Impaired mitochondria homeostasis and function are established hallmarks of aging and increasing evidence suggests a link with lung fibrosis. Mitochondria homeostasis may be also affected in alveolar macrophages (AMs) in idiopathic pulmonary fibrosis (IPF). In this study, we used bronchoalveolar lavage (BAL), a tool for both clinical and research purposes, and a rich source of AMs.BAL samples were examined from 52 patients with IPF and 19 healthy individuals. Measurements of mitochondria reactive oxygen species (mtROS), mitochondria morphology and related gene expression were performed. Additionally, autophagy and mitophagy levels were analysed.Mitochondria in AMs from IPF patients had prominent morphological defects and impaired transcription paralleled to a significant reduction of mitochondria homeostasis regulators PINK1, PARK2 and NRF1. mtROS, was significantly higher in IPF and associated with reduced expression of mitochondria-encoded oxidative phosphorylation (OXPHOS) genes. Age and decline in lung function correlated with higher mtROS levels. Augmentation of damaged, oxidised mitochondria in IPF AMs however was not coupled to increased macroautophagy and mitophagy, central processes in the maintenance of healthy mitochondria levels.Our results suggest a perturbation of mitochondria homeostasis in alveolar macrophages in IPF. Idiopathic Pulmonary Fibrosis (IPF) is a chronic lung disease, characterized by poor prognosis, primarily affecting older individuals . IPF patMitochondria drive ATP production through oxidative phosphorylation (OXPHOS) and they represent the major generator of reactive oxygen species (ROS). In the last decade, it has become evident that cellular metabolism is intertwined with immune responses while, mitochondria activity largely shapes immune cell functions . MitochoAccumulation of damaged mitochondria is associated with IPF and the aging lung , 8, 9. PLung macrophages are a fluctuating and diverse population with a central role in inflammation, host defense, and tissue homeostasis . It is wSeventy one (71) patients were prospectively enrolled in the Department of Thoracic Medicine, University Hospital of Heraklion, Crete, Greece from 2014 to 2018. Fifty two [52] patients with IPF and nineteen [19] healthy controls underwent bronchoscopy and Bronchoalveolar Lavage Fluid (BAL) was obtained.IPF group: The diagnosis of IPF was based on ATS/ERS criteria or on multidisciplinary discussion . Broncho1, forced vital capacity – FVC), using the helium-dilution technique and diffusion capacity  using the single breath technique. The computerized system  was used and predicted values were obtained from the standardized lung function testing of the European Coal and Steel Community, Luxembourg (1993).All patients were evaluated within 1 month from bronchoscopy, with complete pulmonary function tests (PFTs). Lung volumes .Demographic data, pulmonary function tests, and BAL differential cell count are summarised in Table Bronchoalveolar Lavage (BAL) was obtained as previously reported . In brieοC. Cell pellets were washed and re-suspended with cold PBS. Total cell count and cell viability were subsequently assessed using Trypan blue (ICN). Differential cell population count was analysed following May-Grunewald-Giemsa staining as previously described , TOMM20 , p62 [anti-p62 mouse monoclonal antibody (MBL)], LC3 [anti-LC3 mouse monoclonal antibody (Abgent)] and b-actin [anti-b-actin mouse monoclonal antibody (Sigma)]. Appropriate anti-mouse HRP conjugated secondary antibody (Chemicon) was used and immunodetection was performed with enhanced chemiluminescence reagent Luminata™ (Millipore). Bands were visualised with the ChemiDocXRS+ system (Biorad) and densitometry analyses were performed using Image Lab™ software (Biorad).1–1.5 million cells were centrifuged and cell pellets were homogenised in RIPA buffer (Invitrogen) containing protease and phosphatase inhibitors, Pierce), followed by storage at -80Permeabilisation buffer  was added for 10 min followed by blocking buffer  for 10 min at room temperature. Primary antibody incubations were carried out for 60 min at room temperature followed by washing with TBS. Secondary antibody incubations were performed for 30 min followed by washing with TBS. ToPro or DAPI was added for nuclear staining. Finally, TrueBlack (Biotium) was added for 30 s so as to eliminate autofluorescence signal due to intracellular lipofuscin granules. Images were taken by Leica confocal microscope. Mean intensity of protein levels/cell was performed with ImageJ v2.0.0-rc-69/1.52i. Colocalization of mitochondria with autophagosomes or lysosomes was analysed by coloc2 plugin of Image J software.BAL cells were plated on glass slides or plastic dishes for 1 h as described above. Following removal of non-adherent cells, AMs were treated with 0.1 mM chloroquine, for 30 min and fixed with 4% formaldehyde for 20 min followed by washing with PBS for immunofluorescence analysis or lysed in RIPA buffer for western blot analyses.t test, Mann-Whitney test, or chi-square test, as appropriate. Spearman’s correlation coefficient (r) analysis measured the association between two variables. A p value less than 0.05 was considered statistically significant .Data were analyzed using Prism 5 (Graph Pad) software and comparisons were made by p < 0.001, r = 0.5).The downregulation of both PINK1 and PARK2, two key molecules in mitochondrial homeostasis has been reported in IPF , 13. Ana+FShighSShighcells) by flow cytometry using MitoSOX™red superoxide indicator    (33) Fig. e, lower .35)Fig. f and tot.35)Fig. g. Furthe01) Fig. h and not+FShighSShighCD11c+AM population of the BAL cells. CD163 expression was significantly higher in IPF relative to controls  was observed. TGFb mRNA expression was not higher in IPF BAL cells  and complex V .Persistently elevated levels of mtROS observed during ageing and chronic lung diseases such as IPF may drive mitochondria damage and impair their function. Since alternatively activated macrophages rely on OXPHOS for ATP production, we analyzed the transcription of mt-encoded gene members of OXPHOS in particular. Transcription of MRC complex I and V members, NADH dehydrogenase subunit 1 (ND1) and ATP synthase 6 (ATP6) respectively, was significantly lower in IPF BAL cells Fig. a and b. Mitochondria morphology in IPF AMs was evaluated using transmission electron microscopy (TEM). Ultrastructural qualitative analysis revealed that mitochondria in IPF were dysmorphic and contained disorganized cristae Fig. a. QuantiPrevious studies suggested that mitochondria mass increases in IPF lungs , 26. We In view of the accumulation of oxidized and dysmorphic mitochondria in AMs we subsequently examined commonly used markers of autophagy and mitophagy. Initially, we assessed endogenous basal expression of autophagy markers; microtubule-associated protein light chain 3B (LC3B), forms I and II, and the selective autophagy receptor p62/sequestosome1 (SQSTM1) protein in BAL cells. Western Blot analysis from IPF and control groups showed no significant differences in the cytosolic form of LC3B (LC3B I), the lipidated form present mostly on autophagosomes (LC3B II), the LC3B II/I ratio or the p62 protein  resulted in lower acute mtROS production upon bacterial infection leading to reduced apoptosis and bactericidal activity of AMs . NotablyImmune cell functions including macrophage plasticity are largely shaped by mitochondria activity and cellular metabolism , 42. Act+CD11c+CD163+ alveolar macrophages were significantly higher in IPF BAL. Recent studies propose that a diverse population of macrophages exists in IPF lungs with both pro-inflammatory and pro-fibrotic gene expression [According to the previous paradigm of macrophage categorisation into classical/proinflammatory, alternative/resolving and pro-repair/fibrotic population, alternatively activated macrophages were suggested to predominate in IPF as indicated by the increased surface expression of manose receptor CD206 . In our pression , 49, 50.Some limitations of our study should be considered, mainly regarding the differences in the number of patients included in each experiment, which is based on the number of cells required for each method, and the diversity in total cell count of cells in each BAL sample. However, it needs to be stressed that patients were randomly selected for each method, and furthermore, mtROS levels were evaluated in most patients included in the study.The impact of dysregulated mitochondrial complex expression and increased oxidation levels on the antimicrobial action of lung macrophages in health and disease has been recently described –53. FurtAdditional file 1: Figure S1a. A549 cells treated with 1000 μM H2O2 were stained with 5 μm MitoSOXTMred and examined using confocal microscopy. The characteristic mitochondrial network/web staining in the cytoplasm observed, was significantly enhanced upon H202 treatment. Figure S1b. PMA treated THP1 cells were stained with 5 μm MitoSOXTMred or Propidium Iodide and analysed by flow cytometry. The non-treated PI negative cell population stained positive with MitoSOX while treatment with 1000 μM H2O2 resulted in stronger MitoSOX staining . Following H2O2 treatment the PI positive population showed the highest MitoSOX staining (dark red histogram). Figure S1c. Representative example of BAL sample stained with CD45-FITC/CD11c-PC5 or CD45-FITC/CD14-PC. The CD45 + FShighSShigh population in panel (i) comprises of CD11c positive cells (panel ii) and a lower percentage of CD14 positive cells (iii). The CD45 + FShighSShigh population of alveolar macrophages/monocyte derived phagocytes, was used for MitoSOXTMred analyses. Figure S1d. Representative examples of control and IPF BAL MitoSOX analyses.Additional file 2: Table S1. Primer sequences for qPCR. Table S2. Clinicopathological characteristics of the subjects included in Fig. Table S3. Clinicopathological characteristics of the subjects included in Fig. Table S4. Clinicopathological characteristics of the subjects included in Fig. Table S5. Clinicopathological characteristics of the subjects included in Fig. Additional file 3: Figure S2. Mitochondrial DNA content assessed by mtDNA/gDNA ratio measuring both ND1(A) and ND5(B) relative to HGB1 in BAL cells. No statistical difference between control (n = 10) and IPF (n = 18). Representative western blot (C) and densitometry analysis (D) of mitochondria protein TOMM20 showing no statistical difference between control (n = 5) and IPF (n = 11). TOMM20 mean fluorescence intensity/cell measured from images acquired by confocal microscopy, per patient (E) and group (F). Non significant differences are highlighted by doted lines, all other comparisons showed statistically significant differences according to Kruskal Wallis test with Dunn’s test for multiple comparisons. (G) Representative image of TOMM20 staining of alveolar macrophages from IPF patient (p1). With the exception of (E) all for all other comparisons Mann-Whitney test was used, data are represented as median with interquartile ranges.Additional file 4: Figure S3. A, B: (i) LC3b I, (ii)II and (iii) LC3bII/I densitometry analyses from western blots performed on 2 independent IPF/control cohorts, C and D: relative mRNA expression of p62 and Beclin1. E. Representative images of LC3b immunostained alveolar macrophages from IPF and control samples treated with CQ or left untreated. All graphs represent median and interquartile ranges, no significant differences observed according to Mann-Whitney test.


In this work, we propose a novel non-resonant scheme, which utilizes strong light enhancement of the epsilon-near-zero (ENZ) mode to realize optical bistability. We used graphene as a non-linear ENZ material and designed an integrated optical bistability device composed of a graphene-embedded Si waveguide, which supports an ENZ mode. The proposed scheme can overcome the trade-off necessary in resonance-based optical bistability, and the designed optical bistability device simultaneously allows for a short response time (~200 fs) and low switching intensity (~700 kW/cm The optical bistability is a nonlinear phenomenon that has two stable output states for a given input state and exhibits hysteresis; the steady-state output depends on the history of the excitation. This phenomenon can be induced by a bell-shaped output response to an input variation, which is generally caused by a feed-back mechanism in a resonator with nonlinear refractive index or absorption. For practical applications of the optical bistability, it is important to realize a low switching intensity and short response time simultaneously. So far, numerous studies have focused on reducing the switching intensity, and various resonance-based schemes have been proposed to reduce the switching intensity with high quality factor (Q) and strong field enhancement, such as photonic crystals5, surface plasmons6, ring resonators8, and waveguide gratings with guided mode resonance9. However, because the response time is proportional to the Q factor, reducing switching intensity by increasing Q factor inevitably increases the response time9. Therefore, these resonant schemes cannot avoid a trade-off between a response time and a switching intensity.Optical bistability is one of the key functionalities required to implement all-optical switching and optical memory that are essential functions for all-optical signal processing10 and the hyperbolic dispersion property11 of the metal-dielectric structure, resulting in response times of ~1 ps and ~350 fs, respectively. However, the switching intensity is above 100 MW/cm2, which should be reduced.To avoid this trade-off, non-resonant schemes for optical bistability have been proposed, which achieve fast optical bistability by effective permittivity variationµm. The ENZ mode defined as an even-symmetry plasmonic mode (long-range surface plasmonic mode) in ultra-thin ENZ material (|ε| = ~0) confines most of the electric field in the ultra-thin film14. We realized optical bistability with strong non-resonant light confinement of the ENZ mode in a nonlinear ENZ material. We used monolayer graphene as a nonlinear ENZ material. Graphene is widely used as an active nonlinear material for optical bistability because of its tunable permittivity and high nonlinear coefficient18. We show that graphene supports the ENZ mode and the nonlinearity of graphene combined with the ENZ mode effect results in optical bistability, simultaneously achieving a short response time and low switching intensity. All calculations in this paper have been carried out using finite-difference time-domain (FDTD) method.In this study, a simple integrated waveguide structure supporting the epsilon-near-zero (ENZ) mode is proposed to realize optical bistability at a wavelength of 1.55 20 assuming a Fermi velocity of νF = 106 m/s and a mobility of μ = 10,000 cm2/Vs. The permittivity of graphene is obtained from εG = 1 + iσ/(ωε0dG), assuming the thickness of monolayer graphene, dG = 0.34 nm. The permittivity of Si is set as 3.45. Figure F = 0.5 eV as a function of frequency. It can be seen that the real part of the permittivity of graphene is zero and the magnitude of graphene permittivity is minimized at the plasma frequency (ωp). We also plot a dispersion curve of the guided mode in Si/graphene/Si structure for EF = 0.5 eV in Fig. 12. Figure 1 (ω = 0.99ωp) in Fig. 2 (ω = 0.85ωp) in Fig. 1, most of the electric field is confined to the graphene layer, resulting in large optical absorption although Im(εG) is very small. Contrastingly, at P2, the absorption is negligibly small because the electric field spreads into the Si region. Figure For the investigation of the ENZ mode in graphene, a Si/graphene/Si structure as shown in Fig. µm as a function of the Fermi level of graphene for different mobility values, which represents the loss in the guided mode. It can be seen that the imaginary part of the wave-number increases when the Fermi level approaches EF = 0.5 eV, where the permittivity of graphene is almost zero at λ = 1.55 µm. As the Fermi level approaches the ENZ region (EF = 0.5 eV), the electric field becomes confined to the graphene layer owing to the ENZ mode, which results in an increase in the loss in the graphene. In addition, the loss in the guided mode can be tuned by adjusting the Fermi level at fixed wavelength.The proposed structure to realize optical bistability is schematically illustrated in the inset of Fig. We exploited the strong and tunable field confinement and nonlinearity of graphene to realize optical bistability. Because the permittivity of graphene can be modified through the nonlinear Kerr effect, the same effect as the Fermi level shift can be implemented by varying the input intensity. In other words, by modifying the input intensity, the light confinement can be tuned. Therefore, the loss in the mode can be tuned to a considerable extent by adjusting the input intensity.µ = 5,000 cm2/Vs is sufficient for obtaining high performance optical bistability because the imaginary part of wave-number does not vary much for graphene mobility values larger than µ = 5,000 cm2/Vs.The imaginary part of wave number  varies with respect to the variation in mobility, and its slope and peak value deteriorate as the mobility decreases. This stems from the degradation of the ENZ effect due to poor graphene quality. It appears that a graphene mobility of F = 0.515 eV, which deviates slightly from the ENZ region, and in this case, the permittivity of graphene is εG = −1.07527 + 0.217745i at λ = 1.55 µm. The nonlinear susceptibility of graphene is assumed to be 2.095 × 10−15 22. Because the non-ENZ mode is supported for the operational Fermi level (EF = 0.515 eV) and low input intensity, the loss associated with the mode is very small. By contrast, as the input intensity increases, the permittivity of graphene approaches the ENZ region and the guided mode changes to the ENZ mode. Consequently, the loss associated with the mode rapidly increases because of the enhanced electric field confinement in graphene. However, if the input intensity increases further, the permittivity of graphene drifts away from the ENZ region and thus, the loss decreases again as a result of the weakened confinement of the non-ENZ mode. This functions as a feedback mechanism for optical bistability, which shows features similar to the bell-shaped transmission-input power relationship in resonator-based optical bistable devices23. Figures l) of the proposed structure: (a) l = 500 nm and (b) l = 1 µm. The red and blue curves represent the output intensities for the increasing and decreasing input intensities, respectively. The calculated switching intensities are the same as 700 kW/cm2 regardless of the device length. However, the hysteresis width decreases as the device length decreases because the propagation length in the ENZ mode is shorter, which results in the weaker ENZ mode effect. Figure l = 500 nm and (d) l = 1 µm. To analyze the temporal response, we first set the input intensity below the switching intensity (denoted as P1) for 500 fs and applied an additional 500-fs wide square pulse of 450 kW/cm2 height to the input, triggering the output transition from P1 to P1* through P2. Then, we triggered the output transition from P1* to P1 through P3 by applying another 500-fs wide square pulse of −300 kW/cm2 height to the input. As seen in Fig. 1 → P2 and P1* → P3. The amplitude of the overshooting variation appears to be nearly the same as the abrupt variation in output intensity in each nonlinear process. Note that for the transitions of P2 → P1* and P3 → P1, the overshooting and oscillating behavior is not observed where there is no nonlinear variation of the output. In nonlinear processes, the abrupt change in intensity inside the device will cause abrupt changes in the local guided mode profile, and mode mismatch occurs in addition to the change in propagation loss. In general, at the mode mismatch, the incident wave requires a certain propagation distance to adapt to the mode. During the mode adaptation, the local propagation loss will also change, resulting in another change in the local mode. Therefore, this interaction between the change in mode profile and the propagation loss at the local mode mismatch seems to cause the oscillation behavior, which takes some time for stabilization. By contrast, in the linear processes, the gradual variation in the loss causes no abrupt local mode mismatch and thus, no oscillating behavior. The estimated rising and falling response times for the nonlinear transitions are about 200 fs and 150 fs, respectively. In the proposed structure, optical bistability is realized based on the guided-mode confinement variation near the ENZ mode, which is the non-resonant scheme. Therefore, the buildup time for the change in refractive index of graphene to support the ENZ mode is very short, and fast optical bistability behavior could be achieved. It should be noted that the device length does not affect the response time considerably because the propagation time of the guided mode for a few hundred nanometers is just a few femtoseconds. It appears that in the short device at the wavelength scale, the response time is mainly determined by the stabilizing time of the overshoot power.We set the operating Fermi level to E2 and 200 fs, respectively. The proposed scheme may lead to a new class of non-resonant optically bistable devices that can avoid the hitherto necessary tradeoff between the switching intensity and response time. In addition, we believe that the proposed scheme can be applied to other material systems that support the ENZ mode such as an ultra-thin doped semiconductor layer, achieving similar optical bistability behavior.We numerically investigated the optical bistability behavior based on the ENZ mode in graphene. We showed that a simple, graphene-embedded Si waveguide structure supports an ENZ mode and its propagation loss varies drastically with the permittivity change in graphene, which enables optical bistability by virtue of the optical nonlinearity of graphene. The switching intensity and response time in the proposed structure are approximately 700 kW/cm6 m/s, and mobility of 10,000 cm2/Vs, and the nonlinear susceptibility of graphene was assumed to be χ(3) = 2.095 × 10−15 22. The optical bistability curve and the temporal response were calculated using the commercial FDTD software . In the FDTD calculation, the third-order (Kerr-type) nonlinearity is handled by the relation of E(t) = D(t)/(εοεr + εοχ(3)|E(t-Δt)|2) assuming an instantaneous nonlinear response, where Δt is the time step of the iterative field update24. The latest value of E calculated from the latest value of D and the previous value of E is used for the update of H in the next iteration, which is followed by the update of D. This process repeats cyclically. The input and output intensities were calculated by integrating the Poynting vector over the waveguide cross section and calculating its time average.The dispersion relation of the guided mode was calculated by solving the one-dimensional Maxwell’s equation using the root-finding algorithm. In our numerical analysis of the optical bistability, the permittivity of graphene was calculated using the Kubo formula, assuming a graphene thickness of 0.34 nm, Fermi velocity of 10


An important task in facilitating the development of thermally conducting graphene/polymer nanocomposites is to suppress the intrinsically strong intersheet π-π stacking of graphene, and thereby to improve the exfoliation and dispersion of graphene in the matrix. Here, a pre-programmed intercalation approach to realize the in situ growth of graphene nanosheets at the inorganic template is demonstrated. Specifically, microsized MgO granules with controlled geometrical size were synthesized using a precipitation method, allowing the simultaneous realization of high surface activity. In the presence of a carbon and nitrogen source, the MgO granules were ready to induce the formation of graphene nanosheets (G@MgO), which allowed for the creation of tenacious linkages between graphene and template. More importantly, the incorporation of G@MgO into polymer composites largely pushed up the thermal conductivity, climbing from 0.39 W/m∙K for pristine polyethylene to 8.64 W/m∙K for polyethylene/G@MgO (60/40). This was accompanied by the simultaneous promotion of mechanical properties (tensile strength of around 30 MPa until 40 wt % addition of G@MgO), in contrast to the noteworthy decline of tensile strength for MgO-filled composites with over 20 wt.% fillers. In the areas of thermal management, heat dissipation and heat exchanging materials, intrinsic low thermal conductivity (TC) remains the main challenge for the application of polymer composites, regardless of low weight, desirable processing feasibility, good corrosion resistance, and low cost ,2. IncorThe surface chemistry of graphene is of importance for the stacking order and dispersion morphology in polymer composites , which pEmerging as two main routes to harvest the specialties of graphene in development of polymer composites, surface modification and pre-programmed intercalation of graphene sheets have been used to tailor the dispersion morphology and the interfacial adhesion. The former pathway focuses on the covalent decoration of sheet surfaces with functional groups like small molecules or special chemical structure, which was hypothesized to decrease the intersheet interactions and improve the exfoliation of graphene sheets in the polymer matrix ,15. For While recognizing the promising potential to develop high-performance graphene nanocomposites using the pre-programmed intercalation principles, we attempt the launch of hierarchical structure design by introducing inorganic platform to trigger the formation of graphene nanosheets. In the proposed conception, our key elements are (1) rational design of a reliable template that is highly active to induce the growth of graphene; (2) appropriate regulation of the template size at the considerable level with graphene sheets; (3) strong interfacial bonding to endows the promotion of mechanical properties by incorporation of the well-organized graphene-template entities; (4) facile and affordable generation of graphene at the template that supports the large-scale and low-cost fabrication of graphene nanocomposites. This effort sheds light on the flexibility in the reliable regulation of hierarchically structured nanofillers by the in situ formation of graphene nanosheets at the templates, that encourage the pursuit of high-performance graphene nanocomposites toward an optimized balance of TC gains and mechanical property enhancement.2CO3), magnesium chloride (MgCl2), HCl, distilled water and other chemicals were obtained from Sinopharm Chemical Reagent Co., Ltd. , and were used as received.Sodium carbonate (Na2CO3 solution (0.11 mol/mL) was gently added to aqueous MgCl2 (0.1 mol/mL), which was accompanied by mechanical mixing. The mixture was sent to hydrothermal reaction in a reactor at 200 °C and 0.6 MPa within 30 min, yielding the formation of MgCO3 granules with highly ordered crystal plates [3 particles were filtered, followed by drying at 110 °C for 6 h. The MgCO3 granules were calcined to MgO granules at 500 °C for 4 h under nitrogen atmosphere.Using a precipitation method, aqueous Nal plates . The pre2 (100 sccm) into the gas bubbler containing acetonitrile, and the CVD reaction was held for 0.5 h to obtain the sufficient formation of graphene layers at the MgO template (G@MgO). After that, nitrogen was used to purge away any remaining H2, during the cooling procedure.Using the MgO granules as the template, porous nanocarbons were grown at MgO by the chemical vapor deposition (CVD) method. The MgO granules were heated to 600 °C in a tube furnace at a rate of 20 °C/min and annealed at 600 °C for 0.5 h. The growth of graphene was triggered with the introduction of HUsing a HAAKE mill, the G@MgO was melt compounded with high-density polyethylene  at 200 °C with a filler content ranging from 5 wt % to 40 wt %. The composites were compression molded into thin films with a thickness of 2 mm.3 precursors, the MgO template, the G@MgO particles, and the mesoporous graphene without MgO template, as well as the fracture morphology of polyethylene composites. To observe the mesoporous graphene, the G@MgO particles were immersed in 1 M HCl solution for 24 h to etch the interior MgO template, followed by vacuum drying at 120 °C for 8 h. All the samples were sputter-coated with a 3.5 nm thick gold layer prior to the SEM observations. An SE-4800 scanning electron microscopy (SEM) , operating at an accelerated voltage of 5 keV, was employed to trace the morphological features of the MgCOTransmission electron microscopy (TEM) was used to image the morphology of graphene induced by the MgO template. Mesoporous graphene was obtained using the same method for SEM observation. Droplets of G@MgO and mesoporous graphene suspensions in ethanol were deposited onto a lacey carbon film 400 mesh copper TEM grid  and allowed to dry in ambient conditions prior to TEM imaging .2 adsorption–desorption isotherms were measured on a Micromeritics ASAP 2020 at 77 K, using vacuum dried samples (150 °C/6 h). The isotherms were analyzed using the two-parameter Brunauer–Emmett–Teller (BET) model for specific surface area, the Dubinin–Radushkevitch model for micropore volume, the Horvath–Kawazoe method for micropore size distribution, and non-local density functional theory (NLDFT) isotherm fitting for meso–macropore size distribution.NRaman spectroscopy was performed on a Thermo Nicolet Almega XR Dispersive Raman microscope, comprising a 0.9 numerical aperture microscope objective, a ×50 lens and 10 exposures of 5 s. The laser wavelength is 532 nm (24 mW).Following the standard GB/T3399-1982, the guarded hot plate method was used to evaluate the thermal conductivity (TC) of the composites on a DRH-V  at 25 °C.Following the ASTM standard D638, tensile testing was performed on an Instron universal test instrument  with a load cell of 500 N at 23 °C and relative humidity of 50%. The crosshead speed was set at 50 mm/min and the gauge length was 20 mm.The composites were machined to thin films (thickness of ~20 μm) and were imaged on an Olympus BX43 microscope equipped with a digital camera. 3 precursors prepared by precipitation were directly examined by SEM observations  allow us to hypothesize that the CVD grown graphene was primarily composed of mesopores (P/P0 range of 0.2–0.8) [P/P0 > 0.8) that pointed to the capillary condensation in the finite volume of the mesopores. The specific surface area (SSA) of graphene was evaluated to be 175 m2/g, revealing the predominance of mesopores during the CVD growth at the MgO template. This was in line with the pore volume of 0.342 cm3/g, essentially arising from the existence of mesopores with probable collapsing of neighboring pores [Measurements of surface area and porosity of the microporous graphene were conducted using Nesopores a, giving0.2–0.8) ,25. It wng pores .−1, assigned to the G band of graphite [2 carbons, which trigger the stretching motions of E2g in-plane bonds. Unlike the generally observed peak at around 1580 cm−1, the downshift of G band was probably due to the existence of numerous mesopores  located at 2677 cm−1 was attributed to the double resonance effects of the D band, indicating the existence of few-layer graphene presented in G@MgO [Raman spectroscopy affords an assessment of the ordering and graphitization degree for the carbons in the CVD-grown graphene . The maxgraphite . This inesopores f, which in G@MgO ,29. The in G@MgO .To examine the unique functionality of the hierarchical structure design, the G@MgO particles were melt-compounded with polyethylene, while the MgO-filled composite counterparts were fabricated. The presence of graphene layers is expected to bridge the polymer matrix and the host MgO entities, thus conferring the enhancements of TC and mechanical properties. The plots of TC values in In addition to remarkable enhancements in TC properties, G@MgO significantly enhanced the mechanical properties of polyethylene, as manifested by the measurements of tensile properties b. AlthouUsing a precipitation method, microsized MgO granules with a controlled geometrical size were synthesized, allowing the simultaneous realization of high porosity and surface activity. By incorporation of carbon and nitrogen source, the MgO templates were ready to induce the formation of few-layer graphene nanosheets, which allowed the creation of tenacious linkages between graphene and template. The structural features allowed the suppression of intrinsically strong intersheet π-π stacking of graphene, as well as the desired exfoliation and dispersion of graphene in the polyethylene matrix. More importantly, the incorporation of G@MgO into polymer composites largely pushed up the thermal conductivity, climbing from 0.39 W/m∙K for pristine polyethylene to 8.64 W/m∙K for polyethylene/G@MgO (60/40). Meanwhile, the simultaneous promotion of mechanical properties was observed after the addition of G@MgO, reaching a tensile strength of around 30 MPa until the content of 40 wt %, in contrast to the noteworthy decline of tensile strength for MgO-filled composites with over 20 wt % fillers. The concept of pre-programmed intercalation signifies a facile method to control the morphology and regioselectivity of graphene, laying down the essential prerequisites for the fabrication of high-performance polymer composites with a combination of high thermal conductivity and mechanical properties.


Dry-spinning method is extensively employed in fiber industry, comparing to the counter-part of wet-spinning process, it has advantages of environmentally friendly, high yield rate and no need for purification. Here, we report the synthesis of graphene oxide (GO) fibers via dry spinning GO inks with extremely high concentrations. The proper rheology properties of such GO inks allow us to dry spin GO fiber directly. Various dry spinning conditions are investigated, and the relationship between mechanical performance and micro-structure of the obtained GO fiber are established. We found that the existence of larger GO liquid crystal domains does not necessarily result to higher mechanical properties, and it is because those large GO liquid crystal domains evolve into thick GO films during drying process and thus prevent the intimate compaction of the whole GOF and leave behind gaps. This is detrimental for the mechanical properties, and thus the dry spin GOF are much weaker than that of wet spin ones. Importantly, Barus effects, that generally arise during the melt spinning of polymers, were not observed, indicating that caution must be taken when classical polymer rheology theories are applied to investigate the dynamic behaviors of GO solution. The assembly of graphene into graphene based macro-sized objects (GMO) that can inherit some outstanding characteristics of graphene is extremely important for the practical application of graphene. In the past several years, there has indeed witnessed significant advancement10. For example, Ruoff’s group firstly reported graphene oxide (GO) paper, in which graphene nanosheets are stacked tightly layer-by-layer, and these GO papers exhibited high strength and modulus4. Graphene aerogel/hydrogel is another typical GMO. Shi et al. employed hydrothermal method to synthesize graphene hydrogel, and such GMP possesses high electrical conductivity, porosity and accessible surface area, and thus provides competitive candidate for the electrodes in energy storage materials. Cheng and Ren creatively replaced the original 2-D metal catalyst foil by 3D porous one to grow graphene foam, which significantly push and trigger the research in this area10. All the above development manifests the versatility and great potential for GMOs.Graphene has super mechanical, electrical and thermal properties, due to its sp15. Wet spinning method is a quite general strategy to prepare fibers, and in principle, any nanoparticle dispersion can be gelled into fiber when the right combination of dispersion agent and coagulation solution are employed17. Gao et al. took the advantage of spontaneously developed liquid crystal behaviors of GO with relatively high concentration, successfully developed a series of high performance GFs by wet-spinning18. Wallace et al. further employed DNA to wet spin synthesized GFs, aiming for the GFs based tissue engineering19. Interestingly, Qu et al. expanded the hydrothermal process to the synthesis of GFs, by using hollow glass tube as autoclave20. Very recently, Chen further advanced this strategy by replacing the hollow glass tube by flexible silica hollow tube, which significantly improved the GF yield21. The obtained graphene hybrid fibers showed excellent energy storage performance.Among all GMOs, graphene fiber (GF) is very interesting and attractive, since it is strong, lightweight, flexible and conductive, based on which a large amount of new applications might be envisioned24. Comparing wet spinning method, the productivity of dry spin is much higher, and even more importantly, purification is not necessary22. Unfortunately, for the best of our knowledges, the studies of the dry spinning GFs are still very limited. When this paper is still under review, Gao’s group firstly reported dry spinning GFs25. Even though extruding high concentrated GO gel has been announced by other groups in their investigation of 3D printing graphene structures27, the rheological properties of GO, as well as its physical impact on the drying dynamics, micro-structures and mechanical properties of the prepared fibers still need to be clarified. In addition, the highly hydrophilic characteristics of GO limited the maximum concentration of GO solution we can achieve, the GO fibers immediately obtained by wet/dry spin still contain a large amount of water. This makes the drying process, during which GO sheets are assembled into closely packed structure, become the key step in order to control and modify the performance of the final GO fibers. Keeping the above considering in mind, we focused, in this study, on the dry spinnability of GO inks, and relationship between spinning conditions, including rheology properties of GO and size of spinneret, and GF mechanical properties, are established. A model for the development of microstructure during drying process of gel GOFs was also provided.However, it worth to be pointed out here, that almost all the reported GFs are synthesized either by hydrothermal or wet-spin. Fiber spinning is actually a method that has been extensively used since several decades ago in textile industry, and various spinning strategies have been tested and optimized. Wet spin and dry spin are the two most used spinning methodThe rate of GF synthesis by our dry spin method is very high, which is mainly determined by the spin rate. This is because comparing with wet spin, there is no need for extra treatment, such as purification, for dry spin GO fibers, which not only time consuming, but also involve chemical solvent that make potential pollution. This advantage of dry spin makes it very competitive. On the other hand, considering the GO concentration of the dry spin ink is significantly higher than that in wet spin, the behaviors of GO assembly during the spinning and drying process, as well as the micro-structure of obtained solid GO fibers could be very different. The evolvement of liquid crystal distribution as the GO ink concentration increased can be seen in Fig. The gel GOFs immediately extruded from spinneret still has a large amount of water (90–95%), however, it can still perfectly be self-supported with no observable changes of the shape during spinning process. This is guaranteed by the proper rheology properties of GO ink as will be elaborated in the following. After the GOFs were dried by fixing two ends with controlled force, it was observed that, all GFs shrink along their axial direction by ~8%, while the radial direction by ~85%. Such asymmetry shrinkage manifested that most of liquid crystal domains are aligned in the axial direction, which is induced by the shear stress generated by the spinneret during the spinning process. Because of the structure stability of the gel GOFs, they can form various complex shapes and structures shown in Fig. 12, and thus rheology property of the GO ink is almost irrelevant. In contrast, for dry-spinning method, proper rheology performance is the key factor. It is required that once the GO ink is extruded out of the spinneret, it must have the capability to self-supported. As can be seen in Fig. There is a critical difference between the inks for dry spin and wet spin that should be clarified, in order to elaborate the fundamental mechanisms for the micro-structure formation during drying process and related mechanical properties of GO fiber. Since coagulation agents, such as metal ions, are employed for the formation of gel GO fiber in wet-spin process, the minimum spinnable concentration of GO can be very low (less than 2 mg/ml)12. Therefore, the gel GOF immediately extruded from the spinneret has “core-shell” structure, with the shell consists of closely packed GO liquid crystal domains and core of relatively randomly distributed GO nanosheets or small GO liquid crystal domains . Thermal treatment (at 220 °C) can further enhance the modulus but not the strength, and also decrease the fracture strain significantly. “Yield” stage is not observed for the reduced samples. Indeed, as reported by Pei, there would be significant amount of iodine laminated between GO layers, which might reinforce the whole structures29. Therefore, the gaps and defects in GOFs are probably filled at least partially with the residue iodine, and thus prevent the slippery of GO shells relative to each other. After annealing at 550 °C for two hours, at which most of iodine residue is volatilized to gas, the strength even decreased, and this can be related to the inevitable gas generated porosity. We microstructure and chemical composition of GOF after different reduction treatment was also investigated by SEM and XPS, respectively  cannot be avoided during the polymer fiber extrusion12. Such difference is probably caused by the much larger and thicker domains of GO liquid crystal than that in ink for wet-spinning, which constrain the dense packaging of GO nanosheets and leave behind pores and gaps that eventually limit the strength of GO fibers. However, direct evidence for such conjecture still requires in-situ experiments. The comparison between the drying process for wet spin GO fiber and dry spin GO fiber also indicates both the GO liquid crystal domain size and availability of flexible GO nanosheets should be taken into consideration for the synthesis of high strong and conductive graphene fibers. The Barus effects were not observed for the dry spinning of GOFs, which suggests that it should be cautious when polymer rheology theories are applied to study the colloidal behaviors of GO solutions.In summary, we reported the synthesis of graphene fiber via dry-spinning method. The graphene fibers exhibited a strength of ~120 MPa, comparative to the firstly reported wet-spin fibers by Gao’s group, and high fracture strain of 9%, which is much higher than that of wet-spin GO fiberGraphene oxide was synthesized from purified natural graphite by the modified Hummers method. The size distribution can be seen in Fig. −1. Conductivity measurements were carried out on a multi-meter. SEM images were obtained BY using a supra 55 sapphire operated at an accelerating voltage of 10 KV.The graphene oxide fiber (GOF) was made by printing the highly concentrated GO use a dispenser , followed by air drying with both ends of the flexible fixed. The fiber diameter just spun out was measured using Transmission polarized light microscope . The GOFs were reduced by HI with concentration of 20 wt% at 80 °C for 10 h, and then washed by distilled water for three times, and the obtained fibers are termed as H_GFs. To prepare the annealing samples, the H_GFs were annealed at temperature of 220 °C or 550 °C, in a tube furnace oven  under the protection of argon. The thermal reduced fibers are termed as HT220_GF and HT550_GF, with the number indicating annealing temperatures. If it is not clearly pointed out, the fibers are fabricated by using ink with the concentration of 8 wt% and spinneret with diameter of 0.4 mm, since it can result to the best mechanical properties as will be discussed. The rheology and viscosity of the GO solution were measured using a discover HR-2 rheometer. The fiber static tensile tests were conducted with a dynamic mechanical analyzer . The sample was glued to the paper for mechanical testing and was gripped using a film tension clamp. All tensile tests were conducted in a controlled force rate mode with a force ramp rate of 0.5 NminSupplementary Information


Bacterial and fungal communities in biofilms are important components in driving biogeochemical processes in stream ecosystems. Previous studies have well documented the patterns of bacterial alpha diversity in stream biofilms in glacier-fed streams, where, however, beta diversity of the microbial communities has received much less attention especially considering both bacterial and fungal communities. A focus on beta diversity can provide insights into the mechanisms driving community changes associated to large environmental fluctuations and disturbances, such as in glacier-fed streams. Moreover, modularity of co-occurrence networks can reveal more ecological and evolutionary properties of microbial communities beyond taxonomic groups. Here, integrating beta diversity and co-occurrence approach, we explored the network topology and modularity of the bacterial and fungal communities with consideration of environmental variation in glacier-fed streams in Central Asia. Combining results from hydrological modeling and normalized difference of vegetation index, this study highlighted that hydrological variables and vegetation status are major variables determining the environmental heterogeneity of glacier-fed streams. Bacterial communities formed a more complex and connected network, while the fungal communities formed a more clustered network. Moreover, the strong interrelations among the taxonomic dissimilarities of bacterial community (BC) and modules suggest they had common processes in driving diversity and taxonomic compositions across the heterogeneous environment. In contrast, fungal community (FC) and modules generally showed distinct driving processes to each other. Moreover, bacterial and fungal communities also had different driving processes. Furthermore, the variation of BC and modules were strongly correlated with hydrological properties and vegetation status but not with nutrients, while FC and modules (except one module) were not associated with environmental variation. Our results suggest that bacterial and fungal communities had distinct mechanisms in structuring microbial networks, and environmental variation had strong influences on bacterial communities but not on fungal communities. The fungal communities have unique assembly mechanisms and physiological properties which might lead to their insensitive responses to environmental variations compared to bacterial communities. Overall, beyond alpha diversity in previous studies, these results add our knowledge that bacterial and fungal communities have contrasting assembly mechanisms and respond differently to environmental variation in glacier-fed streams. Glaciers cover approximately 10% of the land surface on the Earth  and are Biofilms are hot spots of microbial diversity and activity in stream ecosystems . Within Glacier-fed streams in Tian Shan Mountains in Central Asia are particularly vulnerable to climate change, where glaciers contribute significantly to stream runoff . Glacier2 and a total volume of 707 km3 , ammonium (NH4+), soluble reactive phosphorus (SRP), and dissolved organic carbon (DOC). NO3− was analyzed using ion chromatography (EPA 300.0). NH4+ was analyzed using the indophenol colorimetric method (EPA 350.1). SRP was measured according to the ammonium molybdate method (EPA 365.3). DOC was measured using a total organic carbon (TOC) analyzer . Water chemistry data was reported in our previous research , and elevation were measured in situ using a handheld pH meter , YSI meter , and GPS unit , respectively. Unfiltered water samples were directly used to measure total nitrogen (TN) and total phosphorus (TP). TN was analyzed by ion chromatography with prior persulfate oxidation (EPA 300.0). TP was analyzed using the ammonium molybdate method with prior oxidation (EPA 365.3). Filtered water samples (filtered with pre-combusted GF/F filters) were used to test nitrate   status was measured by the normalized difference vegetation index (NDVI) using the Terra moderate resolution imaging spectroradiometer Vegetation Indices (MOD13Q1) Version 6 data downloaded from USGS (gs.gov/) . The MODgs.gov/) . The equgs.gov/) . For eacBacterial 16S rRNA gene sequences and fungal 18S rRNA gene sequences were analyzed to determine the bacterial community (BC) and fungal community (FC), respectively. To determine the fungal community, the internal transcribed spacer regions and 18S rRNA genes are commonly used and provide similar results and congruent conclusions . We usedPRJNA398147, SRP115356) and fungal 18S rRNA  were processed using QIIME 1.9.0  were used to assess the pairwise relationships between environmental variables and visualized using corrplot function in corrplot 0.84 package. Mantel tests (mantel function in vegan 2.5-3 package) were used to assess the relationships among spatial dissimilarity (represented by geographic distance), overall environmental distance, hydrological dissimilarity, nutrient dissimilarity, and vegetation dissimilarity. Partial Mantel tests  were used to assess those relationships by controlling nutrient dissimilarity. The geographic distance was calculated based on the GPS coordinates of sample sites using distGeo function in geosphere 1.5-10 package. The environmental distance was represented by Euclidean distance based on all analyzed environmental variables. Hydrological dissimilarity was represented by Euclidean distance based on GD, GA, and GS. Nutrient dissimilarity was represented by Euclidean distance based on TN, NO3−, NH4+, TP, and SRP. Vegetation dissimilarity was represented by Euclidean distance based on NDVI. Euclidean distances were calculated using vegdist function in vegan 2.5-3 package . Only strong (R > 0.7 OR R < −0.7) and significant (P < 0.01) correlations were considered in network analysis. ClusterMaker app  . In netwaker app  was usedaker app . The groaker app . Moreove3−, while positively correlated with NDVI and pH , respectively  and 4B. Bacterial and fungal communities in stream biofilms are major components of glacier-fed stream ecosystems. The strong correlations between bacterial communities and environmental, hydrological, and vegetation characteristics suggest substantial influences of spatial heterogeneity and potential influences of glacier shrinkage on bacterial communities . HoweverIn contrast to bacterial communities, environmental, hydrological, and vegetation dissimilarities were not significantly associated with the dissimilarity of fungal communities. Moreover, the variation fungal communities were also not associated to nutrient variations. The results suggest that FC variations were not affected by the environmental variation and might be insensitive to glacier shrinkage. We proposed that the unique responses of fungi may relate to the low temperature which can suppress the response of fungal communities to environmental variation. Fungi can survive and grow in harsh conditions with low temperatures such as glacier and snow by evolving various adaptive features . These fThe different patterns of bacterial and fungal communities in glacier-fed streams were further supported by network analysis, which showed that the bacterial communities formed a more complex and connected network, while the fungal communities formed a more clustered network ; Table 1Glacier shrinkage imposes significant influences on glacier-fed streams. Integrating beta diversity, our study provides the first co-occurrence network analyses of bacterial and fungal communities in glacier-fed streams. Firstly, this study highlighted that hydrological variables and vegetation status are important components in determining environment heterogeneity of glacier-fed streams and are indicator variables of glacier shrinkage. Then we identified co-occurrence properties of the microbial communities and their responses to environmental variations. Bacterial communities formed a more complex and connected network, while the fungal communities formed a more clustered network. Nutrients were insignificant to the assemblies of both bacterial and fungal communities in these glacier-fed streams. However, hydrological properties and vegetation status impose significant influences on assemblies of the BC but not on the FC. The results suggest the influences of glacier shrinkage on bacterial communities. However, fungi communities might be insensitive to glacier shrinkage. The results would add our knowledge of microbial community assembly mechanisms and the responses of microbial communities to environmental variations caused by glacier shrinkage.10.7717/peerj.7715/supp-1Supplemental Information 1Click here for additional data file.10.7717/peerj.7715/supp-2Supplemental Information 2adonis function in vegan package 2.5-3). R2 and P-values (in bracket) are shown.adonis function in vegan package 2.5-3). R2 and P-values (in bracket) are shown.Click here for additional data file.


Prominent cognitive models of insomnia have emphasized the notion that the disorder is in part maintained by an attentional bias for sleep related “threat” cues which may be internal  or external  in nature Harvey, . To suppFirst, we consider the role of the serotonin transporter polymorphism (5HTTLPR). Some authors have demonstrated the 5HTTLPR short allele to be related to an increased risk for insomnia/poor sleep quality relative to the long allele , a relationship between the short allele and an attentional bias for emotionally salient words and images has been evidenced  consequently feeding back to accentuate sleep-related worry  and misperception of sleep attributes  in a cyclical nature  in relation to attentional bias outcomes  in reaction time tasks, Harris et al.  determinMoving forward from reaction time assessments of attentional bias, which can be considered an indirect measure of attention, a number of recent studies have employed eye-tracking paradigms with the aim to examine selective attention in insomnia  to be effective in ameliorating disorder consistent symptoms amongst individuals who elicit an attentional bias (MacLeod and Grafton, A recent review tentatively supports the notion of a sleep-related attentional bias in insomnia based on six out of nine studies which confirm group differences in relation to attentional allocation to sleep-related stimuli (Harris et al., All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Community detection algorithms are fundamental tools to uncover important features in networks. There are several studies focused on social networks but only a few deal with biological networks. Directly or indirectly, most of the methods maximize modularity, a measure of the density of links within communities as compared to links between communities.Saccharomyces cerevisiae (Yeast) with 6532 nodes and 229,696 edges and the second is a network of PPI in Homo sapiens (Human) with 20,644 nodes and 241,008 edges. All six methods perform well, i.e., find reasonably sized and biologically interpretable communities, for the Yeast PPI network but the Conclude method does not find reasonably sized communities for the Human PPI network. Louvain method maximizes modularity by using an agglomerative approach, and is the fastest method for community detection. For the Yeast PPI network, the results of Spinglass method are most similar to the results of Louvain method with regard to the size of communities and core pathways they identify, whereas for the Human PPI network, Combo and Spinglass methods yield the most similar results, with Louvain being the next closest.Here we analyze six different community detection algorithms, namely, Combo, Conclude, Fast Greedy, Leading Eigen, Louvain and Spinglass, on two important biological networks to find their communities and evaluate the results in terms of topological and functional features through Kyoto Encyclopedia of Genes and Genomes pathway and Gene Ontology term enrichment analysis. At a high level, the main assessment criteria are 1) appropriate community size , 2) representation within the community of only one or two broad biological functions, 3) most genes from the network belonging to a pathway should also belong to only one or two communities, and 4) performance speed. The first network in this study is a network of Protein-Protein Interactions (PPI) in For Yeast and Human PPI networks, Louvain method is likely the best method to find communities in terms of detecting known core pathways in a reasonable time.The online version of this article (10.1186/s12859-019-2746-0) contains supplementary material, which is available to authorized users. The use of networks to study complex interacting systems has been applied to many domains during the last two decades, including sociology, physics, computer science and biology. An important task in the analysis of networks lies in the identification of communities or modules whose membership share one or more common features of the system. The problem that community detection attempts to solve is the identification of groups of nodes with more and/or better interactions amongst its members than between its members and the remainder of the network , 2. For Edges in a biological network may represent various types of direct interactions and indirect effects. Examples of direct interactions include protein-protein interactions as part of signaling pathways or as part of protein complexes and substrate-enzyme interactions. Indirect effects may include transport processes and regulatory effects, which, in most cases, can be substituted with a subnetwork of several direct interactions when modeled at a finer granularity. Examples of the latter are cholesterol and ion transport across the plasma membrane and protein-DNA interactions in gene-regulatory networks. Thus, in the context of a cell or tissue, subnetworks or communities may correspond to various cellular processes, pathways and functions, in which its components (nodes) exhibit a higher-degree of interaction as compared to those from outside the pathway.Majority of the methods for community detection in networks are based on maximization of modularity. While the modularity metric Q, of a network, is defined in the Methods section, intuitively, given a network, if it can be partitioned in such a way that only a few connections exist between the nodes of different partitions and most connections are among the nodes within the partitions, then the modularity will be high. It is interesting to note that the modularity of a sparse network of fully connected subnetworks is higher than that of a fully connected network, which is zero. Any partition of a fully connected network results in Q < 0. Brandes et al. have carried out extensive theoretical analysis of properties of modularity and complexity of its maximization .One of the most important objectives of any large-scale omics study is to identify mechanisms for specific functions and phenotypes in a chosen context. Biological networks derived from genome-scale experimental data and/or legacy knowledge are generally large and complex with thousands of nodes and many thousands of connections. Associating meaningful biological functions and interpretations to such networks is impossible. However, these large networks can be broken down into smaller (sub) networks  which are more amenable to biological interpretation. Such communities are expected to represent one or a few biological functions and they may facilitate discovery of mechanisms relating the causes or perturbations to the observed phenotypes. Thus, community detection can provide valuable biological insights.Several methods have been developed to find communities in networks using tools and techniques from different disciplines such as applied mathematics or statistical physics . All theO(m2n) for a network with n nodes and m edges, practically restricts its use to networks of at most a few thousand nodes. There are other optimization-based algorithms with different objective functions that provide different approaches to solve the community detection problem. For example, Leading Eigen [Classical community detection algorithms initially divide networks into communities according to some network features such as edge betweenness. One of the most popular and prominent algorithms that uses edge betweenness is the Girvan-Newman algorithm , 7. In tng Eigen  algorithng Eigen .GA-net that uses a special assessment function described as the community score in addition to the modularity function [Since the early 2000s, several methods have been developed that divide networks into communities based on the modularity –15. The function . There aIn this manuscript, we briefly review eight algorithms for finding communities in biological networks such as Protein-Protein Interaction (PPI) networks (discussed in the Methods section). In such networks, each node represents a protein (or gene) and each edge represents an interaction between two proteins. In particular, we will apply six algorithms to the Yeast PPI network with 6532 nodes and 229,696 edges and the Human PPI network with 20,644 nodes and 241,008 edges. Using several topological metrics, we assess which methods provide similar (or dissimilar) results. We evaluate the biological interpretation of the communities identified and compare the results in terms of their functional features. At a high level, the main criteria for assessment of the methods are 1) appropriate community size , 2) representation within the community of only one or two broad biological functions, 3) most genes from the network belonging to a pathway should also belong to only one or two communities, and 4) performance speed.This paper is organized as follows: in the next section we will present the results of applying six methods on the Yeast and Human PPI networks and compare the communities based on their topological and functional features. In the last part of this section, we will describe an orthology analysis between the communities detected for the Yeast PPI network and the communities detected for the Human PPI network. In the following section, we will present discussion on the results providing insights into the algorithmic similarities and robustness of some of the methods. In the section after that, we will provide the conclusion of our paper. In the Methods section, we will describe eight different methods for finding communities in networks. We will also introduce three metrics to compare the communities identified by the algorithms.Six community detection methods, namely, Combo, Conclude, Fast Greedy, Leading Eigen, Louvain and Spinglass, have been applied to the Yeast PPI network with 6532 nodes and 229,696 edges and the Human PPI network with 20,644 nodes and 241,008 edges. A detailed description of the methods is included in the Methods section. We used the BioGRID database , 22 for In the first part of this section, we will present the results for the Yeast PPI network. In the second part, the results for the Human PPI network will be presented. In the third part, an orthology comparison will be provided between the Yeast and Human PPI networks.m2n (where n is the number of nodes and m is the number of edges), so, it will take ~ 148 days to find communities in the Yeast PPI network . Infomap, is also not a good method based on the size of communities it detects; the largest community has 6195 nodes and the smallest one has just 2 nodes. Since very small communities  are not expected to yield significant biological insights, we will not consider them in our analysis. We note that there may be some exceptions.Among the methods tested to find communities of the Yeast PPI network, Combo, Conclude, Fast Greedy, Leading Eigen, Louvain and Spinglass give good partitioning results, i.e., the size of communities detected are not too small or too large compared to the size of the original network. Since the Yeast PPI network has 6532 nodes, Girvan-Newman algorithm is not an appropriate method to detect communities. It takes 44 min (on a PC with 4 GB RAM with 4 2.4 GHz processors) for Rattus PPI network which has 3379 nodes and 4580 edges. Its computational complexity is proportional to In the next subsection, first we will compare the methods from a topological perspective of the communities identified. Then we will provide a functional comparison. To begin with, the results for all these methods are described in Table The following table Table  represenUsing three different metrics, namely, Rand Index (RI), Adjusted Rand Index (ARI), and Normalized Mutual Information (NMI) (described in the Methods section), we are able to compare different pair of methods. Table Based on the results of Table Intersect function in R to find common genes between two communities and then divided the number of common genes by the total number of unique genes between the two communities (union function in R) to get the Jaccard index. Table Table p-values less than or equal to 0.01. The number in parenthesis  is the number of genes that DAVID could annotate for that specific community for the Yeast PPI network. For example, the first community of Louvain (L1) has 1538 genes  represent p-values for those pathways in the communities compared, and columns 5 and 9 (FE) represent Fold Enrichment for the pathways. FE is defined as (s/b)/(k/N) where b is the total number of genes in a chosen pathway; s, the number of genes from the community in this pathway; N, the total number of genes for the species; and k, the number of genes in the community; all the four numbers are based on intersection/overlap with the respective DAVID database . Essentially, FE represents the relative increase or decrease of the fraction of genes from the set of interest belonging to a pathway as compared to the genes from a background set  belonging to the same pathway. The values in columns 5 and 9 are shaded light to dark with increasing FE. Column 6 (common) is the number of genes common to both communities for the different pathways.As described in the previous subsection, Louvain and Spinglass are most similar to each other and Louvain and Leading Eigen are most dissimilar. In order to know which communities of similar and dissimilar methods have to be compared to each other, we analyzed Tables As the first column of Table p-value.Based on Table In terms of enzyme commission annotation, there are 1738 enzyme-coding genes in the entire network. L1 and S1 have 571 and 605 enzyme-coding genes, respectively. Of these, 529 enzyme-coding genes are common between the two communities, which shows a significant overlap. There are a few enzyme-coding genes which are present in L1 but not in S1 such as aminoacyl-tRNA hydrolase (PTH1) or glutamate 5-kinase (PRO1). Similarly, for genes that are present in S1 but not in L1, sulfuric ester hydrolase (BDS1) is an example. Since both Louvain and Spinglass find 9 non-overlapping communities, all enzyme-coding genes are part of one of the communities.p-value is ribosome which is a complex molecule made of ribosomal RNA molecules and proteins. There are 151 genes enriched in L2 and 141 genes enriched in S2 for this pathway. Of these, 139 genes are common (a 92% overlap). Similar trend is observed for other pathways as well, e.g., there is a 95% overlap between L2 and S2 for Spliceosome and 95% overlap for RNA transport.Table The GO term enrichment results shown in Additional file Additional file L4 and S4 are 81% similar to each other based on Table Additional file In this subsection we will compare the methods that are most dissimilar to each other, namely Louvain and Leading Eigen. As Table p-value is metabolic pathways with 346 genes enriched in L1 and 253 genes enriched in LE4. Of these genes, 224 genes are common between the two communities which is a 65% overlap. In contrast, the first pathway of Table p-value for the pathway is higher than the defined cut-off of 0.01. Counting all genes for all pathways yields 406 unique genes for L1 and 273 unique genes for LE4 and of these, 239 genes are common between the two communities which is a 59% overlap. Based on GO term enrichment analysis shown in Additional file The first pathway of Table Based on Table Six methods, namely, Combo, Conclude, Fast Greedy, Leading Eigen, Louvain, and Spinglass, have been applied to the Human PPI network with 20,644 nodes and 241,008 edges. Although all of them were able to find communities, we will not consider the results of Conclude because it finds 495 communities, many of which are very small communities with less than 50 nodes. For Combo and Spinglass, since they use a random number generator in the procedure of finding communities, we ran them 10 times with 10 different seeds between 0 and 10,000 and used the results from the run with the largest modularity. Modularity scores and the number of communities detected in each run for Combo and Spinglass are summarized in Table After finding modularity scores and communities for 10 runs, we selected communities corresponding to the largest modularity score which is 0.3735 for Combo (11 communities) and 0.3729 (21 communities) for Spinglass.The results of comparing all methods excluding Conclude are presented in Table p-values less than 0.01) are illustrated in Fig. From Table As seen in Table As seen in Fig. p-values less than 0.01 for L1 and S1. Comparison of Figs. Next, we will compare Louvain and Spinglass. The results of comparing the top 10 pathways for L1 and S1 are summarized in Table In this sub-section, we will compare communities detected by Louvain for the Yeast PPI network and communities detected by the same method for the Human PPI network. Louvain could find 9 communities with sizes ranging from 4 to 1538 for the Yeast PPI network  and 14 communities with sizes ranging from 3 to 3585 for the Human PPI network. Using biomaRt package of R , we wereAs seen in Table Q) whereas Spinglass tries to minimize the Hamiltonian (H). However, it has been shown that there is a relation between Q and H as Q. Still, since they use different algorithms to optimize their objective functions, the results are not exactly the same. Combo also tries to maximize modularity but in a different way than that in Louvain, thus resulting in slightly different communities as compared to those obtained by the Louvain method.As mentioned in the Results section, Louvain and Spinglass are most similar to each other for the Yeast PPI network Table . Louvainp-values less than 0.01) for L1 and S1 (black columns), and for L1 and LE4 (grey columns). As seen in Fig. Table KEGG pathway enrichment results for communities detected for the Yeast PPI network show that almost all pathways of each community belong to one broad function. For example, the first community of Louvain mostly includes pathways related to metabolic processes, the second community consists of pathways related to genetic information processing. On the other hand, the functions/pathways represented by communities detected for the Human PPI network are somewhat mixed and include several broad biological functions. Vis-a-vis the functional similarity of the methods, for the Human PPI network, Combo and Spinglass are similar, e.g., Fig. In order to confirm that the size of communities detected by different methods are reliable, we found sub-communities of the communities detected by Combo, Louvain and Spinglass for the Yeast PPI network and analyzed the results to see if detected sub-communities of one community include pathways related to different biological functions or to the same one as the main community. As an example, most pathways of L1 belong to metabolic processes and the pathways for its sub-communities also belong to metabolic processes. Due to the result of this comparison and other comparisons for all communities and sub-communities detected by Combo, Louvain and Spinglass, we can conclude that the size of communities detected are reliable.p-values are larger than the cut-off of 0.01. As seen in these tables, most enriched genes in each pathway belong to one community and the corresponding pathway is also significantly enriched. There are only a few exceptions such as metabolic pathways  and one or two other (dissimilar) methods, and compare and interpret the results to obtain a consensus best method.Remove 1% of nodes randomly .Find the communities of the new network using Louvain method.From the communities of the original network, delete the random nodes of step 1.Calculate the Jaccard index matrix between the communities obtained in steps 2 and 3. We considered all communities with more than 100 nodes.Compute the maximum value for each column of the Jaccard index matrix.Compute the average of the resulting row-vector.We also analyzed the robustness of communities obtained by Louvain method for small perturbations in the network. Essentially, the network is randomly perturbed by deleting some nodes (and edges involving them) and the communities are identified. This is carried out 100 times to assess the robustness of the communities. First, the communities of the original Yeast PPI network are identified using Louvain method. Then, the following steps are repeated 100 times:After performing the above steps 100 times, we have the vector of average of column-wise-maximum (avg-max) of Jaccard index values. Then, we generate scatter plots of avg-max. The scatter plots of avg-max for the Yeast and the Human PPI networks are shown in Fig. The mean and standard deviation of the avg-max vector are 72.21 and 9.02%, respectively for the Yeast PPI network, whereas, for the Human PPI network, they are 60.11 and 7.14%, respectively. These relatively large numbers for the mean suggest that the communities identified by Louvain method are robust to small perturbations. We repeated the process for Leading Eigen. The mean and standard deviation of the avg-max vector for the Yeast network is 53.4 and 5.63%, respectively. Thus, Louvain is a better method, at least for the Yeast PPI network; for the Human PPI network, Leading Eigen finds only two or three very large communities, making avg-max artificially high (98%).The PPI networks that we used in our analysis were from BioGRID and included both physical and genetic interactions (combined network). Hence, we have also applied the various approaches for finding communities to a Yeast PPI network comprising of only physical interactions, which has 6298 nodes and 83,788 edges, to find out if our broad conclusions based on the combined network are still valid for the physical interaction-only network. Additional file We have compared the various methods using three topological metrics  with respect to the physical interaction-only network. The results for these comparisons are given in Additional file 2-value suggests good agreement between the two degree distributions.Two main results from Additional file We wanted to find out if the Q value for the different methods could be improved by optimizing their parameters, if any, or if their results varied across different runs. Of six methods, three of them, namely Combo, Conclude and Spinglass used a random number generator in the procedure for finding communities, although they do not have any parameters to be optimized. We carried out 10 repeats of Combo, Conclude and Spinglass on the combined Yeast PPI network to assess the variation in Q across the runs. Additional file We selected the run with the highest modularity for Conclude method and performed KEGG pathway enrichment analysis. Then we compared these enrichment results with the enrichment results for the communities from the Conclude method reported earlier. Although the size of communities are a little different, the broad categories of pathways for majority of the communities are still the same. For example, there is one community in both runs which has pathways mainly related to metabolic processes. Additional file Spinglass method uses simulated annealing in its procedure. Hence, we ran it 10 times with 10 different start and stop temperatures and cooling factor, but the default values in the igraph package yielded the best result in terms of the largest modularity. Overall, at a broad level, we found that in our case studies, the methods providing well-interpretable communities also resulted in near-optimal (largest) Q values. The fact that the Q value for Conclude in one of the runs is slightly higher (0.29) than those for Combo and Spinglass (0.265) does not violate this conclusion because some of the communities from Conclude are also well-interpretable. However, we note that the Q values across different runs vary substantially for Conclude as compared to those for Combo and Spinglass, suggesting that Combo and Spinglass methods are likely more robust than the Conclude method.In this paper, we tested six methods to detect communities within the Yeast and Human PPI networks. An in-depth comparison of communities detected by these different methods has led us to conclude that Louvain and Spinglass are most similar for the Yeast PPI network whereas Combo and Spinglass are most similar for the Human PPI network. In terms of finding communities that include core pathways based on KEGG pathway and GO term enrichment results, Combo, Louvain and Spinglass were able to find similar communities in which important biological functions and pathways were enriched. For the Yeast PPI network, all genes from the network belonging to a pathway also generally belong to only one or two communities. In terms of running time or computational complexity, for the Yeast PPI network, Louvain was the fastest method and Combo was faster than Spinglass. For the Human PPI network, Louvain was much faster than Spinglass, and Spinglass was faster than Combo. Overall, Combo, Louvain and Spinglass provide reasonable results for community detection in biological networks. Their corresponding modularity values were also among the highest, except that Conclude yielded slightly better modularity for the Yeast PPI network in some runs; variation in modularity for Conclude was much larger than that for Combo and Spinglass across multiple runs. Overall, since Combo and Spinglass use stochastic search in their procedure and their running time is also more than that for Louvain, Louvain is likely the best method to find reasonably sized communities for biological networks in a reasonable time. While we applied these methods to PPI networks, we expect the broad results to be applicable to other types of networks such as gene-coexpression networks and hybrid/integrated networks.G where n = {n1, n2, …, n|n|} is an ordered set of nodes and m a subset of n*n, is the set of edges; for convenience, here, n and m represent sets. In our case studies on the Yeast and Human PPI networks, each node represents an Entrez gene ID and each edge represents an interaction between two nodes. By finding communities, we imply the segregation of nodes into groups such that there is a higher density of edges within each group than between groups. Although there are many algorithms for detecting communities, we selected six algorithms that performed well in terms of finding core pathways in biological networks with several thousands of nodes and hundreds of thousands of edges within reasonable computing time .The focus of this work is on undirected, unweighted and connected graphs defined as Each of these algorithms tries to optimize an objective function which in most cases is modularity. However, two algorithms with the same objective function will generally yield slightly different communities using different amounts of run time if they use different optimization strategies. The algorithms that will be briefly described below are: Girvan-Newman , 7, FastCalculate betweenness score for all edges in the network. Betweenness is a measure that favors edges that lies between communities and disfavors those that lie inside communities. While there are many measures to find betweenness, Girvan-Newman algorithm uses the fast algorithm of Newman to find betweenness scores .Find the edge that has the maximum value of betweenness and remove it from the network.Recalculate betweenness for all remaining edges in the network and repeat from step 2 for the new scores until there are no edges remaining.This is a divisive algorithm for identifying communities in networks where edges are iteratively removed based on the value of their betweenness. The steps of the algorithm are as follows , 7:CalcuAij is the weight of the edge between node i and j , ki is the sum of the weights of the edges attached to node i or degree of node i, ci is the community to which node i belongs to and the δ function is defined as δ = 1 if u = v and 0 otherwise. Local peaks in the modularity during the process of community detection indicate good divisions of the network into communities. While using this algorithm gives good results in many cases, its computational complexity is O(m2n) or O(n3) on a sparse graph, where n is the number of nodes and m is the number of edges. This makes it impractical for very large graphs with several thousands of nodes and hundreds of thousands of edges.The output of this algorithm is a dendrogram that captures the possible divisions of the network into communities. In order to select the optimal division among all possible options, Modularity (Q) is used.i and j) corresponds to replacing the ith and jth rows and columns of the adjacency matrix by a single row and column formed by their sum, respectively; the record of the list of nodes in the communities formed thus far is updated. In the algorithm proposed by Newman [Q) and finding the pair i, j with the largest gain is time-consuming. Hence, here, instead of using the adjacency matrix and calculating ΔQij, a matrix of ΔQij values is initialized and updated directly. For sparse matrices, e.g., adjacency matrices for large networks, this results in substantial reduction in computation. The following parameters have to be set initially:i. The next steps are as follows:Qij and ai based on Eqs. H, which contains the largest element of each row of the matrix ΔQij along with the labels i, j of the corresponding pair of communities.Calculate the initial values of ΔQij from H, combine the corresponding communities, update the matrix ΔQ, H and ai  involves finding the changes in modularity that results from combining pair of communities, selecting the combination yielding largest gain in modularity, and implementing the combination of the corresponding pair . At the y Newman , this opA, we will be able to perform updates in step 2 quickly and we need to only adjust a few elements of ΔQ. If communities i and j are joined together, labeling the combined community as j, we update the jth row and column, and delete the ith row and column altogether. The update rules are as follows:Due to the sparsity of the original adjacency matrix k is connected to both i and j, then:If community k is connected to i but not to j, then:If k is connected to j but not to i, then:If a: To update O(m.d.logn) for a network with n nodes and m edges where d ~ logn is the depth of the dendrogram. For sparse networks (m ~ n), the running time is O(nlog2n), which is essentially linear [Fast Greedy algorithm runs in time y linear .For each source community, the best possible repartition of every source node into each destination community (either an existing community or a new community) is calculated. It would be possible that the source community totally joined the destination community in this step.The best merger, split, or recombination is performed.Most community detection algorithms use one of the following steps in the process of finding communities: they may join two communities, split a community into two, or move nodes between two distinct communities. Combo involves all three possibilities . After sThe basis of Combo is the selection of the best repartition of nodes between two communities. For each pair of source and (maybe empty) destination communities, a shift of all the nodes using Kernighan-Lin algorithm  is perfoi in the list which when switched to another community results in the largest gain in modularity.Find the node i to the other community, remove it from the original list and save the intermediate result.Switch For each starting configuration, a series of Kernighan-Lin shifts  is iteraAfter performing a series of Kernighan-Lin iterations for each of the starting configurations, the intermediate result with the best score in terms of objective function (modularity) is selected.O(n2logc) where n is the number of nodes and c is the number of communities in the network [Combo outperforms all other known algorithms when the objective function is modularity. However, it has limitations on the size of the network it could handle within a reasonable time, which is currently around 30,000 nodes and is not a serious limitation for most biological networks. When the objective function is description code length, Combo’s results are similar to Infomap (which will be described later in this section) in most cases. Since the sequence of operations depends on the specific network, obtaining exact evaluations of the computational complexity of Combo is difficult, but the upper bound is  network .i from its community and placing it in one of its neighboring communities. The gain of modularity in moving node i into a community C can be computed by:in is the sum of the weights (or count for un-weighted networks) of the edges inside C, Ʃtot is the sum of the weights of the edges incident to nodes in C, ki is the sum of the weights of the edges incident to nodes i (degree of i), ki,in is the sum of the weights of the edges from i to nodes in C and m is the sum of the weights of all the edges in the network. If the gain is positive, the node i is placed in the community for which the gain is maximum. This process is applied repeatedly for all nodes until no further improvement can be achieved.This algorithm detects communities in large networks by maximizing modularity and is much faster as compared to other methods , 37, 38.O(nlogn)) and could be even faster by using some heuristics, e.g., stopping the first phase when the gain of modularity is less than a given threshold [The second phase is to build a network whose nodes are now the communities detected during the first phase. In order to perform that, the weights of the edges between the new nodes are given by the sum of the edges between nodes in the corresponding two communities. Edges between nodes of the same community result in self-loops for this community in the new network. When this phase is completed, the first phase of the algorithm is reapplied to the new network. The combination of these two phases is referred to as a “pass”. The passes are iterated until a maximum of modularity is reached. This algorithm is extremely fast  algorithm  on nodeG and the array of weights from the previous step. It uses the following equation  is the probability of selecting the edge e in a random simple κ-path originating from an arbitrary source node s. The symbol N(i) is the set of neighbors of the node i and CN indicates the subset of neighbors common to i and j.Δ containing all pairs of distances between nodes.The output of this step is a matrix 3.Δ to find communities of G.Finally, apply Louvain method  on matriM), defined as,The Infomap approach closely follows the Louvain approach ; neighboL(M). The equation comprises of two terms: first is the entropy of the movement of nodes between communities and second is the entropy of movements of nodes within communities. Further details about this equation can be found elsewhere [The aim of Infomap is to minimize the lower bound, lsewhere .L(M) (Eq. L(M), the node will stay in its original community. This procedure is repeated in a new random sequential order each time until no move could decrease L(M). In each iteration, the nodes of the new network are the communities found at the last level and the process of joining nodes into communities is repeated on the new network until L(M) cannot be reduced further. The computational complexity of Infomap is a linear function of the number of edges, i.e., O(m) [Each node is initially assigned to its own community. Then, in random sequential order, each node is placed into the neighboring community that results in the largest decrease in L(M) Eq. . If no me., O(m) , 39.A is the adjacency matrix, ki is the sum of the weights of the edges attached to node i (or degree of node i), kj is the degree of node j and m is the total number of edges. The modularity matrix is a characteristic property of the network and is independent of any division of the network into communities. The procedure of finding communities of a network with this method consists of finding the eigenvector corresponding to the most positive eigenvalue of the modularity matrix, and then dividing the network into two groups based on the sign of the elements of the eigenvector. Defining an index vector, s, the sign of elements are:ui(1) is the ith element of u1 . The nodes with positive sign form one community and the rest of the nodes form the other community. To avoid dividing the network into only two communities, an n  by c (the number of non-overlapping communities) index matrix S has to be defined. Each column of this matrix is an index vector of  elements, such that:Leading Eigen method  is also The modularity of this division of the network is then equal to:1/(2 m) but since it has no effect on the position of the maximum of the modularity, it has been omitted from the equation. Writing B=UDUT where U = (u1|u2| …) is the matrix of eigenvectors of B, and D is the diagonal matrix of eigenvalues Dii = βi, Q can be written as:This form of modularity is different from other forms in a leading multiplicative constant Q, but now, there is no constraint on the number of communities, c [The aim is still maximizing the modularity ities, c .c) penalizing existing edges between different communities and d) rewarding non-links between different communities. The following equation  in a network. The minimization is carried out by using simulated annealing on the entire network. This method is rather fast and the computational complexity is approximately O(n3.2). However, it cannot be used for disconnected networks as there is no guarantee that nodes from disconnected parts of the network also have different spin states and belong to different communities.In this method, the community structure of a network is described as the spin configuration that minimizes the energy of the spin glass (Hamiltonian) with respect to the spin states (the community indices) . Similartion Eq.  satisfiepij as γ = 1 in Eq. Substituting mentclass2pt{minimIt is clear from Eq. Table To compare different methods, we used three metrics, namely, Rand Index (RI), Adjusted Rand Index (ARI), and Normalized Mutual Information (NMI). We also used Jaccard Index for measuring similarity between different communities. These metrics are based on topological similarities of the communities identified and hence are relevant for biological networks; we expect that topologically similar communities will likely yield similar biological interpretations.A and B [n11 be the number of pairs of nodes from a network G which are both in the same community detected by method A and are also in the same community detected by method B. Let n00 be the number of pairs of nodes from G which are in different communities in A and are also in different communities in B. n00 and n11 are interpreted as agreements in the classification of the nodes from a pair. Accordingly, two disagreement quantities n01 and n10 are also defined: n01 (n10) is the number of pairs of nodes from G which are in the same community detected by method A (B) but they are in different communities detected by method B (A). Then, Rand Index (RI) is given by [Rand proposes a simple measure of agreement between the results of  two methods A and B . RI reprgiven by :17\documN is the total number of nodes). RI is not a normalized quantity, e.g., the upper bound is 1 but the lower bound is more than zero (network dependent). Due to this lack of normalization, Hubert and Arabie [As seen from Eq. d Arabie  suggesteA and B where rows correspond to the communities in A and columns correspond to the communities in B. Nij, the th entry in this matrix, is the number of nodes in both community i of method A and community j in method B. Denote by Ni. the sum of all columns for row i; thus Ni. is the number of nodes in community i of method A. Define N.j to be the sum of all rows for column j, i.e. N.j is the number of nodes in community j in method B. The Adjusted Rand Index (ARI), is calculated from the values Nij of the confusion matrix for the two methods as follows [cA and cB are the number of communities detected by methods A and B, respectively.ARI is equivalent to a normalized Rand Index. Consider a confusion matrix for methods  follows :18\documA and B are the methods being compared. The terms used in this equation are the same as those used in the equation for ARI . NMI is the normalized form of Mutual Information (MI). MI measures similarity between the results of two methods and is given by :19\docum ARI Eq. . Then, N0 to 1 and is defined as the size of the intersection (overlap) divided by the size of the union of the sets:A and B and the denominator is the number of all the elements in A and B combined.Jaccard index is a measure of similarity for two sets of nodes, with a range from Applying the above methods to PPI networks yields different number of communities with different number of nodes. The communities detected are compared in two ways: topological comparison and functional comparison. In topological comparison, methods are compared using different metrics . Based on the results of these metrics, we are able to figure out which methods are similar to each other and which are dissimilar. When a method is compared with itself, RI, ARI and NMI are 1. Larger  the value of metrics, more (less) similar are the two methods being compared. After finding which methods are similar to each other from a topological perspective, functional comparisons  have been used to further assess the functional similarity of the communities identified by these methods. Figure Additional file 1:Supplemental Tables S1-S31. (XLSX 7912 kb)