylonitrile Butadiene Rubber (NBR), Ethylene Propylene Diene (EPDM), Polyepichlorohydrin (GECO) and Polydimethylsiloxane (PDMS). Adhesion between smooth clean glass balls and all the elastomers is studied both in the dry state and in water. In water, adhesion is observed for the NBR and PDMS elastomers, but not for the EPDM and GECO elastomers, which we attribute to the differences in surface energy and dewetting. The leakage of water is studied with rubber square-ring seals squeezed against sandblasted glass surfaces. Here we observe a strongly non-linear dependence of the leak rate on the water pressure ΔP for the elastomers exhibiting adhesion in water, while the leak rate depends nearly linearly on ΔP for the other elastomers. We attribute the non-linearity to some adhesion-related phenomena, such as dewetting or the (time-dependent) formation of gas bubbles, which blocks fluid flow channels. Finally, rubber friction is studied at low sliding speeds using smooth glass and sandblasted glass as substrates, both in the dry state and in water. The measured friction coefficients are compared to theory, and the origin of the frictional shear stress acting in the area of real contact is discussed. The NBR rubber, which exhibits the strongest adhesion both in the dry state and in water, also shows the highest friction both in the dry state and in water.

The effect of surface roughness and viscoelasticity on rubber adhesion.

Adhesion between silica glass or acrylic balls and silicone elastomers and various industrial rubbers is investigated. The work of adhesion during pull-off is found to strongly vary depending on the system, which we attribute to the two opposite effects: (1) viscoelastic energy dissipation close to an opening crack tip and (2) surface roughness. Introducing surface roughness on the glass ball is found to increase the work of adhesion for soft elastomers, while for the stiffer elastomers it results in a strong reduction in the work of adhesion. For the soft silicone elastomers a strong increase in the work of adhesion with increasing pull-off velocity is observed, which may result from the non-adiabatic processes associated with molecular chain pull-out. In general, the work of adhesion is decreased after repeated contacts due to the transfer of molecules from the elastomers to the glass ball. Thus, extracting the free chains (oligomers) from the silicone elastomers is shown to make the work of adhesion independent of the number of contacts. The viscoelastic properties (linear and nonlinear) of all of the rubber compounds are measured, and the velocity dependent crack opening propagation energy at the interface is calculated. Silicone elastomers show a good agreement between the measured work of adhesion and the predicted results, but carbon black filled hydrogenated nitrile butadiene rubber compounds reveal that strain softening at the crack tip may play an important role in determining the work of adhesion. Additionally, adhesion measurement under submerged conditions in distilled water and water + soap solutions are also performed: a strong reduction in the work of adhesion is measured for the silicone elastomers submerged in water, and a complete elimination of adhesion is found for the water + soap solution attributed to an osmotic repulsion between the negatively charged surface of the glass and the elastomer.

Higgs Boson Pair Production in Gluon Fusion at Next-to-Leading Order with Full Top-Quark Mass Dependence.

We present the calculation of the cross section and invariant mass distribution for Higgs boson pair production in gluon fusion at next-to-leading order (NLO) in QCD. Top-quark masses are fully taken into account throughout the calculation. The virtual two-loop amplitude has been generated using an extension of the program GoSam supplemented with an interface to Reduze for the integral reduction. The occurring integrals have been calculated numerically using the program SecDec. Our results, including the full top-quark mass dependence for the first time, allow us to assess the validity of various approximations proposed in the literature, which we also recalculate. We find substantial deviations between the NLO result and the different approximations, which emphasizes the importance of including the full top-quark mass dependence at NLO.

Erratum: Higgs Boson Pair Production in Gluon Fusion at Next-to-Leading Order with Full Top-Quark Mass Dependence [Phys. Rev. Lett. 117, 012001 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.012001.

The Nef-like effect of murine leukemia virus glycosylated gag on HIV-1 infectivity is mediated by its cytoplasmic domain and depends on the AP-2 adaptor complex.

UNLABELLED: Human immunodeficiency virus type 1 (HIV-1) Nef enhances the infectivity of progeny virions. However, Nef is dispensable for the production of HIV-1 virions of optimal infectivity if the producer cells are superinfected with certain gammaretroviruses. In the case of the ecotropic Moloney murine leukemia virus (M-MLV), the Nef-like effect is mediated by the glycosylated Gag (glycoGag) protein. We now show that the N-terminal intracellular domain of the type II transmembrane protein glycoGag is responsible for its effect on HIV-1 infectivity. In the context of a fully active minimal M-MLV glycoGag construct, truncations of the cytoplasmic domain led to a near total loss of activity. Furthermore, the cytoplasmic domain of M-MLV glycoGag was fully sufficient to transfer the activity to an unrelated type II transmembrane protein. Although the intracellular region of glycoGag is relatively poorly conserved even among ecotropic and xenotropic MLVs, it was also fully sufficient for the rescue of nef-deficient HIV-1 when derived from a xenotropic virus. A mutagenic analysis showed that only a core region of the intracellular domain that exhibits at least some conservation between murine and feline leukemia viruses is crucial for activity. In particular, a conserved YXXL motif in the center of this core region was critical. In addition, expression of the µ2 subunit of the AP-2 adaptor complex in virus producer cells was essential for activity. We conclude that the ability to enhance HIV-1 infectivity is a conserved property of the MLV glycoGag cytoplasmic domain and involves AP-2-mediated endocytosis. IMPORTANCE: The Nef protein of HIV-1 and the entirely unrelated glycosylated Gag (glycoGag) protein of a murine leukemia virus (MLV) similarly enhance the infectiousness of HIV-1 particles by an unknown mechanism. MLV glycoGag is an alternative version of the structural viral Gag protein with an extra upstream region that provides a cytosolic domain and a plasma membrane anchor. We now show for the first time that the cytosolic domain of MLV glycoGag contains all the information needed to enhance HIV-1 infectivity and that this function of the cytosolic domain is conserved despite limited sequence conservation. Within the cytosolic domain, a motif that resembles a cellular sorting signal is critical for activity. Furthermore, the enhancement of HIV-1 infectivity depends on an endocytic cellular protein that is known to interact with such sorting signals. Together, our findings implicate the endocytic machinery in the enhancement of HIV-1 infectivity by MLV glycoGag.

In vitro characterization of self-assembled anterior cruciate ligament cell spheroids for ligament tissue engineering.

Tissue engineering of an anterior cruciate ligament (ACL) implant with functional enthesis requires site-directed seeding of different cell types on the same scaffold. Therefore, we studied the suitability of self-assembled three-dimensional spheroids generated by lapine ACL ligament fibroblasts for directed scaffold colonization. The spheroids were characterized in vitro during 14 days in static and 7 days in dynamic culture. Size maintenance of self-assembled spheroids, the vitality, the morphology and the expression pattern of the cells were monitored. Additionally, we analyzed the total sulfated glycosaminoglycan, collagen contents and the expression of the ligament components type I collagen, decorin and tenascin C on protein and for COL1A1, DCN and TNMD on gene level in the spheroids. Subsequently, the cell colonization of polylactide-co-caprolactone [P(LA-CL)] and polydioxanone (PDS) polymer scaffolds was assessed in response to a directed, spheroid-based seeding technique. ACL cells were able to self-assemble spheroids and survive over 14 days. The spheroids decreased in size but not in cellularity depending on the culture time and maintained or even increased their differentiation state. The area of P[LA-CL] scaffolds, colonized after 14 days by the cells of one spheroid, was in average 4.57 ± 2.3 mm(2). Scaffolds consisting of the polymer P[LA-CL] were more suitable for colonization by spheroids than PDS embroideries. We conclude that ACL cell spheroids are suitable as site-directed seeding strategy for scaffolds in ACL tissue engineering approaches and recommend the use of freshly assembled spheroids for scaffold colonization, due to their balanced proliferation and differentiation.

UPF1 is crucial for the infectivity of human immunodeficiency virus type 1 progeny virions.

The SF1 helicase MOV10 is an antiviral factor that is incorporated into human immunodeficiency virus type 1 (HIV-1) virions. We now report that HIV-1 virions also incorporate UPF1, which belongs to the same SF1 helicase subfamily as MOV10 and functions in the nonsense-mediated decay (NMD) pathway. Unlike ectopic MOV10, the overexpression of UPF1 does not impair the infectivity of HIV-1 progeny virions. However, UPF1 becomes a potent inhibitor of HIV-1 progeny virion infectivity when residues required for its helicase activity are mutated. In contrast, equivalent mutations abolish the antiviral activity of MOV10. Importantly, cells depleted of endogenous UPF1, but not of another NMD core component, produce HIV-1 virions of substantially lower specific infectivity. The defect is at the level of reverse transcription, the same stage of the HIV-1 life cycle inhibited by ectopic MOV10. Thus, whereas ectopic MOV10 restricts HIV-1 replication, the related UPF1 helicase functions as a cofactor at an early postentry step.

Rapid reaction optimization by robust and economical quantitative benchtop 19F NMR spectroscopy.

The instrumental analysis of reaction mixtures is usually the rate-determining step in the optimization of chemical processes. Traditionally, reactions are analyzed by gas chromatography, HPLC or quantitative NMR spectroscopy on high-field spectrometers. However, chromatographic methods require elaborate work-up and calibration protocols, and high-field NMR spectrometers are expensive to purchase and operate. This protocol describes an inexpensive and highly effective analysis method based on low-field benchtop NMR spectroscopy. Its key feature is the use of fluorine-labeled model substrates that, because of the wide chemical shift range and high sensitivity of 19F, enable separate, quantitative detection of product and by-product signals even on low-field, permanent magnet spectrometers. An external lock/shim device obviates the need for deuterated solvents, permitting the direct, noninvasive measurement of crude reaction mixtures with minimal workup. The low field-strength facilitates a homogeneous excitation over a wide chemical shift range, minimizing systematic integration errors. The addition of the optimal amount of the nonshifting relaxation agent tris(acetylacetonato) iron(III) minimizes relaxation delays at full resolution, reducing the analysis time to 32 s per sample. The correct choice of processing parameters is also crucial. A step-by-step guideline is provided, the influence of all parameters, including adjustments needed when using high-field spectrometers, is discussed and potential pitfalls are highlighted. The wide applicability of the analytical protocol for reaction optimization is illustrated by three examples: a Buchwald-Hartwig amination, a Suzuki coupling and a C-H arylation reaction.

Long-term outcomes of a randomized, open-label, phase II study comparing cabazitaxel versus paclitaxel as neoadjuvant treatment in patients with triple-negative or luminal B/HER2-negative breast cancer (GENEVIEVE).

BACKGROUND: The GENEVIEVE study, comparing neoadjuvant cabazitaxel versus paclitaxel in triple-negative breast cancer (TNBC) and luminal B/human epidermal growth factor receptor 2 (HER2)-negative breast cancer (BC), previously reported significant differences in pathological complete response (pCR) rates. Effects on long-term outcome are unknown. PATIENTS AND METHODS: GENEVIEVE randomized patients with cT2-3, any cN or cT1, cN+/pNSLN+, centrally confirmed TNBC or luminal B/HER2-negative BC (latter defined as estrogen/progesterone receptor-positive and >14% Ki-67-stained cells) to receive either cabazitaxel 25 mg/m2 q3w for four cycles or paclitaxel 80 mg/m2 weekly for 12 weeks. Anthracycline-containing chemotherapy was allowed in case of histologically proven invasive residuals as neoadjuvant treatment or after surgery as adjuvant treatment. Here we report the secondary endpoints invasive disease-free survival (iDFS), distant disease-free survival (DDFS), and overall survival (OS). RESULTS: Of the 333 patients randomized, 74.7% and 83.2% completed treatment in the cabazitaxel and paclitaxel arms, respectively. After a median follow-up of 89.3 months (interquartile range 68.8-97.3 months), 80 iDFS events (43 after cabazitaxel and 37 after paclitaxel) and 47 deaths (23 after cabazitaxel and 24 after paclitaxel) were reported. IDFS rates were not significantly different between the cabazitaxel and paclitaxel arms after a 3-year (83.6% versus 85.0%) and 5-year follow-up (76.2% versus 78.3%) [hazard ratio (HR) = 1.27, 95% confidence interval 0.82-1.96, P = 0.294], respectively. DDFS rates at 3 years (88.6% versus 87.8%) and 5 years (82.1% versus 82.8%) for cabazitaxel and paclitaxel were comparable (HR = 1.15, P = 0.573). Similarly, OS rates at 3 years (91.6% versus 91.8%) and 5 years (89.2% versus 86.8%) showed no significant differences (HR = 1.05, P = 0.872). Subgroup analysis for TNBC and luminal B/HER2-negative BCs indicated no significant variations in 3- or 5-year iDFS, DDFS, or OS. CONCLUSIONS: The significant differences in pCR rates observed in both treatment arms did not significantly impact long-term outcomes for patients treated with cabazitaxel versus paclitaxel in the GENEVIEVE trial.

Regulation of CHMP4/ESCRT-III function in human immunodeficiency virus type 1 budding by CC2D1A.

The detachment of human immunodeficiency type 1 (HIV-1) virions depends on CHPM4 family members, which are late-acting components of the ESCRT pathway that mediate the cleavage of bud necks from the cytosolic side. We now show that in human cells, CHMP4 proteins are to a considerable extent bound to two high-molecular-weight proteins that we have identified as CC2D1A and CC2D1B. Both proteins bind to the core domain of CHMP4B, which has a strong propensity to polymerize and to inhibit HIV-1 budding. Further mapping showed that CC2D1A binds to an N-terminal hairpin within the CHMP4 core that has been implicated in polymerization. Consistent with a model in which CC2D1A and CC2D1B regulate CHMP4 polymerization, the overexpression of CC2D1A inhibited both the release of wild-type HIV-1 and the CHMP4-dependent rescue of an HIV-1 L domain mutant by exogenous ALIX. Furthermore, small interfering RNA against CC2D1A or CC2D1B increased HIV-1 budding under certain conditions. CC2D1A and CC2D1B possess four Drosophila melanogaster 14 (DM14) domains, and we demonstrate that these constitute novel CHMP4 binding modules. The DM14 domain that bound most avidly to CHMP4B was by itself sufficient to inhibit the function of ALIX in HIV-1 budding, indicating that the inhibition occurred through CHMP4 sequestration. However, N-terminal fragments of CC2D1A that did not interact with CHMP4B nevertheless retained a significant level of inhibitory activity. Thus, CC2D1A may also affect HIV-1 budding in a CHMP4-independent manner.

Precise QCD predictions for the production of a photon pair in association with two jets.

We compute the cross section for the production of a high-mass photon pair in association with two hadronic jets to next-to-leading order in quantum chromodynamics. Our results allow us for the first time to reliably predict the absolute normalization of this process and demonstrate that the shape of important kinematical distributions is modified by higher-order effects. The perturbative corrections will be an important ingredient in precision studies of Higgs boson properties from its production in association with two jets.

Increased metabolic rate and insulin sensitivity in male mice lacking the carcino-embryonic antigen-related cell adhesion molecule 2.

AIMS/HYPOTHESIS: The carcino-embryonic antigen-related cell adhesion molecule (CEACAM)2 is produced in many feeding control centres in the brain, but not in peripheral insulin-targeted tissues. Global Ceacam2 null mutation causes insulin resistance and obesity resulting from hyperphagia and hypometabolism in female Ceacam2 homozygous null mutant mice (Cc2 [also known as Ceacam2](-/-)) mice. Because male mice are not obese, the current study examined their metabolic phenotype. METHODS: The phenotype of male Cc2(-/-) mice was characterised by body fat composition, indirect calorimetry, hyperinsulinaemic-euglycaemic clamp analysis and direct recording of sympathetic nerve activity. RESULTS: Despite hyperphagia, total fat mass was reduced, owing to the hypermetabolic state in male Cc2(-/-) mice. In contrast to females, male mice also exhibited insulin sensitivity with elevated ß-oxidation in skeletal muscle, which is likely to offset the effects of increased food intake. Males and females had increased brown adipogenesis. However, only males had increased activation of sympathetic tone regulation of adipose tissue and increased spontaneous activity. The mechanisms underlying sexual dimorphism in energy balance with the loss of Ceacam2 remain unknown. CONCLUSIONS/INTERPRETATION: These studies identified a novel role for CEACAM2 in the regulation of metabolic rate and insulin sensitivity via effects on brown adipogenesis, sympathetic nervous outflow to brown adipose tissue, spontaneous activity and energy expenditure in skeletal muscle.

A randomized phase III adjuvant study in high-risk cervical cancer: simultaneous radiochemotherapy with cisplatin (S-RC) versus systemic paclitaxel and carboplatin followed by percutaneous radiation (PC-R): a NOGGO-AGO Intergroup Study.

BACKGROUND: Simultaneous adjuvant platinum-based radiochemotherapy in high-risk cervical cancer (CC) is an established treatment strategy. Sequential paclitaxel (Taxol) and platinum followed by radiotherapy may offer further advantages regarding toxicity. PATIENTS AND METHODS: An open-labeled randomized phase III trial was conducted to compare paclitaxel (175 mg/m(2)) plus carboplatin (AUC5) followed by radiation (50.4 Gy) (experimental arm-A) versus simultaneous radiochemotherapy with cisplatin (40 mg/m(2)/week) (arm-B) in patients with stage IB-IIB CC after surgery. Primary objective was progression-free survival (PFS). RESULTS: Overall, 271 patients were randomized and 263 were eligible for evaluation; 132 in arm-A and 131 in arm-B appropriately balanced. The estimated 2-year PFS was 81.8% [95% confidence interval (CI) 74.4-89.1] in arm-B versus 87.2% (95% CI 81.2-93.3) in arm-A (P = 0.235) and the corresponding 5-year survival rates were 85.8% in arm-A and 78.9% in arm-B (P = 0.25). Hematological grade 3/4 toxicity was higher in arm-B. Alopecia (87.9% versus 4.1%; P < 0.001) and neurotoxicity (65.9% versus 15.6%; P < 0.001) were significantly higher in arm-A. Early treatment termination was significantly more frequent in arm-B than in arm-A (32.1% versus 12.9%; P = 0.001). CONCLUSIONS: Sequential chemotherapy and radiation in high-risk CC could not show any significant survival benefit; however, a different toxicity profile appeared. This sequential regime may constitute an alternative option when contraindications for immediate postoperative radiation are present.

Human immunodeficiency virus type 1 and related primate lentiviruses engage clathrin through Gag-Pol or Gag.

The Gag-Pol polyprotein of human immunodeficiency virus type 1 (HIV-1) is not required for efficient viral particle production. However, premature termination codons in pol, particularly in the integrase (IN)-coding region, can markedly impair HIV-1 particle formation, apparently due to the premature activation of the viral protease (PR). We now report that the IN domain of Gag-Pol is required for the incorporation of clathrin into HIV-1 virions. Significantly, PR-dependent effects of point mutations in IN on particle production correlated strictly with their effects on clathrin incorporation. A possible interpretation of these findings is that certain IN mutations impair particle production in a PR-dependent manner by promoting Gag-Pol dimerization, which also occludes a binding site for clathrin. Consistently with this model, the reverse transcriptase (RT) inhibitor efavirenz, which is thought to promote Gag-Pol dimerization, inhibited the incorporation of clathrin into HIV-1 virions. Clathrin-depleted cells produced normal amounts of HIV-1 virions; however, their infectivity was reduced. We also observed that HIV-2 and the simian immunodeficiency virus SIVmac interact with clathrin through one or two copies of a peptide motif in the p6 domain of Gag that resembles the clathrin box of cellular adaptor proteins. Furthermore, the substitution of the hydrophobic residues in the single clathrin box motif of SIVmac caused a replication defect in primary cells. Taken together, our results indicate that primate lentiviruses from two different subgroups functionally interact with clathrin during assembly.

Theory of light-induced deformation of azobenzene elastomers: influence of network structure.

Azobenzene elastomers have been extensively explored in the last decade as photo-deformable smart materials which are able to transform light energy into mechanical stress. Presently, there is a great need for theoretical approaches to accurately predict the quantitative response of these materials based on their microscopic structure. Recently, we proposed a theory of light-induced deformation of azobenzene elastomers using a simple regular cubic network model [V. Toshchevikov, M. Saphiannikova, and G. Heinrich, J. Phys. Chem. B 116, 913 (2012)]. In the present study, we extend the previous theory using more realistic network models which take into account the random orientation of end-to-end vectors of network strands as well as the molecular weight distribution of the strands. Interaction of the chromophores with the linearly polarized light is described by an effective orientation potential which orients the chromophores perpendicular to the polarization direction. We show that both monodisperse and polydisperse azobenzene elastomers can demonstrate either a uniaxial expansion or contraction along the polarization direction. The sign of deformation (expansion/contraction) depends on the orientation distribution of chromophores with respect to the main chains which is defined by the chemical structure and by the lengths of spacers. The degree of cross-linking and the polydispersity of network strands do not affect the sign of deformation but influence the magnitude of light-induced deformation. We demonstrate that photo-mechanical properties of mono- and poly-disperse azobenzene elastomers with random spatial distribution of network strands can be described in a very good approximation by a regular cubic network model with an appropriately chosen length of the strands.