Cell fate decisions are critical for life, yet little is known about how theirreliability is achieved when signals are noisy and fluctuating with time. In thisstudy, we show that in budding yeast, the decision of cell cycle commitment (Start)is determined by the time integration of its triggering signal Cln3. We furtheridentify the Start repressor, Whi5, as the integrator. The instantaneous kinaseactivity of Cln3-Cdk1 is recorded over time on the phosphorylated Whi5, and thedecision is made only when phosphorylated Whi5 reaches a threshold. Cells adjust thethreshold by modulating Whi5 concentration in different nutrient conditions tocoordinate growth and division. Our work shows that the strategy of signalintegration, which was previously found in decision-making behaviors of animals, isadopted at the cellular level to reduce noise and minimize uncertainty.DOI:http://dx.doi.org/10.7554/eLife.03977.001 Budding yeast and other single-celled organisms can reproduce by dividing to producetwo daughter cells. The timing of the cell division is critical because if the cellis still small when it divides, the resulting daughter cells may not be big enough tosurvive.In budding yeast, the irreversible decision to divide—known as the‘Start’ checkpoint—is only made once a cell reaches a certainsize and is triggered by a protein called Cln3. This protein controls the activity ofanother protein called Whi5, which normally prevents the cell from dividing byswitching off particular genes. Cln3 adds phosphate groups to Whi5 to make‘phosphorylated Whi5’, which allows the genes involved in cell divisionto be switched on.It is commonly believed that the level of Cln3 reflects the size of the cell and thenutrient conditions. Therefore, one model of cell division proposes that the cellpasses the Start checkpoint when the level of Cln3 reaches a threshold value.However, levels of the Cln3 protein in cells can naturally fluctuate, and computersimulations based on this model showed that this would not produce reliable decisionson when to divide. So how do cells manage to distinguish noise from the genuinesignals that indicate it is the right time to divide?To address this question, Liu et al. studied yeast cells containing an artificialversion of the gene encoding the Cln3 protein whose levels could be adjusted byadding a particular chemical. This revealed that cells with higher levels of Cln3passed through the Start checkpoint sooner than cells that had lower levels ofCln3.The observation suggests that cells add up the amount of Cln3 present over a periodof time to see if this reaches the threshold needed for the Start checkpoint. Thiscould be possible if, instead of sensing Cln3 levels directly, the cell senses theaccumulation of phosphorylated Whi5. To test this idea, Liu et al. carried outadditional experiments and found that the decision to pass the Start checkpoint onlyoccurs when the amount of phosphorylated Whi5 reaches a certain threshold.The cells are able to coordinate their growth and division under different nutrientconditions by altering the threshold of phosphorylated Whi5. When the nutrient supplyis poor, more phosphorylated Whi5 needs to be accumulated to allow the cell to passthe Start checkpoint. In this way, cells adjust when they divide according tonutrient conditions. Similar strategies may be found in other signaling ordecision-making systems.DOI:http://dx.doi.org/10.7554/eLife.03977.002 Saccharomycescerevisiae) as a model system. Start is a major cell cycle checkpoint inbudding yeast , which decideswhether or not the cell should make the irreversible commitment to the next round ofdivision increases with cell size and the Start transition is triggered when Cln3 level reaches acritical threshold . There alf-lives ) atverylf-lives  and100–lf-lives ), enabliIn this study, by quantitatively measuring an inducible Cln3 mutant and simultaneouslymonitoring the timing of Start transition in single cells, we address the question ofwhat information in the Cln3 profile the cell is using to make the Start decision. Wefound that the Start transition is triggered by the time integration of Cln3 activity onphosphorylated Whi5. Furthermore, cells modulate Whi5 concentration in differentnutrient conditions. Cln3 and Whi5 together control G1 length through the timeintegration mechanism to coordinate cell division with cell growth. The time integrationstrategy can reduce noise and minimize uncertainty in the decision and may be widelyimplied in decision making systems at the cellular level.CLN3 onto the genome in a strainlacking the native CLN3 and BCK2 and fused theendogenous WHI5 with the red fluorescent protein tdTomato. The G1length TG1 is defined as the timeinterval between Whi5 nuclear entry in late mitosis and its exclusion from thenucleus at the Start transition  was used infollowing experiments . To better quantitate the observednegative correlation between G1 length and Cln3 level, we screened for Cln3 mutantswith lower activity and longer half-life based on a homolog modeling of the Cln3-Cdk1complex . Lower a3Δcells ;3) the eriments , which ieriments . It was eriments  and/orEeriments .HoweverCLN3D166A was used as the signal, or G1 length isdefined by the MCM marker  againstlog(<Cln3> − Cln3c)in T0 is the horizontal asymptoterepresenting the minimum G1 length (time from Whi5 nuclear entry to cytokinesis) andCln3c is the vertical asymptoterepresenting the minimum Cln3 concentration for cell to eventually pass Start. Theslope of the linear fit is very close to −1 (R2 = 0.91)  . Thus G1t = TG1) whenthe time integration of the Start signal is above a threshold(A).The above equation implies that the Start transition is triggered  = 0, thusWhi5tot is the nuclear Whi5concentration when the phosphorylation reaction becomes dominant. At the Starttransition t =TG1, the nuclear Whi5 concentrationdrops to Whi5c, which is the criticalWhi5 threshold determined by the positive feedback loop (Whi5P(t = TG1) =Whi5tot− Whi5c. By integrating T0 toTG1, we have:By our definition, G1 starts from Whi5 nuclear entry, when Cdc14 is the majorphosphatase that is responsible for Whi5 dephosphorylation . Cln3 caack loop , sothatA =(Whi5tot−Whi5c)/k1and Cln3c=k2/k1.We thus identified Whi5 as the integrator: the number of phosphorylated Whi5,Whi5P, accumulates with Cln3-Cdk1activity and the increase of Whi5Pcauses a decrease in the nuclear Whi5 concentration. The Start transition happenswhen the nuclear Whi5 concentration drops belowWhi5c, or the accumulation ofWhi5P reaches a threshold. In thecase where the phosphatase operates in the linear region, 1/k2, beyond which the integrationeffect is erased.In this case, there is a window of ‘memory’ of lengthcdc28-as1 allele increases Cln3c and Aproportionally, requiring an increased Cln3 concentration to pass Start.The mathematical model of Whi5 kinetics makes several predictions. The first is thatthere is a linear relation between the integration threshold Whi5tot ).The sestrength ). Note twhi5Δ strain, most cellspass Start with minimal G1 length . After normalizing byWhi5tot, inverse correlations inboth 1X and 2X WHI5 strains are more converged andcollapse to the same curve  and increaseCln3c. We measured G1 length vs Cln3intensity in cln1Δ and cln2Δ strainsand observed that Cln3cs increase andthe inverse correlations shift upward in log–log scale as predicted  sensing , (ii) information processing (of thesensed information), and (iii) actuating . Previous workshave been mainly focused on the first and the last steps. Even in many cases wherethe molecular players and the circuitry are mapped out, how cells process informationto make the best decision is largely unknown. This is intrinsically a quantitativequestion and is especially important when the signals are noisy and withuncertainties. Information processing is the brain of decision making; understandingthis step is critical to understand the rationale and the strategy the cell adopts tomake better decisions.We address this question with a well-studied model system: the budding yeast Startcheckpoint. Using a quantitative single cell assay with a controllable andquantifiable Cln3 signal, we discovered that it is not the instantaneous value of theCln3 concentration, but rather the integration of the concentration over time, thattriggers the switch. Cln3 is a sensor that senses, with a fast response time, theinstant information/condition relevant to making cell cycle commitment. We found thatthe instant Cln3 activity is memorized on phosphorylated Whi5, and the memory lengthis about 10 min in SD medium. This implies that the cell uses information within atime window of the past in order to get an assessment of the future.This strategy of signal integration averages out noise and fluctuations and minimizeserror and uncertainty in decision making. Signal integration has been seen indecision-making behaviors of animals . OurworWhi5  serves as the integrator in thesystem, that is, the physical memory onto which the integration is being recorded. Wefound that cells modulate Whi5 level to set different integration thresholds indifferent nutrient conditions. Whi5 level is higher in poor nutrients, thus cells aremore cautious and wait for longer time to make the decision.Whi5tot intensity and steeperslope between Whi5tot and G1 length thanmother cells  for deletion were amplified from the plasmid pFA6-KAN-MX6 , with the TEF1ter amplified from thesame plasmid; then replaced the mCherry fragment between PacI andAscI with the tdTomato fragment amplified from pRS304-tdTomato; nextthe 300 bp upstream of the WHI5 stop codon amplified from theW303 genome was inserted between HindIII and PacI sites; finallythe 300 bp downstream of the WHI5 stop codon amplified from theW303 genome was inserted by using ClaI, along with an additionalHindIII site at the 3′ end. Each inducible Cln3 plasmid contains threetranscription units: the lactose transporter, the constantly expressed LacI and theinducible promoter controlled Cln3 signal. The STE5pr (−602to −1 of STE5) amplified from the W303genome, the LAC12 amplified from pKR1B-LAC4-1  withtwo LacI binding sites (one on each side of the TATA box), was obtained byoverlapping PCR . Venus was amplified from pVenus-N1-NPY with SacI-NotII and ClaI-XhoI respectively.Finally, the transcription unit of transporter was amplified by PCR and inserted intothe plasmid with SacI site to accomplish the inducible Cln3 plasmids pCT2002-pCT2005.The pCT2006 plasmid was constructed by inserting the ADH1pramplified from the genome, the HTB2 without stop codon amplifiedfrom the genome, the CFP with linker at the N-terminal amplifiedfrom BBa_E0020 (iGEM Registry) and the CYC1ter into pRS304with SacI-NotI-SpeI-SalI-XhoI. The pCT2007 and pCT2008 plasmids were constructed byinserting the ADH1pr, the MCM marker amplified frompML103 (GFP (for pCT2007), or mCherry (for pCT2008) withlinker at the N terminal and the CYC1ter into pRS306  amplified from the genome into HindIII-PacIand subcloning the HindIII-BglII fragment of the resultant plasmid into pRS306.pCT2010 was constructed by inserting the GPDpr, theCDC14 amplified from the genome and the CYC1terinto pRS306 with SacI-BamHI-SalI-XhoI. All the plasmids were verified by sequencingon both strands and summarized in The plasmid pCT2001 was constructed as following: first replaced theB-LAC4-1 , and thepGREG506  were inspGREG506  withSacS424-GPD , the Lacping PCR . GFP wass-N1-NPY. A 11-ammpML103 ,GFP (foo pRS306  withSacAll the inverse correlations were measured in Synthetic Dextrose (SD) mediumcontaining 2% (wt/vol) glucose, 1× amino acid (AA) dropout, 6.7 g/L yeastnitrogen base (YNB) without amino acid, 100 mg/L leucine, 20 mg/L histidine, 20 mg/Ltryptophan, 20 mg/L adenine, and 20 mg/L urea, unless otherwise indicated. Theformula of 1× amino acid dropout is 20 mg/L arginine, 20 mg/L methionine, 30mg/L tyrosine, 30 mg/L isoleucine, 30 mg/L lysine, 50 mg/L phenylalanine, 100 mg/Lglutamic acid, 100 mg/L aspartic acid, 150 mg/L valine, 2 g/L threonine and 4 g/Lserine. The limited nitrogen medium contains 2% (wt/vol) glucose, 0.05 mM ammoniumsulfate, 6.7 g/L yeast nitrogen base (YNB) without ammonium sulfate and amino acid,100 mg/L leucine, 20 mg/L histidine, 20 mg/L tryptophan, 20 mg/L adenine, and 20 mg/Lurea . The limhttp://meta.bioinfo.pl/) (We constructed the homologous structure of Cln3 based on the cyclin A chain (chain B)in 3DDQ (PDB ID). Two other structures, the cyclin D3 chain (chain B) in 3G33 (PDBID) and the cyclin E1 chain (chain B) in 1W98 (PDB ID), were chosen for reference aswell. The amino acid sequences of those proteins were aligned by the 3D-Jury server(nfo.pl/) , and thenfo.pl/) .Similarnfo.pl/) , taking nfo.pl/) .To screen for the desired Cln3 mutants, we selected 12 single amino acid sites inclustered charged residues . Three mGlacSpr. Each construct was integratedat the HIS3 locus of the cln3Δ strainYCT2011. The GFP brightness and cell size under full induction was quantified byfluorescent microscopy. Only mutants with significantly higher GFP intensity thanwild-type were shown in BCK2 in those strains andinvestigate their cell division without IPTG under microscopy. The shut-off of cellcycle was considered tight if less than 5% cells budded in 6 hr.To check the brightness and the activity of the Cln3 mutants, the wild-type andmutant Cln3s were fused with two tandem GFPs on the N terminus and expressed by thesynthetic inducible promoter μL/hr. In thenutrient switching experiments, both the tubing and the syringe providing the mediumwere changed within 3 min, to make sure the transition is as fast as possible.Similar molds and methods as described previously  were useExcept for the measurement of Whi5 dephosphorylation rate, cells were grown in themicrofluidic chip to maintain the constant IPTG concentration and nutrient condition.Temperature of the microfluidic chip was kept at 30°C with a stage top incubator.Time lapse movies werecollected with epi-fluorescence microscopy using a Nikon Ti-E inverted microscopeequipped with the objective lens Plan Apo VC 100×/1.40 Oil DIC N2, the motorizedXY stage and the Perfect-Focus System . Images were acquiredevery 3 min with an Andor iXon3 897 EMCCD  and Lambda SC shutter controllers . NIS Elements AR v3.2  was used to automateimage acquisition and microscope control. There is no significant photo-toxicity orperturbations of cell cycle time caused by the detection of either GFP-GFP-Cln3 orWhi5-tdTomato or both. There is no significant photo-bleaching in the GFP or tdTomatochannel (data not shown). The brightness of the mercury lamp on different days wasnormalized by fluorescent reference slides .To measure Whi5 dephosphorylation rate, cells were immobilized on glass bottomed dishby conA. Temperature was kept by ZILCS incubation chamber . Cells were monitored for 30 min and then another 2 hr afteradding 50 μM 1-NM-PP-1 to the medium. Time lapse movie was collected with aUltraVIEW VoX Laser Confocal Imaging System  and a CSU-X1spinning disk confocal  on a Nikon Ti-E inverted microscopeequipped with the APO TIRF 100X OIL NA 1.45 objective lens, the motorized XY stageand the Perfect-Focus System . Whi5-tdTomato fluorescencewas excited with the 561 nm 50 mW laser line and collected by the appropriatefilters. Images were acquired every 3 min by a Hamamatsu C9100-13 EMCCD  camera. At each time point, 5 Z-seriesoptical sections were collected with a step size of 1.6 μm, using a NanoScanZ400 μm Piezo focusing drive . Maximumprojections of Z stacks were performed with ImageJ.cellseg as describedpreviously . The brightest 3 × 3 pixels werededucted from the brightest 9 × 9 pixels to eliminate the artifact ofaggregates. Cell size was taken as cell area in two dimensional. Cells were assumedgrow exponentially in G1. Growth rate fitted by more than six data points and withstandard error smaller than 0.02 were used in the final statistics. Export of thefluorescent intensities and cell area was automatically accomplished bycellseg with minor revision. Following analysis was accomplishedby the MATLAB custom software analyzestart, which was developedbefore   .TG1 correlations in log–logscale were fitted by the following criteria:T0 was set as 5 min for strainswith the Whi5 marker  converted from the Ordinary Differential Equations :d[mRNAclThe meaning, value and reference of the parameters to generate Constant transcription rate of CLN3 gene.Constant degradation rate of Cln3 mRNA and protein.Exponential growth of cell volume.Ribosome number (reflected by translation rate) is proportional to cellvolume.r ratio offull capacity) to mimic the Ace2 suppression in daughter cells.Cln3 transcription gets suppressed at early G1  within this model.Extrinsic noise was simulated by randomizing the model parameters around theirnominal values within a certain percentage range. Extrinsic noise of 20% CV wasapplied to all parameters . Similarly, the author response typically shows only responsesto the major concerns raised by the reviewers.eLife posts the editorial decision letter and author response on a selection of thepublished articles . An edited version of theletter sent to the authors after peer review is shown, indicating the substantiveconcerns or comments; minor concerns are not usually shown. Reviewers have theopportunity to discuss the decision before the letter is sent  and a member of the Board of Reviewing Editors (James Ferrell), and hasbeen reviewed in depth by three peer reviewers.Thank you for sending your work entitled “Reliable cell cycle commitment inbudding yeast is ensured by signal integration” for consideration atThe Reviewing editor and the reviewers discussed their comments before we reached thisdecision, and the Reviewing editor has assembled the following comments to help youprepare a revised submission.The manuscript “Reliable cell cycle commitment in budding yeast is ensured bysignal integration” by Liu et al. addresses the important problem of how yeastcells make the decision to commit to a new round of cell division at the Starttransition. The authors reach the interesting conclusion that cells integrate Cln3activity over time to make a reliable decision. This is in principle an importantfinding and the integration model could be very general.We have two main criticisms that need to be addressed prior to publication. There are anumber of minor criticisms as well, which would improve the rigor and understandabilityof the paper.Major concerns:1) One major concern is that the integration model is not compared to alternativemodels. I would suggest that the authors use statistical methods to prove that theintegration model provides a significantly better fit of the experimental data thanalternative models . Notice that equation number 4 in the 2) An important assumption of the integrator model is that Whi5 has a'memory', namely that its activity depends not only on the instantaneous Cln3but also on previous events. This means that its dephosphorylation rate is slow. In thesupplementary materials, the authors cite published work from What Charvin et al. showed their  isthat There are two ways the authors could deal with this issue. They could directly measurefor themselves how fast Whi5 returns to the nucleus after inhibition of CDK1. One waywould be to use an analog-sensitive CDK1 mutant, which would obviate the need to guesshow long CLN2 remains above the level required for Whi5 phosphorylation after theinduction of CLN2 is terminated. While this might be the ideal solution, we appreciatethat there is already a lot of data in the paper, and we would be satisfied if theauthors would just accurately state Charvin et al.'s findings in the main text andacknowledge that slow Whi5 dephosphorylation kinetics remains a key incompletely-testedassumption of the authors' model. 1) One major concern is that the integration model is not compared toalternative models. I would suggest that the authors use statistical methods to provethat the integration model provides a significantly better fit of the experimentaldata than alternative models . Notice that equation number 4 intheactually suggests that the total amount of Cln3 in a cell should be a goodestimator of when cells divide. The authors need to provide stronger arguments todistinguish among models. This should be readily doable, as they have alreadyacquired the necessary data.We acknowledge the referees’ suggestion.When deducting equation number 4 in the Whi5p, reaches the thresholdWhi5p(G1)=Whi5tot-Whi5c.When considering the fluctuation of Cln3 concentration with time,Start is triggered when phosphorylated Whi5,G1 length cannot be estimated by the instantaneous Cln3 concentration at one time pointbut by the Cln3 integration through the whole G1 phase. We added an additional sectionin We tested the Instantaneous Model with the Cln3 profiles measured in experiment, whichare more meaningful than stochastic simulations. In our experimental setup, Cln3 levelduring G1 in one cell fluctuates with about 20% CV see . If the 2) An important assumption of the integrator model is that Whi5 has a'memory', namely that its activity depends not only on the instantaneousCln3 but also on previous events. This means that its dephosphorylation rate is slow.In the supplementary materials, the authors cite published work fromthat they say indicates that the half-time for Cln3 dephosphorylation is longerthan 30 min. However this is not exactly what Charvin et al. said or what Charvin etal.'s data show.What Charvin et al. showed (their) is thatfollowing a 15 min pulse of CLN2 expression in the presence of Clb-inhibitory levelsof Sic1-4A expression, Whi5 exits the nucleus and then begins to reenter it. Re-entrybegins very soon after the inducer of CLN2 expression is washed away and ishalf-maximal by 35 min. Some of this time interval-Charvin et al. guess about 5-10min-is probably due to the kinetics of CLN2 degradation. Presumably the remaining∼25-30 min is partly attributable to the kinetics of Whi5 dephosphorylation,and partly to the kinetics of Whi5 nuclear transport. So based on these experiments,one might conclude that Whi5 dephosphorylation could have a half-time of up to 30min, not that it has a half-time of longer than 30 min.There are two ways the authors could deal with this issue. They could directlymeasure for themselves how fast Whi5 returns to the nucleus after inhibition of CDK1.One way would be to use an analog-sensitive CDK1 mutant, which would obviate the needto guess how long CLN2 remains above the level required for Whi5 phosphorylationafter the induction of CLN2 is terminated. While this might be the ideal solution, weappreciate that there is already a lot of data in the paper, and we would besatisfied if the authors would just accurately state Charvin et al.'s findingsin the main text and acknowledge that slow Whi5 dephosphorylation kinetics remains akey incompletely-tested assumption of the authors' model.cdc28-as1 allele. Theaverage half time of Whi5 nuclear entry, which corresponds to the memory length in themathematical model, is 13.7 min in mother cells and 10.6 min in daughter cells,respectively. Note that the average G1 length (from cytokinesis to Start) in daughtercells is 13.6 min in SD medium, a memory length of about 10 min should be long enoughfor the cell to take the advantage of integration.We acknowledge the referees’ correction for our interpretation of Charvin etal.'s data. To better understand the integration mechanism, we measured Whi5dephosphorylation kinetics as the referees suggested. As most Whi5 is dephosphorylatedand resides in the nucleus during G1 phase, we could not directly measure Whi5dephosphorylation in G1. Thus we measured Whi5 nuclear entry right after G1 byinhibiting Cdk1 activity with a strain bearing a We added this result as


N-acetylglucosamine moieties. The LysM sequence is present singly or repeatedly in a large number of proteins of prokaryotes and eukaryotes. Since the mid-1990s, domains containing one or more of these LysM sequences originating from different LysM-containing proteins have been examined for purely scientific reasons as well as for their possible use in various medical and industrial applications. These studies range from detecting localized binding of LysM-containing proteins onto bacteria to actual bacterial cell surface analysis. On a more applied level, the possibilities of employing the LysM domains for cell immobilization, for the display of peptides, proteins, or enzymes on  surfaces as well as their utility in the development of novel vaccines have been scrutinized. To serve these purposes, the chimeric proteins containing one or more of the LysM sequences have been produced and isolated from various prokaryotic and eukaryotic expression hosts. This review gives a succinct overview of the characteristics of the LysM domain and of current developments in its application potential.The lysin motif (LysM) was first identified by Garvey et al. in 1986 and, in subsequent studies, has been shown to bind noncovalently to peptidoglycan and chitin by interacting with  The cell envelope of Gram-positive bacteria consists of a cytoplasmic membrane and a cell wall. Besides protecting and maintaining cell integrity, the cell wall is important for interactions of the cell with its external milieu. The major component of the Gram-positive cell wall is peptidoglycan (PG), which consists of glycan chains cross-linked through short peptides and interpeptide bridges. PG can be divided into multiple types on the basis of variations in the glycan strands, the peptide stem, or in the position or composition and degree of the interpeptide bridge formation. Additional variations of the PG can occur through amidation, hydroxylation, acetylation, or attachment of amino acids or other groups  has been shown to specifically bind PG although the ligand had not been identified yet  specifically bind PG. Fusion of this domain with nuclease (Nuc) of Staphylococcus aureus, an enzyme that is normally secreted, resulted in binding of the fusion protein to purified PG from Bacillus subtilis and whole cells of E. faecalis, B. subtilis, Streptococcus agalactiae, Lactobacillus johnsonii, Staphylococcus aureus, and Listeria innocua when it was added from the outside. Also for this domain, the specific ligand has not been identified yet. Gründling and Schneewind . Multiple LysM sequences in a protein are often separated by small Ser-, Thr-, and Asn-rich intervening sequences. The number of LysM sequences in a domain varies from 1 to up to 12; the domain is found mainly at the N- or C-termini of proteins and less frequently in the central region of some LysM-containing proteins  membrane or have a cytosolic location  and several Gram-positive bacteria , in yeast (Pichia pastoris), insect cells  , this method is especially successful when these are first removed from the recipient cells by TCA treatment. For instance, bacterium-like particles (BLPs), formerly called Gram-positive enhancer matrix (GEM)  from B. thuringiensis was successfully expressed and displayed on the whole cell surface of B. thuringiensis cells  binding to bacterial cell surfaces Table . A GFP fS. aureus revealed the crucial role of the LysM domain in localized binding of the two enzymes to the septum, thereby likely facilitating PG hydrolysis in daughter cell separation  was recently performed to determine the nanoscale organization in living L. lactis, are regarded as food-grade bacteria and might be good alternative biocatalysts as well. L. lactis cells have been immobilized on cellulose using a cellulose-binding domain fused to either the C-terminal LPxTG domain of the major proteinase PrtP  or to LysMAcmA . Immobilization of L. lactis cells to cellulose was achieved with both fusion proteins. Cells expressing the LPxTGPrtP-anchored fusion protein bound 34 % more efficiently than those with the LysMAcmA domain  of chitinase A1 from Bacillus circulans fused to the LPxTGPrtP domain or the LysMAcmA domain  as biocatalysts have significantly increased. Certain species of LAB are mostly employed for the production of lantibiotics, β-galactosidase, nisin, lactic acid, and gamma-aminobutyric acid. LAB have also been used for the surface display of various heterologous proteins  fusion proteins onto cells of different bacterial species and various substrates Table . The firt et al.  showed tB. licheniformis α-amylase with LysMAcmA was used to show that an increase of 10- to 15-fold in enzyme activity could be obtained when the fusion protein was loaded onto L. lactis BLPs instead of L. lactis cells  was obtained for the purified N-terminal fusion with β-lactamase. Using immunofluorescence microscopy, it was shown that this fusion bound at high density to the entire B. subtilis cell surface.The LysM domain of the Paenibacillus sp. carrying the LysM domain of the endolysin Lyb5 of L. fermentum followed by a His-tag at its C-terminus in E. coli. The purified active fusion protein could be displayed on TCA-pretreated cells of L. lactis and on untreated cells of L. casei, L. brevis, or L. plantarum.Hu et al.  producedL. lactis AcmA, with its C-terminal LysM domain, to GFP or the endo-β-1,3-1,4-glucanase from B. subtilis was functionally immobilized and displayed on the cell surface of the L. lactis producer cells , i.n. influenza vaccines  via multiple LysM sequences does not require the motifs to be present in the same protein monomer. Using a similar approach, the influenza neuraminidase (NA) antigen was attached to BLPs in its native homotetrameric conformation . These examples show that complex proteins such as viral oligomeric proteins can also be successfully bound to BLPs.BLPs still have the ability to stimulate the innate immune system . This pentavalent vaccine was compared with a vaccine in which the five antigens were individually bound to a BLP carrier after which the five BLP carriers were combined. Both types of vaccines were administered intranasally in mice and generated similar results in terms of serology and protection after challenge. Although the possibility to bind multiple antigens to a single carrier particle is easy and seems attractive, batch-to-batch consistency is a challenge, and therefore, it is more practical from a quality control point of view to combine different batches of BLPs with different antigens to generate combination or multivalent vaccines.L. monocytogenes p60 endopeptidase itself has an effect on the immune system by activating natural killer (NK) cells -binding affibody on L. lactis cells. These could be effectively used to bind TNF-α. This setup was suggested to have potential in the treatment of inflammatory bowel disease.Besides the vaccine applications described above, LysM domains are also being explored in additional potential health applications and for other purposes. Ravnikar et al.  used a CAcmA has also been suggested to be of possible use to improve delivery of viable microorganisms to the intestinal tract  cells to the adverse gastric conditions, for instance by firmly encapsulating the bacteria in porous starch granules  vaccine area, entails the increased and more stable binding of antigens fused to (a) LysM sequence(s) to acid-pretreated bacterial cells.L. lactis ∆htrA∆acmA. This strain lacks all extracellular proteolytic activity and does not autolyse, not even during the stationary phase of growth  bacteria in different (bodily) fluids. One way to do this would be to fuse a LysM domain to a fluorescent protein, as was done for LysMAcmA and the LysM domains of the staphylococcal proteins LytN and SleI  binding domain  could be used for whole-cell immobilization. Such an approach might be useful in various industrial applications employing bacteria or chitin-containing fungal species to, for instance, avoid loss of cells.Using the LysM domain, binding of multiple different antigens and active enzymes has been achieved on living and nonliving cells, on spores, and to chitin. Removing cell wall components such as LTA, which hinder binding via the LysM domain, increases the strength of binding and the number of molecules that can be bound. This is most effectively realized by pretreating bacterial cells with trichloroacetic acid, which also eliminates proteases that could otherwise degrade the fusion proteins. Using LysM domains allows immobilizing purified fusion proteins on any Gram-positive bacterium in a non-GMO manner. The production of the LysM-containing proteins can best be performed in an autolysis- and proteolysis-negative protein expression host, such as eI Table . In anotThe successful display of active enzymes using the LysM sequence could be extended by a display of a combination of enzymatic activities that together form a combined (metabolic) pathway or biosynthesis route. This method could potentially be extended or improved by making use of different noncovalent PG-binding domains Table  in orderIn conclusion, a lot has been learned on the structure and function of the LysM domain, and this knowledge has been successfully explored in various potential applications. These studies have mainly been based on the use of bacterial LysM sequences in fusion proteins. Apart from the role of plant LysM sequences in plant-microbe signaling, virtually nothing is known about the function of LysM sequences in other eukaryotes. Much remains to be discovered in this area, especially with respect to possible future applications, e.g., in stimulating or steering beneficial eukaryote-microbe interactions or, possibly, identifying, typing, sensing, targeting, and/or combating plant and animal pathogens.


These data allow us to construct an informed model for EGF10-13 which, in conjunction with comparative binding studies, demonstrates that EGF10 has an important role in determining Notch receptor sensitivity to Dll-4.The Notch receptor is a key component of a core metazoan signaling pathway activated by Delta/Serrate/Lag-2 ligands expressed on an adjacent cell. This results in a short-range signal with profound effects on cell-fate determination, cell proliferation, and cell death. Key to understanding receptor function is structural knowledge of the large extracellular portion of Notch which contains multiple repeats of epidermal growth factor (EGF)-like domains. Here we investigate the EGF4-13 region of human Notch1 (hN1) using a multidisciplinary approach. Ca  •The EGF4-13 region of human Notch1 contains both bent and flexible interfaces•This changes the classical view of the receptor as a rigid linear structure•Extra interaction sites of Notch with ligand may occur along its longitudinal axis•Interfaces next to ligand-binding site differentially modulate ligand interactions The structure of the extracellular domain of Notch receptor is key to understanding Notch biology. Weisshuhn et al. identify both bent and flexible regions within the receptor, changing the classical view of the receptor as a rigid linear structure extending from the cell surface. The Notch pathway plays a key role in cell-fate determination, cell proliferation, and apoptosis during development with a crucial impact on most tissues and organs . In adulDrosophila Notch) -like domains (36 in human Notch1 and a Notch) A. Liganda Notch) . The fina Notch) . This tra Notch) .trans), or on the same cell (in cis)  . Notch l(in cis) . This ca(in cis) . In addi(in cis) .trans or cis, respectively, and to explain the effects of various mutations and post-translational modifications such as O-glycosylation. The three EGF domains of the ligand-binding site all adopt a canonical EGF fold and each contains a Ca2+-binding site at its N terminus, which together with a conserved hydrophobic packing interaction results in a near-linear and rigid conformation  measurements, allow modeling of EGF4-13, which suggests a non-linear, but not jack-knifed, organization. Superposition of EGF10-13 on EGF11-13 of the recently solved Notch/Dll-4 complex indicates that further interaction sites with ligand outside the core recognition site are possible, notably at EGF10/EGF1. Comparative binding analyses, by flow cytometry, indicate that the presence of EGF10 modulates the ability of the core recognition site to interact with Dll-4, but not Jagged1 (J1), revealing greater complexity to the molecular basis of ligand specificity than previously thought.In this study, we have used nuclear magnetic resonance (NMR) spectroscopy and X-ray crystallography to investigate the structure and flexibility of the EGF4-13 region of the Notch ectodomain by analyzing a series of limited fragments with the non-Ca context A. We rep2+ affinities for Ca2+-binding (cb) EGF domains of the EGF4-13 region of human Notch1 were measured to gain insight into the rigidity of interdomain interfaces in this region. In EGF domains, a consensus sequence of D/N-x-D/N-E/Q-xm-D/N∗-xn-Y/F  is predictive for Ca2+ binding , while  domains B  when it is preceded by EGF4. In the domains for which Kd values have been measured, only the presence of a preceding domain has an influence on the Kd value. For example, EGF9 has the same Kd, within experimental error, in the EGF7-9 and EGF8-11 constructs. The Kd values for EGF domains 7, 8, 9, 11, 12, and 13 are in the range of ∼1–60 μM, and under the conditions of extracellular Ca2+ concentration (∼1.4 mM) (2+ (Kd ∼170 μM); this site will still be occupied in ∼90% of molecules. The high Ca2+ affinity observed for all the cbEGF domains , and the observation that the affinity is enhanced by at least a factor of 50 when a preceding domain is present, suggests that the cbEGF domains studied here form a packing interaction with the preceding domain leading to a rigid interdomain interface.Ca∼1.4 mM)  these si1 and C2) were determined for hN1 EGF4-7 using X-ray crystallography  , is absent.The {seconds) . Data fo1HN-15N RDCs were measured for EGF4-7, EGF7-9, EGF8-11, and EGF11-13 using C12E6/n-hexanol as the alignment medium  are a useful NMR parameter for assessing the relative orientations of protein domains in solution and for identifying interdomain dynamics on a wider range of timescales than the heteronuclear NOE . 1HN-15Nt medium  and S2   . This suGF10-11) . Thus thg domain , the absg domain , on the The interdomain tilt and twist angles obtained from X-ray structures and RDC refinement allow a model for the EGF4-13 region to be constructed . As a reA number of possible orientations will exist for EGF4-9 with respect to EGF10-13 as a result of the flexible EGF9-10 linker. A tight U-shaped structure has been reported for an EGF domain pair from the Merozoite surface protein 1 . This stThe recent X-ray structure of Notch EGF11-13 in an antiparallel complex with Dll-4 shows interactions between EGF12 of Notch and the C2 domain of Dll-4 and between EGF11 of Notch and the DSL domain of Dll-4 . Our modThe influence of the rigid interface between EGF10 and EGF11 on the binding to Dll-4 was probed using an established flow cytometry assay A Cordle. Additio2+-binding EGF domains on the shape of the EGF4-13 region of Notch. The majority of EGF domains in this region bind Ca2+, which confers the expected rigidity to the domain interface formed between the cbEGF domain and the preceding N-terminal EGF domain. Various solution NMR and X-ray structures have confirmed previously that high-affinity Ca2+ binding to the C-terminal EGF domain of a pair is predictive for a rod-like organization for tandem cbEGF domains and EGF-cbEGF pairs , which would be expected to be saturated under the physiological conditions of the extracellular milieu and insensitive to changes in Ca2+ flux at the cell membrane. However, the two non-Ca2+-binding EGF domains (EGF6 and EGF10) confer very different properties to the region. Both crystallography and NMR analysis demonstrate that the EGF5-6 interface is bent and rigid, introducing a tilt angle of ∼70°–90°, while the EGF9-10 interface is flexible. Thus, unlike the cbEGF domain, the non-Ca2+-binding EGF, when in a C-terminal position, can confer very different properties to a domain interface, which are not obviously predictable from sequence.The Utilizing the new structural information from this study, together with published data for the EGF11-13 ligand-binding region , it is pThe rigid interface formed between EGF10-11 provides new information with which to model the receptor-ligand complex. Superposition of the EGF10-13 region on the structure of the Notch/Dll-4 complex shows that, instead of facing away from the ligand, EGF10 is in close proximity, suggesting a possible contact site between Notch EGF10 and Dll-4 EGF1 . PreviouDrosophila Serrate binding (The five-residue flexible linker between EGF9 and 10 is likely to preclude folding back (via a U-shaped structure at EGF9-10) of the EGF4-9 region such that it would impede the core recognition region of EGF11-12 by direct interactions. Instead, the near-linear section of EGF6-9, upstream of the flexible linkage at EGF9-10, suggests that Notch may align with ligand along its longitudinal axis, and overall a number of weak interactions along the length of the molecule may contribute to the overall binding affinity of receptor to ligand A. EGF8 o binding . Furthercis and in trans. This would necessitate a rotation, C-terminal of the core recognition region within each protein to maintain the binding interface. The identification of a flexible cbEGF/EGF linker in this study suggests that a homologous domain pair within each molecule could facilitate the necessary rotation.Since we postulated that EGF10 was likely to make contacts with EGF1 of Dll-4 ligand, we compared the ligand binding of two fragments, EGF10-13 and EGF9-13, with that of the core recognition fragment EGF11-13. Utilizing a well-established flow cytometry assay, we demonstrated that the presence of EGF10 substantially reduced binding to Dll-4 (compared with that observed with EGF11-13). The addition of EGF9 did not further reduce binding. These data can be explained if addition of EGF10, which may have a steric clash with EGF1 of Dll-4, requires the readjustment of the positions of EGF10 and EGF1, which in turn affects the EGF11-DSL interaction site. It is notable that in the structure of the Notch/Dll-4 complex, where EGF11 is in a non-native context (not bound to EGF10), EGF11 makes many more protein:protein contacts with DSL than EGF12 does with the C2 domain. It is therefore plausible that covalent linkage of EGF10 and small rearrangements that occur on interaction with Dll-4 could disrupt some EGF11-mediated contacts within the N-terminal region of this domain B and 7C.Kd increases from 130 μM to 200 μM), indicating that not all contacts between DSL of Dll-1 and EGF11 are lost as a consequence of EGF10 addition. The importance of the EGF10-11 interface in modulating ligand binding was further shown by the introduction of a Ca2+-binding-site NG substitution in EGF11. This decouples the rigid interface between EGF10-11, which causes the steric clash with ligand, and restores binding. It is notable that the effect of EGF10 is ligand specific and observed only with the Delta family of ligands. This can be reconciled by the ligand-specific differences in amino acid sequences within the DSL domain, which are reflected in the substantially weaker binding of unmodified EGF11-13 to J1 compared with Dll-4 -based protein expression construct and a pREP4 plasmid for control of expression via the Lac Repressor. All expression vectors contained an N-terminal His6 tag for purification and either a factor Xa  or an enterokinase (EGF8-11) recognition site for later removal of the His6 tag. The tag was not cleaved for EGF7-9 and EGF9-11; the His6 tag shows no evidence of Ca2+ binding. The final protein products were analyzed by SDS-PAGE  and NOE spectroscopy (NOESY)-HSQC spectra were collected to assign the 1H-15N HSQC spectrum of EGF7-9.Resonance assignments for EGF4-7, EGF8-11, and EGF11-13 have been described previously   made with 99.9% D2O containing 150 mM NaCl ; samples were initially Ca2+ free and the Ca2+ concentration was increased by addition of CaCl2 aliquots up to saturating concentrations . Ca2+ binding was monitored using 2D 1H-1H NOESY spectra collected with a mixing time of 150 ms  were titrated with Ca2+-stock buffer  in the presence of 5,5′-Br2BAPTA (Kd of 1.6 μM under these conditions). All titrations were performed with 20–30 μM chelator and 20–30 μM protein at room temperature (approx. 23°C) using a Shimadzu UV mini 1240 spectrophotometer. Dissociation constants were calculated by least-squares fitting to the data using in-house software  with 18% w/v PEG 2000 MME. The C2 form crystallized in 0.2 M imidazole malate (pH 8.5) with 7.5% w/v PEG 10,000. The Diamond facility was used for data collection (beamline I03). Both datasets were indexed and scaled using Xia2 , 1 mM CaCling Xia2 . The string Xia2 . Structuing Xia2 . MolProbing Xia2 .Flow cytometry was carried out as described previously . BrieflyP.C.W. collected and analyzed calcium binding and NMR data. P.T. and P.W. collected and analyzed flow cytometry data. D.S. collected and refined X-ray data. S.M.L conceived and supervised the X-ray studies. P.A.H. and C.R. conceived and supervised all other aspects of the research and wrote the manuscript. All authors discussed the results and implications and commented on the manuscript at all stages.


The RhoGEF (Rho GTPase guanine-nucleotide-exchange factor) domain of AKAP-Lbc  catalyses nucleotide exchange on RhoA and is involved in the development of cardiac hypertrophy. The RhoGEF activity of AKAP-Lbc has also been implicated in cancer. We have determined the X-ray crystal structure of the complex between RhoA–GDP and the AKAP-Lbc RhoGEF [DH (Dbl-homologous)–PH (pleckstrin homology)] domain to 2.1 Å (1 Å=0.1 nm) resolution. The structure reveals important differences compared with related RhoGEF proteins such as leukaemia-associated RhoGEF. Nucleotide-exchange assays comparing the activity of the DH–PH domain to the DH domain alone showed no role for the PH domain in nucleotide exchange, which is explained by the RhoA–AKAP-Lbc structure. Comparison with a structure of the isolated AKAP-Lbc DH domain revealed a change in conformation of the N-terminal ‘GEF switch’ region upon binding to RhoA. Isothermal titration calorimetry showed that AKAP-Lbc has only micromolar affinity for RhoA, which combined with the presence of potential binding pockets for small molecules on AKAP-Lbc, raises the possibility of targeting AKAP-Lbc with GEF inhibitors. The crystal structure of the RhoGEF domain of AKAP-Lbc in complex with RhoA combined with nucleotide exchange assays explain differences to related RhoGEF proteins and allow the possibility of targeting the AKAP-Lbc RhoGEF domain with small molecules. AKAP-Lbc  is a member of the A-kinase-anchoring proteins . AKAPs aRhoGEF domains are composed of a DH (Dbl-homologous) domain followed by a PH (pleckstrin homology) domain. This tandem DH–PH domain is a conserved unit in most RhoGEF proteins . The DH AKAP-Lbc has a RhoGEF DH–PH domain between residues 1972 and 2342 A. Its PHAKAP-Lbc has been shown to have a role in the development of cardiac hypertrophy ,7,27,28.6-tags and TEV (tobacco etch virus) protease tag cleavage sites (extension MHHHHHHSSGVDLGTENLYFQ*SM). AKAP13 DH domain point mutant constructs were created by PCR using the His6-tag DH–PH domain expression construct as a template. All mutations were verified by DNA sequencing.DNA for RhoA (gi|10835049) or AKAP13  was PCR amplified and subcloned into an in-house pET-based vector pNIC28-Bsa4  using liEscherichia coli BL21(DE3) competent cells containing the pRARE2 plasmid from the commercial Rosetta strain, and the transformants used to inoculate 50 ml of LB medium containing 50 μg/ml kanamycin and 34 μg/ml chloramphenicol. These cultures were incubated overnight at 37°C. These cultures were used to inoculate larger cultures of TB medium (RhoA) or LB medium (AKAP13) with 40 μg/ml kanamycin and grown at 37°C until an D600 of 1.0 (RhoA) or 0.4–0.5 (AKAP13) was reached. The temperature was then reduced to 20°C and the cultures induced with 0.5 mM IPTG. Expression was continued overnight. The cells were harvested by centrifugation, resuspended in binding buffer  and frozen until further use.RhoA and AKAP13 DH–PH constructs were transformed into 2+-Sepharose resin . After washing, the protein was eluted with 25 ml of binding buffer containing 250 mM imidazole. The His6-tags were removed using TEV protease. AKAP13 was then mixed in equimolar ratio with RhoA, and the complex was concentrated and injected on to a S75 16/60 gel filtration column pre-equilibrated into GF buffer . After passing through a gravity column of 5 ml of Ni2+-Sepharose to remove impurities, the RhoA–AKAP13 complex was concentrated to 5.1 mg/ml. Protein concentrations were measured by UV absorbance, using the calculated molecular masses and estimated molar absorption coefficients, using a NanoDrop spectrophotometer (Thermo Scientific). The constructs of the AKAP13 DH domain and the DH domain point mutations were used to express and purify protein following a similar protocol.For purification, the cells were thawed and lysed by sonication on ice. PEI (polyethyleneimine) was added to a final concentration of 0.15% and the cell debris and precipitated DNA were spun down. RhoA and AKAP13 were each purified by passing the supernatants through a column of 5 ml of NiRhoA–AKAP13 domain crystals grew by vapour diffusion at 4°C from a mixture of 50 nl of protein and 100 nl of a well solution containing 0.2 M ammonium sulfate, 0.1 M Bis-Tris, pH 5.5, and 25% (w/v) PEG 3350. Crystals were equilibrated into reservoir solution plus 25% ethylene glycol before freezing in liquid nitrogen. Data were collected at 100 K at the Diamond Synchrotron beamline I02. Data collection statistics can be found in DH domain crystals grew under identical conditions  and were equilibrated into reservoir solution plus 20% ethylene glycol before freezing in liquid nitrogen. Data were collected at 100 K at the Diamond Synchrotron beamline I03.The diffraction data were indexed and integrated using MOSFLM  and scalMeasurements were made on a MicroCal iTC200  at 15°C. For measurements in the presence of GDP, all proteins were dialysed overnight into a buffer consisting of GF buffer with the addition of 50 μM GDP. For measurements in the absence of GDP, RhoA was incubated overnight with 5 mM ETDA and 6 units/ml alkaline phosphatase followed by gel filtration in GF buffer, and finally concentrated as before and dialysed overnight in GF buffer. For each measurement, the syringe was loaded with 0.6 mM RhoA (in the absence or presence of GDP) and 20×2 μl injections were made into the cell, which was filled with 0.04 mM of either AKAP-Lbc DH domain or AKAP-Lbc DH–PH domain. Data were analysed using MicroCal and Origin software. The results after fitting to a single-site model are shown in N-methylanthraniloyl)-GDP (Life Technologies) for 15 min. The protein was then passed through a PD-10 column pre-equilibrated in GF buffer to remove excess MANT-GDP. Guanine-nucleotide-exchange assays were conducted in 20 μl aliquots in black 384-well low-volume plates (Greiner). The progress of the nucleotide exchange was monitored by fluorescence on a PheraStar plate reader (BMG Labtech) with excitation at 360 nm and detection at 440 nm. Exchange reactions were measured in GF buffer containing 10 mM MgCl2, with 0.5 μM RhoA–MANT-GDP and 50 μM unlabelled GMP-PNP, and in the presence or absence of varying concentrations of DH or DH–PH domain protein.RhoA was incubated with alkaline phosphatase to remove bound nucleotide and then purified by gel filtration under the same conditions as above. The nucleotide-free RhoA was incubated with MANT . All protein chains except the chain of interest were deleted. Hydrogen atoms were added and missing side chains were rebuilt using Prime (Schrödinger). Druggability scores were calculated using SiteMap (Schrödinger), using the default settings as implemented in Maestro, using the OPLS_2005 force field definition. For calculation of SiteMap scores from bromodomains, the conserved water molecules that form part of the acetyl-lysine binding pocket were retained in the structure used in the analysis.Bacterial overexpression constructs were prepared for RhoA (residues 1–184) and the DH–PH domain of AKAP-Lbc  . After iR-factor of 23.8%. Residues 3–181 of RhoA and residues 1972–2340 of AKAP-Lbc (including the DH and PH domains) were resolved in the electron density.Crystals of the RhoA–DH–PH domain complex were obtained in the presence of GDP which allowed the structure to be determined by X-ray diffraction to 2.1 Å (1 Å=0.1 nm) resolution . There w2  the PH domain contributes to GEF activity. The AKAP-Lbc PH domain made no contacts with RhoA in the crystal structure , the other residues are entirely non-conserved. For example, the LARG PH domain residues Tyr1039 and Glu1023 are replaced with Gln2255 and the shorter Asp2239 in AKAP-Lbc. The result is that the binding arrangement is quite different in AKAP-Lbc and results in an entirely straight long α-helix (αI) with four turns of this α-helix separating the residues interacting with switch II from the residues interacting with the PH domain . This helix forms crucial binding interactions with the GTPase switch II loop. Crucial residues for this stabilization are not conserved in AKAP-Lbc. In LARG, RhoA Argd Asn983 C and 2D.us of αI B. FurtheH domain D and 2E.H domain A and 2B.To investigate whether for our constructs the AKAP-Lbc PH domain contributes to catalysis of nucleotide exchange on RhoA we cloned an expression construct containing just the DH domain  for comparison with the combined DH–PH domain . We perfKd) within experimental error of ~20 μM for RhoA against either the DH–PH domain or the DH domain alone, in the presence or absence of GDP  to alanine or aspartate reduced GEF activity to 15–20% of wild-type [34.The N-terminus of some DH domains contains a ‘GEF switch’ region , a shortild-type . Further34 packs against the conserved Glu2001 (LARG Glu790), whereas forming a hydrogen bond to the also conserved Glu2005 (LARG Glu794). The tryptophan appears to orient the backbone of the GEF switch region so that Glu2001 can form hydrogen bonds to two backbone nitrogens  that were identified. By comparison with a well-known druggable protein with a larger binding side, using the same methodology the protein kinase Aurora A (PDB code 1MQ4) has a Dscore of 0.96 with a pocket volume of 591 Å3. Bromodomains for which small molecule ligands have been identified span a range of Dscores from >1.0 to 0.62 [3. In conclusion, AKAP-Lbc appears at least as druggable as bromodomains for which many ligands have already been identified [We analysed the two potential binding pockets for small molecules using SiteMap (Schrödinger) which takes into account the volume of the pocket, degree of enclosure and degree of hydrophobicity. AKAP-Lbc had SiteMap Dscores of 0.74 and 0.83 respectively for the switch I and switch II binding pockets, with pocket volumes of 133 and 145 Å to 0.62 . Within  to 0.62 . For comentified .Finally, the analysis of the sequence and structural reasons for the lack of involvement of the AKAP-Lbc PH domain in GEF activity may allow useful predictions to be made for other RhoGEFs, of which there are approximately 72 human members having the DH–PH domain architecture .


This work highlights that charged domain walls, far from being exotic, unstable structures, as might have been assumed previously, can be robust, stable easily-controlled features in ferroelectric thin films.Charged domain walls in ferroelectric materials are of high interest due to their potential use in nanoelectronic devices. While previous approaches have utilized complex scanning probe techniques or frustrative poling here we show the creation of charged domain walls in ferroelectric thin films during simple polarization switching using either a conductive probe tip or patterned top electrodes. We demonstrate that ferroelectric switching is accompanied - without exception - by the appearance of charged domain walls and that these walls can be displaced and erased reliably. We ascertain from a combination of scanning probe microscopy, transmission electron microscopy and phase field simulations that creation of charged domain walls is a by-product of, and as such is always coupled to, ferroelectric switching. This is due to the (110) orientation of the tetragonal TiO Domain walls in ferroelectric materials can exhibit unique properties, different from the bulk material, due to the local change in strain, charge or symmetry1345689101314The creation and control of CDWs remains a challenge. Traditionally, CDWs are assumed to be energetically highly unfavorable and as such suitably difficult to create. It has been shown recently that under special circumstances, involving polarization switching, CDWs can be created but these techniques tend to be complex and time consuming14163 (PST) thin films for the demonstration of the concept. PST is a practical choice due to the good lattice match with SrTiO3 183 films. Like the case of tetragonal BTO single crystal3 21We use epitaxial (110) oriented TiOThe topography of a PST (110) thin film is shown in irection  is highl2 rectangular area. Whereas the vertical phase  plane to obtain a perpendicular section through the domain walls. 3. The details in switching process may differ between the two materials, but the qualitative features of side domain nucleation is clearly robust which we tested by variation of simulation parameters such as temperature and electrostriction coefficients. A lateral electric field component, EL, at the electrode edges induces nucleation of the secondary domain which inevitably faces the as-grown state in a head-to-head arrangement. The simulation assumes purely dielectric material and therefore cannot result in free carrier compensated CDWs but still demonstrates the principle of the in-plane switching process. The lateral electric field, which must be present to create and displace the observed CDWs, will always appear in the vicinity of a PFM tip or electrode edge. However, as this field is highly inhomogeneous, it would rapidly decrease in the lateral direction and is usually negligible around distances corresponding to the film thickness. As the observed secondary domain is much larger (~500 nm) than the film thickness (70 nm) this excludes the field inhomogeneity at the PFM tip or the electrode edges as the only contribution to the CDW formation. In fact the secondary domain propagates to a larger distance only if a high resistivity bottom electrode is taken into account, where slowly redistributing electric charges create an in-plane potential drop during switching, as is the case for the phase field simulations presented here (ted here .3 (150 μΩ cm)EL, as illustrated in The mechanism demonstrated both experimentally and by the simulation can be understood as follows: Switching an area of the as-grown single domain film by 180° flips the polarization downwards thereby pushing the positive polarization charge to the bottom electrode. The switched polarization charge needs to be compensated by charge carriers transported through the LSMO electrode. However, the resistivity of high quality (001) plane LSMO is reported to be as large as 1000 μΩ cm at room temperatureThe understanding of the mechanism involved in the creation of the secondary domain offers us the possibility to control its behavior. The strict connection of the CDW to the switched area was confirmed by PFM on the bare surface, causing the CDW to move or disappear if the switched area is changed or removed, respectively see . In orde313 The most intriguing property of CDWs presented in several previously published works561314We have shown by the combination of vertical and lateral PFM data that switching (110) oriented epitaxial tetragonal ferroelectric thin films results in the creation of a secondary domain accompanied by a charged domain wall. This is attributed to the inhomogeneity of the electric field at sharp electrode edges in combination with the low conductivity of the bottom electrode. Both effects together cause the build-up of a lateral electric field able to switch and propagate the in-plane polarization component of the weakly tetragonal material, hence forming a charged domain wall. Furthermore, our investigations evidenced that the creation and dimension of the charged domain wall are determined by the characteristics of the applied voltage during the 180° switching of the film. Combining this with a low conductivity top electrode allows for a precise control of the position of the switched area and simultaneously of the charged domain wall. Moreover, the presented system is based on STO as a substrate material which can be grown as a buffer layer on Si and therefore might allow the realization of these structures on Si platform as well. These results represent a further step in the ongoing effort to precisely tune domain structures as building blocks of envisioned ‘nanoelectronics’.2, conditions for growth of the bottom electrode La0.67Sr0.33MnO3 (LSMO) layer and the ferroelectric Pb0.6Sr0.4TiO3 layer were TS = 625 °C, pO2 = 0.14 mbar, f = 2 Hz and TS = 575 °C, pO2 = 0.25 mbar, f = 3 Hz, respectively.Thin films were fabricated by pulsed laser deposition on (110) plane STO substrates  after etching in buffered HF and annealing at 900 °C in air. Using a laser fluence of ~1 J/cmPFM was performed on an Asylum Research Cypher with Ti/Ir coated ASYELEC-01 silicon probes with a force constant of 2 N/m.Focused ion beam (FIB) cutting was conducted with a ZEISS NVision using a 30 kV acceleration voltage and beam current from 700 pA down to 40 pA after having deposited a protective carbon coating of 1 μm.Transmission electron microscopy (TEM) was carried out with a Tecnai Osiris instrument using an acceleration voltage of 200 kV.3 from ref. 19 cm−3 and mobility was varied in order to mimic the effect of the limited conductivity. When the mobility is <10−24 cm2/(Vs) (note that mobility must be considered relatively to the simulation time) the secondary domain always propagates to a distance larger than the film thickness. Zero potential and constant electrode charge is defined 1 μm from the switching event. Note that the 50–100 nm long secondary domain appears always even in the case with an ideal bottom electrode, but it retracts and disappears after the switching event. In reality it could be pinned and survive, i.e. the secondary domain could be possibly observed even when using high quality bottom electrodes.The two-dimensional phase field model .


Drosophila species spanning ~45 million years of evolution. Remarkably, we uncovered that a significant fraction of all C2H2-ZF 1-to-1 orthologs in flies exhibit variations that can affect their DNA-binding specificities. In addition to loss and recruitment of C2H2-ZF domains, we found diverging DNA-contacting residues in ~44% of domains shared between D. melanogaster and the other fly species. These diverging DNA-contacting residues, found in ~70% of the D. melanogaster C2H2-ZF genes in our analysis and corresponding to ~26% of all annotated D. melanogaster TFs, show evidence of functional constraint: they tend to be conserved across phylogenetic clades and evolve slower than other diverging residues. These same variations were rarely found as polymorphisms within a population of D. melanogaster flies, indicating their rapid fixation. The predicted specificities of these dynamic domains gradually change across phylogenetic distances, suggesting stepwise evolutionary trajectories for TF divergence. Further, whereas proteins with conserved C2H2-ZF domains are enriched in developmental functions, those with varying domains exhibit no functional enrichments. Our work suggests that a subset of highly dynamic and largely unstudied TFs are a likely source of regulatory variation in Drosophila and other metazoans.Differences in transcriptional regulatory networks underlie much of the phenotypic variation observed across organisms. Changes to cis-regulatory elements are widely believed to be the predominant means by which regulatory networks evolve, yet examples of regulatory network divergence due to transcription factor (TF) variation have also been observed. To systematically ascertain the extent to which TFs contribute to regulatory divergence, we analyzed the evolution of the largest class of metazoan TFs, Cys2-His2 zinc finger (C2H2-ZF) TFs, across 12  cis binding sites, for which there are numerous known examples, as well as via binding specificity variation in transcription factors (TFs), a less studied phenomenon that has been observed primarily in multi-gene families. Though large-scale experimental studies ascertaining the extent to which TFs contribute to regulatory network variation across organisms are lacking and would be time-consuming, computational methods can begin to address this challenge. Here, we present a systematic, large-scale analysis of DNA-binding specificity evolution in TF orthologs by computationally leveraging specific features of Cys2-His2 zinc finger proteins, the largest class of TFs in animals and major components of their regulatory programs. We find not only that divergence of DNA-binding residues in 1-to-1 orthologous C2H2-ZFs is pervasive but also that these changes show evidence of functional constraint and occur in a gradual, evolutionarily viable manner. We conclude that the diversification of orthologous TFs has most likely played a major and largely unstudied role in gene regulatory network evolution in metazoans.The phenotypic differences observed between closely related organisms are thought to be due largely to changes in regulatory networks. Changes in transcriptional networks can occur via mutations in  The predominant view is that regulatory evolution results mainly from the gain and loss of binding sites in cis-regulatory regions because incremental, evolutionarily viable steps can occur , where Ψ is a large, hydrophobic amino acid. Hits that did not match this expression and thus no longer have the structure necessary to bind DNA are considered degenerate, and are not identified as domains. HMMER hits below the corresponding bitscore thresholds but which matched this regular expression were retained in these proteins because C2H2-ZFs are known to occur in tandem, and therefore we are more confident about all C2H2-ZF domains which co-occur with at least one high scoring domain. All C2H2-ZF domains can be found in C2H2-ZF domains themselves were identified from these proteins as any HMMER hit matching the regular expression CXWhere possible, the longest protein splice form per gene containing all C2H2-ZF domains was selected to represent each gene. If no single protein isoform contained all domains present in the gene, a minimal set of proteins which together include all unique C2H2-ZF domains was selected to represent the gene.D. melanogaster was downloaded from FlyBase and from the Andolfatto Lab build of D. simulans [D. melanogaster poly-ZF gene were selected. Of 13273 total original orthogroups, 272 had at least one D. melanogaster poly-ZF gene.A list of pairwise orthologs to simulans , and ortD. melanogaster poly-ZF orthogroups with sequences missing from one or more species were augmented according to the 15 insect whole genome alignment (WGA) from the UCSC Genome Browser [ Browser . A missi Browser . Where pD. melanogaster but more than one gene from at least one other species) orthogroups were truncated such that only those species with a single gene in the original orthogroup were included in the new orthogroup. In this manner, our analysis was restricted to variation in 1-to-1 orthologs.All 1-to-many . For cases of duplicate binding motifs, we preferentially selected the PWM generated from SOLEXA sequencing over SANGER sequencing, and the longer PWM over the shorter. To exclude binding motifs that are non-specific, we discarded PWMs with fewer than six columns exhibiting information content (IC) > 0.5. To exclude binding motifs of low complexity (e.g. poly-A motifs), we discarded PWMs where > 80% of columns with IC > 0.5 correspond to the same consensus nucleotide, where consensus is defined as the most common nucleotide in a position, or ‘N’ in the case of a tie. Slight variations to these thresholds do not affect our findings. To exclude TFs which cannot be compared across species, we discarded binding motifs corresponding to TFs with 1-to-1 orthologs in fewer than two non-reference species. This filtering process resulted in 64 binding specificity motifs for 52 genes. These motifs were properly formatted for use by fimo with jaspar2meme, available from the MEME suite [We initially obtained binding specificity motifs, represented as PWMs, for 62 ME suite .D. melanogaster and their alignments to orthologous regions across the other 11 fly species were obtained from the UCSC Genome Browser 15-fly promoter region alignments [The 2000 basepair regions upstream of all genes in ignments . For eacD. melanogaster, we required that each predicted binding site in D melanogaster be found within 25 basepairs in the UCSC genome alignments to binding sites in D. sechellia, D. simulans, D. yakuba, and D. erecta; this allows detection of conserved sites while allowing for slight variations in the genomes and/or slight error in the genome alignment [D. melanogaster binding sites to those found within 15 or 50 basepairs to binding sites in these other four species did not affect results nor significance. Considering alternate definitions of confident binding sites by restricting D. melanogaster binding sites to those found within 25 basepairs in only D. sechellia, only D. sechellia and D. simulans, or only D. sechellia, D. simulans, and D. yakuba also did not affect results nor significance  Distribution of linker region  lengths with a sequence logo of the most common 7 amino acids long linker shown.(A) Distribution of the lengths of all identified C2H2-ZF domains across all species with a sequence logo of domains of length 21 amino acids, the most common domain length, shown. (B) The distribution of number of domains per (TIF)Click here for additional data file.S2 FigD. melanogaster domain in one or more of the four specificity-determining positions -1, 2, 3, or 6. Divergence is shown according to (A) size of tandem array in which the domain appears, (B) average length of the linker(s) bordering the domain, and (C) position  of the domain. A domain may only fall into one of these three position categories; paired domains are labeled as beginning and end with no middle.Overall and by-species divergence of aligned, canonically linked domains. A domain is considered diverged if it differs from its corresponding aligned (TIF)Click here for additional data file.S3 FigD. melanogaster and give the folded site frequency spectra of those sites in D. melanogaster. Specifically, we show the proportion of polymorphic sites, categorized by amino acid residue type, where a minor allele was present in 1 through 69 individuals from a population of 139 D. melanogaster flies [D. melanogaster population and also diverged in a given species with respect to D. melanogaster are considered. Due to the low number of sites where 7 through 69 individuals exhibit the minor allele, these sites are aggregated under the “7+” label in x-axis. The four amino acid residue types are DNA-contacting residues (blue), background residues outside of C2H2-ZF domains (black), non-helical, non-binding residues within C2H2-ZF domains (red), and linker regions between adjacent canonically-linked domains (gray). The blue and black proportions are shown as bars for visual effect; we see that the minor allele frequencies for DNA-contacting residues are heavily skewed toward 0 in comparison to those for background residues. Red and gray residue types are shown as diamonds.For each species, we determine amino acid residue sites that diverged with respect to er flies . Only si(TIF)Click here for additional data file.S4 FigDrosophila fly species. Blue vertical lines at 0, 0.25, 0.5, and 0.75 show the thresholds used for selecting confident predictions.Distribution of the PCCs between the SVM predicted binding specificity (PWM) and the ML predicted (red) and RF predicted (blue) binding specificities for all aligned domains from all (TIF)Click here for additional data file.S5 Figmelanogaster domain, we compared its SVM predicted specificity to the predicted specificity of its orthologous aligned D. melanogaster domain by calculating a PCC at each position b1 through b4. (A) Distribution of divergent domains per species by minimum PCC at any one position b1 through b4 from the aligned D. melanogaster domain. This shows that most divergent domains had a corresponding divergent binding specificity from D. melanogaster in at least one predicted position. (B) Distribution of divergent domains per species by sum of PCCs across positions b1 through b4 from the aligned D. melanogaster domain. All domains with a sum of PCCs < 2.0 must have had a divergent binding specificity in more than one predicted position from D. melanogaster.For each divergent non-(TIF)Click here for additional data file.S6 FigD. melanogaster as confident if it is found to be conserved (Methods M4) in D. sechellia (column 1), both D. sechellia and D. simulans (column 2), or D. sechellia, D. simulans, and D. yakuba (column 3). For each PWM listed in D. melanogaster promoter regions containing a confident binding site for that PWM that also contain a binding site in each of the other species Click here for additional data file.S7 Fig(A) Percent of conserved (red) and diverged (blue) poly-ZF genes present in each tissue. FlyAtlas reports each gene as present or absent in each tissue separately across four replicates based on raw expression values ; we cons(TIF)Click here for additional data file.S1 Tablep-value comparing the -1, 2, 3, 6 residues to BG residues using a binomial test in major columns 1 and 3 and Wilcoxon test in major column 2. In Major Column 1, residues are only included from each species where there is a non-gapped residue of the same type  in an ortholog of its partner species. In Major Column 2, only complete  columns are included, as measurements of evolutionary rate using less complete multiple alignments could not be compared. In Major Column 3, all divergent residues, regardless of alignment to any species apart from the reference D. melanogaster are included.Counts of divergent residues and significance between binding residues and background per non-reference species used for the three calculations of functional importance previously described: (Major Column 1) Conservation Across Clades, (Major Column 2) Evolutionary Rate, and (Major Column 3) Rapid Fixation. The first four subcolumns within each major column correspond to the number of divergent residues in specificity-conferring positions -1, 2, 3, and 6 in C2H2-ZF domains , background divergent residues outside of arrays of canonically linked domains (BG), residues outside of the alpha-helix within C2H2-ZF domains (C2H2), and linker regions between adjacent canonically linked domains (linker). The fifth subcolumn in each major column is the exact (XLS)Click here for additional data file.S2 TablePercent of columns from SVM-predicted binding specificities (represented as PWMs) that are “correct”  when compared to the corresponding experimentally-derived gold standard specificity columns . Rows co(XLS)Click here for additional data file.S3 TableD. melanogaster and non-reference fly species. Confidence is measured by comparing SVM predicted specificities to those produced by ML and RF methods using PCC. The domains included at each confidence threshold are those where the SVM predicted specificities were within a particular PCC cutoff when compared to either the ML or RF predicted specificities. (Row 1) Total number of aligned, ungapped domains across all 12 fly species. (Row 2) Total number of ungapped D. melanogaster domains that have 1-to-1 orthologs in at least 1 other fly and exhibit a divergent binding residue in at least 1 other fly. (Row 3) Total number of aligned orthologous domains across D. melanogaster and at least 1 other fly species where the Spearman correlations relating the phylogenetic distance to D. melanogaster for each non-reference fly domain to the change in predicted specificity from the aligned D. melanogaster domain  is < 0. (Row 4) Total number of aligned orthologous domains where the Spearman correlations, as in Row 3, are < −0.5.Change in binding specificity for aligned domains between the reference (XLS)Click here for additional data file.S4 TableDrosophila conserved and diverged poly-ZF genes as generated by GO Term Finder (go.princeton.edu).GO Term Enrichment for (XLS)Click here for additional data file.S5 TableDrosophila species (Methods M1). Columns are as follows: Drosophila species, genome build, FlyBase protein ID, FlyBase gene ID, domain position within protein, total number of C2H2-ZF domains in protein, Pfam ID of HMM that matched this domain, e-value of HMM match as computed by HMMER, bit score of HMM match as computed by HMMER, index of domain position -1 within protein sequence, index of domain position 7 within protein sequence, protein subsequence of positions -1 through 7 of domain, presence of an alignment gap between the HMM and the protein sequence between positions -1 and 7 of the domain, index of the starting cysteine of the domain in the protein sequence, index of the ending cysteine or histidine of the domain in the protein sequence, and the protein subsequence containing the entire C2H2-ZF domain.C2H2-ZF domains found using HMMER in each protein in each (XLS)Click here for additional data file.S6 TableDrosophila 1-to-1 orthologs (Methods M2 and M3). Columns are as follows: OrthoDB7 group ID, FlyBase protein ID, FlyBase gene ID, Drosophila species, UniProt ID, genome build, gene location , gene start position on chromosome or scaffold, gene end position on chromosome or scaffold, gene coding strand on chromosome or scaffold (“+” is the forward strand and “-” is the reverse strand).Augmented and reconciled groups of (XLS)Click here for additional data file.S1 Text(TXT)Click here for additional data file.


A domain decomposition technique is proposed which is capable of properly connecting arbitrary non-conforming interfaces. The strategy essentially consists in considering a fictitious zero-width interface between the non-matching meshes which is discretized using a Delaunay triangulation. Continuity is satisfied across domains through normal and tangential stresses provided by the discretized interface and inserted in the formulation in the form of Lagrange multipliers. The final structure of the global system of equations resembles the dual assembly of substructures where the Lagrange multipliers are employed to nullify the gap between domains. A new approach to handle floating subdomains is outlined which can be implemented without significantly altering the structure of standard industrial finite element codes. The effectiveness of the developed algorithm is demonstrated through a patch test example and a number of tests that highlight the accuracy of the methodology and independence of the results with respect to the framework parameters. Considering its high degree of flexibility and non-intrusive character, the proposed domain decomposition framework is regarded as an attractive alternative to other established techniques such as the mortar approach. Modern engineering applications require sophisticated simulation techniques which deal with increasing complexity and refinement of the computational models. Consequently, detailed finite element discretizations are commonly used in nowadays structural analysis and a number of practical situations are emerging in which special techniques are indispensable to handle non-matching discretizations. In this introduction we focus on engineering applications and computational techniques concerning the assembly and resolution of models involving non-overlapping meshes.Typical scenarios arise when independent mesh discretizations are applied to different parts of a structure and when large models are divided and distributed among different working teams. A common situation is encountered when particular structural components are reused in evolving designs such as the wings among diverse aircraft models with changing fuselages. The meshes of the structural components are most likely non-matching and need to be assembled along common edges using special techniques that account for the non-conforming interfaces , 35.The field of contact mechanics  has signAn emerging set of techniques intimately related with computational material design are the so-called multiscale and multiresolution methods , 17, 27.Most of the above mentioned applications involve complex models which upon discretization, e.g. using finite elements, lead to large systems of equations. It is then not surprising that most of the existing methodologies to connect different meshes are frequently encountered in domain decomposition techniques . These tIn most of the domain decomposition applications the geometrical compatibility of the interface g meshes  meaning mentclass2pt{minimg meshes , 51. DomStrong coupling constraints refer essentially to collocation techniques where one constraint is assigned to each degree of freedom (DOF) while weak coupling techniques refer to constraints enforced in an integral or average sense along portions of the interface surface assigning one constraint per group of DOFs belonging to the interface portion. In the contact domain literature these techniques are often referred to as node-to-segment techniques and segment-to-segment techniques, respectively.h or p refinement of the coarse mesh at the interface for the strong coupling case. For this reason, weak coupling techniques are preferred in the context of a general non-conforming interface since they relax the constraint such that stiffening and locking effects do not occur. Mortar methods and their formulation in terms of finite elements constitute the most general technique for non-conforming interfaces in which geometrical incompatibilities can be handled [Generally, a reference displacement field entclass1pt{minima handled . The mosinf-sup condition) [The enforcement of constraints at a non-conforming interface is typically done with the introduction of Lagrange multipliers . Basicalndition)  in orderndition)  for an ondition)  which candition) . In ordendition) . Althougndition) , 38 and a priori satisfy the constant stress patch condition. The technique can be viewed as a general and optimal node-to-segment approach applied to the connection frame but still arbitrary highly irregular grids and geometrically incompatible interfaces are not addressed.Domain decomposition frameworks typically found in literature that account for non-conforming interfaces are based on the introduction of Lagrange multipliers to weakly enforce the compatibility constraints. This is the case for the mortar approach  which isIn contrast with the above mentioned techniques we propose a general and flexible methodology to account for the most complex interface situations, i.e. geometrically incompatible and arbitrary non-conforming. The main idea in the domain interface method (DIM) is to explicitly discretize the interface through a Delaunay triangulation. In all previously introduced techniques one slave node or segment belonging to a domain interface was somehow projected on the other domain interface or on an auxiliary one. Therefore, the interface constraints were formulated in a domain which is one dimension lower than the subdivided domains. In the DIM, the interface constraints are formulated on an intermediate interface of the same dimension as the adjacent decomposed domains cf. Fig. . ConsequIn this section the necessary geometrical aspects of the methodology are introduced and strong and weak forms of the problem are outlined. The solvability of the resulting system is discussed in terms of its stabilization and possible resolution choices including a parallel scheme. The main idea behind the DIM method concerns an explicit meshing of the interface between domains and is inspired in the methodology introduced in , 38 for s and q. Discretizations of the two bodies, e.g. using finite elements (FE), leads to a number of Consider the structure assembly depicted in Fig. k. The result will be independent on the chosen magnitude k but in our analyses The interface generation cf. Fig.  starts wD using triangular linear elements Note that, upon discretization of the domain interface r method , where oD at time n.Consider the assembly of two non-overlapping domains cf. Fig.  undergoiIt is important to note that fined in .As depicted in Fig. n for a given point p) and not only defined at the interface nodes as other methodologies would consider. For future use into the variational statement it is convenient to express the gap in terms of the displacement field and, to this end, a Taylor series expansion of The initial normal gap cf. Fig.  is definduced in , 38 is nThe expressions of the gap match the ones obtained in node-to-segment techniques  when \dor et al. , the expIn order to formulate the variational principle in Sect. It is important to note that the gap intensity results singular when a perfect connection is fulfilled at the previous configuration, i.e. entclass1pt{miniman and the normal vector Inserting  in  16)16) the fcf. Fig. . Displaccf. Fig. .Fig. 5LaFor the case of tied contact within the present domain decompositon framework there is no need for a splitting between normal and tangential contributions. However, this splitting is introduced for the sake of completeness presenting a methodology that serves as a basis to tackle, if needed, more complex phenomena in which a different treatment can be considered for the tangential and normal interface components. Such scenarios may involve, for instance, sliding between domains. Additionally, the imposition of particular boundary conditions utilizing the Lagrange multiplier framework can be considered as well in which the tangential component is treated differently due to friction or sliding. Specific cases involving fluid structure interaction could in this manner be treated as well. The case of normal tying along an interface segment between fully tied limit corners has been studied already within a multiscale Domain Decomposition framework  to avoidn, The strong form of the equilibrium problem at domain Note that the compatibility constraints are enforced to nullify the normal cated in . The gaprding to . In addiThe weak form of the problem stated in –28 is exloped in , 38 the Finally, the variational statements of the constraint equationsThe equilibrium equation in  and impoa denotes the discrete nodes corresponding to the displacement interpolation. In a similar fashion, the displacements D are discretized as:b stands for the the discrete nodes corresponding to the Lagrange multipliers interpolation using the shape functions Consider a Galerkin-based discretization in which the displacement solution field and its variations are interpolated using the shape functions It should be noted that a piece-wise constant interpolation of the Lagrange multipliers might not lead to optimal spatial convergence rates. We have not observed any critical convergence behaviour in any of our simulations. However, it is observed in our analyses that the theoretical convergence rates might not be fully recovered due to use of piece-wise constant Lagrange multipliers. A more theoretical and practical study regarding convergence rates with respect to the choice of the Lagrange multiplier space is out of the scope of this work and could be considered as a future research topic for a more mathematically oriented contribution.The FE approximation of the virtual work expression in  can be wFollowing an analogous procedure for the variational expression of the interface constraints , 3555\doL stands for the base-side length of the interface domain element in the previous configuration   \documen methods , 45, thes method . The rigThe mechanical work developed by the domain boundary forces tituting  in the stituting 85\documeThe local problems in  are solvmentclasspt{minimator   91) is gcf. Fig. . In ordeTo this end, we consider the stabilization expressions , 64. Theual Eqs. , 68 can tituting , 98 we ocf. Fig.  correspowidth in  is kept width in –80.Equations , 114 areelations , 114 canIn all our computations we considered all interface patches ected in  and, theThe linearized set of equations in  obtainedmentclasspt{minimaent}Ω(s) .Assuming a fix domain decomposition and a given Delaunay interface discretization, the iterative scheme for the non-linear DIM framework is summarized in Box 1.In the following we present a number of academic examples which highlight the accuracy and convergence properties of the framework. Attention is focused on the continuity of the solution at the interface, the convergence rate upon mesh refinement and a qualitative comparison of the advantages and eventual pitfalls against existing formulations. Infinitesimal strain theory is utilized in all examples except from the one reported in Sect. cf. Eqs. –68 is seThe so-called ‘patch test’ is specially selected to verify the correct transference of information throughout the interface. A compression analysis is performed on a two-dimensional homogeneous quadrilateral specimen. Plane strain conditions are assumed and a linear elastic constitutive law is considered with Young’s modulus The quadrilateral specimen is submitted to an homogeneous strain state whereDisplacement contours for both discretizations are shown in Fig. Since the maximum relative error is order c used to overcome the appearance of RBMs  is monitored and compared to the one obtained with a reference monolithic approach considering a similar spatial discretization. As it can be observed in the contour plots in Fig. The kernel of the proposed DIM to be used in domain decomposition methods and presented in this contribution resides in an explicit discretization of the interface by means of a zero-thickness Delaunay triangulation. This is accomplished through a fictitious contraction of the subdomains at the interface which allows for a proper discretization between the shrunk domain boundaries. The fictitious contraction has no impact on the solution of the problem since all calculations are performed using the original coordinates. Moreover, it is shown that the integrals over the zero-thickness interface are bounded despite the fact that the integrand is not bounded. The method is grounded in the so called Nitsche methods in which a stabilization term is added at the constraint equations. In this manner, zero diagonal terms are not present at the global system and instabilities are avoided if the LBB condition is not fulfilled by the chosen discretization. This process is viewed as a consistent penalty method since the stabilization term vanishes with progressive mesh refinement and the penalty factor can be made significantly small without affecting the results.The methodology is inherited from the field of contact mechanics and, for this reason, is regarded as more general than existing domain decomposition strategies since there is no need for a fixed interface geometry that needs to be shared by the decomposed domains at both sides of the interface. This is for instance the case of some dual domain decomposition techniques in which the limit DOFs at the interface need to be common in both adjacent domain discretizations. Moreover, the generation of interface patches is independent of the choice of slave and master sides in contrast with early mortar methods and, for this reason, the methodology is regarded less prone to errors related with such choice. More evolved mortar methodologies are able to automatically handle these situations by considering, for instance, an extra interface surface from which a particular distribution of DOFs serves to construct an optimal set of interface constraints between adjacent meshes. However, such an intermediate surface involves calculations over extra DOFs which could increase the computational cost and complexity of the approach.A new non-intrusive strategy to handle floating domains is outlined which adds an extra stabilization term to the energy functional with contributions of all adjacent interface patches. This avoids the calculation of a pseudo-inverse at floating domains and does not destroy the band structure of the global system. For this reason, it does not spoil a possible parallel solution as done with existing dual domain decomposition methods.The DIM method passes the patch test also for the case of floating subdomains providing continuity of the stress field across the interface which indicates that all new ingredients do not affect the accuracy of the solution when compared to other established techniques. Remarkable continuity of the displacement field across the interface is shown in all reported experiments. A comparable accuracy degree has been observed with independence of the shape of the interfaces. In addition, good convergence rates are reached upon mesh refinement similar to other accurate techniques for non-conforming interfaces although theoretical convergence rates could not be obtained exactly due to the piece-wise constant interpolation of the Lagrange multipliers.The algorithmic treatment of the subdomains allows for a parallel solution scheme analogous to well established techniques such as dual domain decomposition techniques. In this manner the local factorizations can be tackled by direct solvers and the resulting interface problem can be assembled in a matrix-free fashion and solved with the use of iterative solvers. A full parallel version of the framework involves the construction of adequate preconditioners for the interface problem which was out of the scope of this contribution and it is left as a future research line. In the same spirit, a 3D extension of the method is left as a topic for further research. Preliminary 3D works have been successfully performed for the contact domain case  and it iThe framework presented in this contribution provides the basis to study complex deformation phenomena involving large strains, e.g. bulk metal forming, and shows a clear potential to tackle multifield applications, e.g. mixed formulations for incompressible and thermo-mechanical problems. In this view, the field of Lagrange Multipliers needs to be extended in order to account for the temperature and pressure fields and it is planned for a future contribution.The explicit Delaunay triangulation of the interface is expected to positively impact the field of multiresolution problems and adaptive multiresolution analysis. Since arbitrary discretizations can be handled at non-conforming interfaces, adaptive multiresolution analyses can be performed employing an independent ‘on-the-fly’ refinement at particular domains of interest without meshing restrictions. In the same spirit, existing independent discretizations of particular domains can be easily reused and incorporated to the calculations.Due to its versatility and generality the DIM method is viewed as an attractive alternative to mortar methods and other established dual domain decomposition methods in which the interface geometry and its limits are restricted to the boundary discretization of the connected domains.