Nevertheless, their avalanche characteristics are indistinguishable. The energies, areas and perimeters of the switched regions are power law distributed with exponents close to predicted mean field values. At the coercive field, the area exponent decreases, while the fractal dimension increases. This fine structure of the switching process has not been detected before and suggests that switching occurs via criticality at the coercive field with fundamentally different switching geometries at and near this critical point. We conjecture that the domain switching process in ferroelectrics is universal at the coercive field.Field induced domain wall displacements define ferroelectric/ferroelastic hysteresis loops, which are at the core of piezoelectric, magnetoelectric and memristive devices. These collective displacements are scale invariant jumps with avalanche characteristics. Here, we analyse the spatial distribution of avalanches in ferroelectrics with different domain and transformation patterns: Pb(Mg While classical approaches rely on the study of individual ferroelectric domain wall movement on long time scales, the authors consider collective movements of domain walls during short time scales, characterized by discrete jumps, as indicators of avalanches on a broad range of scales. Furthermore, the recent research on two dimensional functionalities offered by ferroelectric domain walls17 will find further applications once strategies to dynamically deploy the functionalities, through the motion of domain walls, have been found.In ferroelectric materials, domain walls separate regions with different polarization directions. Their dynamical behaviour is subject to intense fundamental and applied research as it is at the core of ferroelectric switching20. The second one aims to understand collective movements during short-time scales22. It considers discrete impulsive jumps, or ‘jerks’, occurring during the motion of domain walls, as indicators of avalanches on a broad range of scales. In such ferroelectric avalanches, any switching event is likely to trigger subsequent switching, and anisotropic long-range interactions between local events are essential, in contrast with classical microscopic ferroelectric models24. This approach is particularly relevant for the development of neuromorphic computing architectures25 where maximal computational performances are achieved through scale-invariant avalanches that develop at a critical point27, similar to neuronal avalanches observed in the brain28. The key question is whether this switching dynamics is a universal process in ferroelectrics with little or no influence from symmetry or structural features of domain walls.Therefore, understanding the response of domain walls to electric fields is particularly appealing. With this aim, two distinct approaches have been developed. The first one relies on the study of individual domain wall movement on long-time scales. It describes the nucleation and growth of domains and their interaction with defects, interfaces and existing domain walls29, which is one of the signatures of scale-free processes, and atomistic simulations show that avalanches are induced by kinks and domain walls junctions32, as well as defects acting as pinning centres33. Ultraslow processes have been modelled34 and reveal that many of the relevant ferroelectric parameters, e.g., the size of the switching events, follow power-law dependences under switching conditions. In order to confirm the origin of the avalanches, optical visualization is required and has been successfully applied during the phase transition of martensitic materials37 and during switching in magnetic thin films38, but not in ferroelectric materials where avalanches are usually studied through indirect methods, e.g., acoustic emission22 or displacement current measurements40. Previous to these observations, avalanche studies already revealed the stepwise behaviour of domain wall movements under electric fields but did not lead to a quantitative analysis of avalanche characteristics43.Mean-field (MF) theory applied to ferroelectrics predicts the power-law distribution of jerks3 (BTO), for which avalanches have already been studied with acoustic emission22, and monoclinic Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN-PT) close to the morphotropic boundary44. They show very different ferroelastic domain and transformation patterns: BTO is dominated by parallel straight charged domain walls , while in PMN-PT straight walls intersections lead to complex domain walls, which are often bent, forming needle and junction patterns whose switching differ greatly depending on the starting domain structure46. Our optical observations bring the experimental evidence that avalanches are triggered at kinks and domain wall junctions. Furthermore, our ability to image directly the avalanches gives us the possibility to explore the spatiotemporal changes of the ferroelectric domain pattern to identify switched regions. We find that the areas of the switched regions, their energies and perimeters are power law distributed with power-law exponents close to the predicted MF values. We also show that during ferroelectric switching, the fractal dimension of the switched regions increases and reaches a maximum at the coercive field. This fine structure of the switching process has not been detected before. Our results suggest that the change of the fractal dimension is the key observable to understand ferroelectric domain motion under electric field and that switching occurs via criticality at the coercive field with fundamentally different switching geometries at and near this critical point. This behaviour is seen in PMN-PT and BTO so that we conjecture that the overall domain switching process in ferroelectrics may be universal and show little dependence on the details of the actual domain patterns.In this work, we combine optical microscopy and statistical analyses to characterize the motion of ferroelastic domain wall during ferroelectric switching in two ferroelectric materials: tetragonal BaTiOFigure 32. These patterns differ greatly from the domain patterns in BTO . We also determine the perimeter P of the switched regions. Scaling P as a function of A yields the Hausdorff dimension HD with 47, Supplementary Notes τ assuming a power-law distribution of the area with the probability distribution per area interval PDF(A) ~ Aτ−, as shown in Fig. τ = 1.7 while the overall exponent is above 2. By comparing Fig. τ and HD is seen when the number of switched regions is high. In the creep regime, at high voltages, we observe few small changes of the domain patterns. The same behaviour, including the anticorrelation between τ and HD, holds independently of the domain pattern in any of the analysed regions. In particular, in PMN-PT, the upper part of the sample—dominated by straight walls—and the lower part of the sample—dominated by needle and junction patterns—behave similarly , while τ increases in the vicinity, but away from the coercive field value (regime 2). The τ-values in the creep regime (regime 3), where the jerks are uncorrelated and do not represent power laws, are approximated by the asymptotic behaviour of the slope near the upper value of the areas (respectively energies or perimeters) in the PDF curves. These values have no direct physical meaning besides showing that in this regime no significant switching occurs. The Hausdorff dimension in this regime is HD = 1.In Figs. τ we find the maxima of HD. The minimum value of τ is 1.7 (energy exponent ε = 1.3) in both materials, the corresponding Hausdorff dimension is ~1.8. The changes of the domain patterns are highly fractal and contain a multitude of large regions with rough surfaces, which contribute greatly to the increase of the number of avalanches at minima in τ , where avalanche behaviour related to the movement of non-ferroelastic 180° domain walls have been observed (but not quantified)52, it is possible that secondary local strain53 accompanying the movement of domain walls plays a role. In fact, in magnetic systems, it has been shown that even magnetic Barkhausen noise depends explicitly and strongly on strain coupling55.Strain fields, which are long ranging and anisotropic, induce correlations that are a key element in avalanchesε decreases before failure58, sometimes down to the MF value ε = 1.3, when the system reaches the critical point58 while the rate of energy released diverges61.We note that our observations for ferroelectrics are also consistent with results obtained in other critical systems, e.g., during the failure of materials where the energy exponent 22. The closeness of the avalanche characteristics with those predicted by MF theory62 is remarkable. Surprising and somewhat counterintuitive is the observation that fine structures appear during the switching process. The presumed critical point of the switching process is the coercive field. At the coercive field, the area and energy exponents correspond to an unrelaxed MF value , while the fractality is maximum with HD = 1.8. In the creep regime, far away from the main switching, the areas are exponentially distributed which indicates uncorrelated noise and HD = 1. In between these two regimes, the switching progresses with exponents near the field integrated MF model with ε = 1.6 and τ ~ 2.2. The switching activity in this regime is reduced but spreads over a longer time so that the overall switching follows ε = 1.6 and τ = 2.2. We do not observe exponent mixing as could be expected63 but our experimental resolution is probably insufficient for the investigation of mixing. Furthermore, the mixing proceeds not simply via two fix points with two exponents but via a continuous distribution of exponents which increase continuously from ε = 1.3 and τ = 1.7 to greater values. Simultaneously HD decreases, which implies that the switched regions become more compact, with interfaces that are much smoother than those at the critical point. At these late stages of the switching process, smooth domain walls progress without much change to their shape. The universal framework presented here suggests operating ferroelectrics close to the coercive field, where criticality and scale-invariant avalanches develop, maximizing their properties.We have shown that ferroelectric/ferroelastic switching progresses via avalanches in two typical ferroelectric materials. We are able to correlate the visible domain switching with predictions of avalanche theory and show the close agreement with the results of previous measurements of acoustic emission in BTOx)[Pb(Mg1/3Nb2/3)O3]−x[PbTiO3], x = 0.32, is a commercial sample from Atom Optics Co., Ltd , with dimensions 5 × 1 × 0.5 mm. The BTO (111) sample is from MTI corporation (USA), with dimensions 6 × 1 × 1 mm.The PMN-PT (001) sample, with composition  and the [−110]pc direction for BTO (1-mm-thick) with two silver-paint electrodes on the sides of the samples. We used a picoammeter (Keithley 6487) to measure the displacement current of the sample while cycling the applied electric field . The results presented are obtained after more than 10 cycles to avoid ‘virgin’ effects.We visualized the ferroelectric domain structure with an optical microscope in transmission mode (Leica), using an objective with magnification ×20 and numerical aperture 0.4. The experimental setup is described in ref. Keithley 487 to meJij in intensity as a function of time are defined as (1):Bij is the intensity at each pixel . The areas A of the switched regions are defined as topological connected entities where the values of Jij are greater than a threshold. Detailed analysis shows that these regions contain an almost constant intensity  as slopes of the log–log PDF curves and independently by the maximum likelihood method64 (Supplementary Note For exponents, we use p contains the normalized histogram counts of switched pixels and we fit its evolution with the avalanche occupancy with a parabolic function, following percolation theory65 (Supplementary Notes We compute the entropy of the avalanche images as entclass1pt{minimaSupplementary Information


Entropy and relative entropy measures play a crucial role in mathematical information theory. The relative entropies are also widely used in statistics under the name of divergence measures which link these two fields of science through the minimum divergence principle. Divergence measures are popular among statisticians as many of the corresponding minimum divergence methods lead to robust inference in the presence of outliers in the observed data; examples include the  P and Q are two probability measures on a measurable space p and q, respectively, with respect to a common dominating P is defined asP and Q is given byU is the uniform measure on P within a suitable convex set Q [Q, namely its forward projection, and other geometric properties of Decision making under uncertainty is the backbone of modern information science. The works of C. E. Shannon and the development of his famous entropy measure ,2,3 reprguessing ,15. In gbility Q ,17. The ure; see ,27,28,29f-entropies [Although the maximum entropy or the minimum divergence criterion based on the classical Shannon entropy atistics ,41,42,43atistics ,45 which order α  and coveexample, ,54,55,56ntropies , the Tsantropies  as well -entropy ,60 among-entropy ,68,69,70P and a (prior) mismatched compressor distribution Q, the penalty in the normalized cumulant of compression length is not P and Q and coincides with the KLD at We have noted that there is a direct information theoretic connection of KLD to the Shannon entropy under mismatched guessing by minimizing the expected compressed length. However, such a connection does not exist between the Renyi entropy noted by ,71. Hereology of  and has recently ,73; see only, by  while deonly, by . Later aonly, by  as the lonly, by ,74. Fujionly, by , Fujisawonly, by  have alslogy of [REα:Motivated by the substantial advantages of the minimum LDPD inference in terms of statistical robustness against outlying observations, Maji et al. ,79 have amily by . As showamily by ,79, the Relative ” and study its properties for different values of The statistical benefits of the LSD family over the LDPD family raise a natural question: is it possible to translate this robustness advantage of the LSD family of divergences to the information theoretic context, through the development of a corresponding generalization of the relative tropy in ? In thisS-divergence measures. These divergence measures are known to generate more robust statistical inference compared to the LDPD measures related to the relative We present a two parameter extension of the relative asure in  motivateIn the new formulation of the relative As a by-product of our new formulation, we get a new two-parameter generalization of the Renyi entropy measure, which we refer to as the Generalized Renyi entropy (GRE). This opens up a new area of research to examine the detailed properties of GRE and its use in complex problems in statistical physics and information theory. In this paper, we show that this new GRE satisfies the basic entropic characteristics, i.e., it is zero when the argument probability is degenerate and is maximum when the probability is uniform.Here we provide a detailed geometric analysis of the robust LSD measure, or equivalently the relative We also study the convexity of the LSD measures  under constraints in order to determine an optimal probability assignment leads to inconsistencies for information measures other than the Kullback-Leibler divergence. See, for instance ,94,95,96ions, by ,79; in tP and Q is obtained as a function of the Cressie-Read power divergence measure [P and Q is defined asP with respect to Q can be obtained asIn order to motivate the development of our generalized relative ollowing . Conside measure , definedfined in . Note the family ,102,103 the formDλ=Din =mulation . We ofteP and Q, respectively. Instead of considering the re-parametrization We can now change the tuning parameters in the formulation given by  suitablyfined in  which enon as in , after sDefinition 1 (Relative .Given any The cases quations  and 16)β=0 and λA straightforward simplification gives a simpler form of this new relative follows.REα,β.Ω, we define the generalized Renyi entropy (GRE) of order For any probability measure P over a measurable space Note that, at The GRE is a new entropy to the best of our knowledge, and does not belong to the general class of entropy functionals as given in  which coTheorem 1 (Entropic characteristics of GRE).Ω, we have For any probability measure P over a finite measure space 1 Ω (no uncertainty).2 Ω (maximum uncertainty).if P is uniform over Example 1 .Consider distributions With the new entropy measure, GRE, the entropy of the normal distribution Interestingly, the GRE of a normal distribution is effectively the same as its Shannon entropy or Renyi entropy up to an additive constant. However, similar characteristic does not hold between the relative entropy (KLD) and relative whereas the general relative Note that the relative Example 2 .Consider the exponential distribution P having density A simple calculation leads to the following form of the our new GRE measure of the exponential distribution P.Once again, the new GRE is effectively the same as the Shannon entropy or the Renyi entropy, up to an additive constant, for the exponential distribution as well.Further, if for P and Q on Before concluding this section, we study the nature of our relative vergence  given byications  which caWe start the exploration of the geometric properties of the relative opy from ,73 to ouProposition 5.For a given Proof. First let us consider any llowing  equipped with the counting measure μ, all integrals in the definition of Whenever Remark 3.Ω, the function For a general infinite space ark 3 of . HoweverProposition 6.For a given Proof. Fix an sed from  as(25)R5 using D−(λ+1)(qombining  through Remark 4.Ω is finite (discrete) and is equipped with the counting measure μ, the function As in Remark 2, whenever p. For general It has been shown in  that theTheorem 2.For any given Proof. Note that, at ion 5 of ; so we wu, we finally get Now, from , we have, we getsign(βλ)∫REα,β.Fix Proof. It follows by using the Jensen’s inequality and the convexity of the function q over a different power transformed space of densities. This leads to the following theorem.Next, note in view of Proposition 4 that, for any Theorem 3.For any given Remark 5.Note that, at Motivated by the quasi-convexity of -entropy ; the pro-entropy  with necTheorem 4 (Pythagorean Property).Fix an (i) Suppose (ii) Suppose Proof of Part (i).Let ).Thus,  is equivOnly if statement: Now, let us assume that roof of =lime we gett′(0)=∫p0If statement: Now, let us assume that | view of , this imProof of Part (ii).if statement follows directly from Part (i).Note that the only if statement, we first show that c is a constant. Similarly one can also show that To prove the nd using , we get Therefore, we can apply Part (i) to conclude thatproof of . Now, ifREα,β|βqα−λdμ,and sign(ply thatsign(βλ)|βqα−λdμ,and sign(46)REα,βNote that, at rem 9 of . HoweverThe forward projection, i.e., minimization with respect to the first argument given a fixed second argument, leads to the important maximum entropy principle of information theory; it also relates to the Gibbs conditioning principle from statistical physics . Let us Definition 3 τDλ, i.e.,limn→∞∫|pq on Next, as in the proof of  at the empirical data distribution and minimize the relative entropy with respect to the model family of distributions in its second argument. The resulting estimator, commonly known as the minimum distance or minimum divergence estimator, yields the reverse projection of the observed data distribution on the family of model distributions with respect to the relative entropy or divergence under consideration. This approach was initially studied by ,11,12,13G having density g with respect to some common dominating measure g by a parametric model family of g and g and G, say g in the LSD sense. In fact, for g on the model family Suppose we have independent and identically distributed data i et al.  have conguage of ,79. Noteduced by  in termsCorollary 2 .θ.Consider the above parametric estimation problem with (1) Suppose (2) Suppose Further, under standard differentiability assumptions, we can obtain the estimating equation of the MRE functional given by∫fθαuθdμ∫ α and β ,79 as weg and the resulting value of the MRE functional is called the minimum relative g given by the relative frequencies A; the corresponding MREE is then obtained by solving , herg having support m. We model g by the Binomialthe formTn,α,β(2)The same approach can also be used to develop robust tests for more complex hypothesis testing problems based on the relative ion from  and 64)-entWe have explored the geometric properties of the LSD measures through a new information theoretic formulation when we develop this divergence measure as a natural extension of the relative It is worthwhile to note that the information theoretic divergences can also be used to define new measures of robustness and efficiency of a parameter estimate; one can then obtain the optimum robust estimator, along Hampel’s infinitesimal principle, to achieve the best trade-off between these divergence-based summary measures ,112,113.ertainty ,71. As a


The ubiquitin‐proteasome system (UPS) governs the protein degradation process and balances proteostasis and cellular homeostasis. It is a well‐controlled mechanism, in which removal of the damaged or excessive proteins is essential in driving signal pathways for cell survival or death. Accumulation of damaged proteins and failure in removal may contribute to disease initiation such as in cancers and neurodegenerative diseases. In this notion, specific protein‐protein interaction is essential for the recognition of targeted proteins in UPS. WW domain plays an indispensable role in the protein‐protein interactions during signaling. Among the 51 WW domain‐containing proteins in the human proteomics, near one‐quarter of them are involved in the UPS, suggesting that WW domains are crucial modules for driving the protein‐protein binding and subsequent ubiquitination and degradation. In this review, we detail a broad spectrum of WW domains in protein‐protein recognition, signal transduction, and relevance to diseases. New perspectives in dissecting the molecular interactions are provided. ACK1activated Cdc42‐associated kinase 1AMOTL1angiomotin like 1BH3Bcl‐2 homology 3BMPbone morphogenetic proteinsCx43Connexin 43CyldCYLD Lysine 63 DeubiquitinaseDMBA7,12‐dimethylbenz(a)anthraceneEGFepidermal growth factorEGFRepidermal growth factor receptorEGR2early growth response 2ENaCepithelial sodium channelGDNF/Retglial cell‐derived neurotrophic factorHECThomologous to the E6‐AP carboxyl terminusHtthuntingtinId1inhibitor of DNA binding 1IRF‐3interferon regulatory factor‐3ITCHitchy E3 ubiquitin protein ligaseJNK2c‐jun N‐terminal kinase 2KLF5Krüppel‐like factor 5LATS1large tumor suppressor 1LPSlipopolysaccharidesMAPKmitogen‐activated protein kinaseMEKK2mitogen‐activated protein kinase kinase kinase 2NDRG1N‐myc Downstream Regulated 1NEDD4the neural precursor cell expressed, developmentally downregulated protein 4NEDD4Lneural precursor cell expressed, developmentally downregulated 4‐likeNEDL1/HECW1HECT, C2, and WW domain‐containing E3 ubiquitin protein ligase 1NEDL2/HECW2HECT, C2, and WW domain‐containing E3 ubiquitin protein ligase 2NF‐kBnuclear factor kappa light chain enhancer of activated B cellsPCPplanar cell polarityPI3Kphosphoinositide 3‐kinasePk1Prickle 1PTENphosphatase and tensin homologRASSF5ras association domain family member 5RBRRing‐Between‐RingRTKsreceptor tyrosine kinasesSH3Src homology domain 3SHHsonic HedgehogSMURF1Smad ubiquitination regulatory factor 1SMURF2Smad ubiquitination regulatory factor 2SOD1superoxide dismutase‐1TACEtumor necrosis factor‐converting enzymeTAK1transforming growth factor beta‐activated kinase 1TGF‐βtransforming growth factor betaTLRtoll‐like receptorTRAP‐δtranslocon‐associated protein‐δTRIFTIR‐domain‐containing adapter‐inducing interferon‐βUPSubiquitin‐proteasome systemWWP1WW domain‐containing E3 ubiquitin protein ligase 1WWP2WW domain‐containing E3 ubiquitin protein ligase 1YY1Yin Yang 11C‐terminus of ubiquitin is transferred to the ubiquitin‐conjugating E2 enzyme. Lastly, the E3 enzyme recognizes the substrate and catalyzes the transfer of ubiquitin from the E2 to the substrate. To date, there are at least 600 E3 ligases for determining the fate of tens of thousands of proteins in the human body.Eukaryotic cells possess at least two proteolytic systems to tackle misfolded or damaged proteins. One is the ubiquitin‐proteasome system (UPS), which is target‐specific and is responsible for most of the proteolytic events. The other one is autophagy, which accounts for approximately 10%‐20% of the cellular proteolysis.C‐terminal HECT domain and the N‐terminal extension, which contains a distinct domain recognizing specific target proteins. There are 51 WW domain‐containing proteins identified in the human proteome. Among them, nine WW domain‐containing proteins are involved in UPS, and these proteins belong to the NEDD4 subfamily of HECT‐type ubiquitin E3 ligase. In other words, all the E3 ligases in the NEDD4 subfamily contain WW domains in their tertiary structures, implying a unique role of the WW domain in determining the substrate specificity and protein‐protein interactions during signaling. Disruption of the normal signaling process might lead to enhanced disease development and progression.In particular, among the E3s, HECT‐type ubiquitin E3 ligases have the 2WW domain is a compact protein module comprising 35‐40 amino acids and two conserved tryptophan (W) residues spaced apart by ~20 amino acids.N‐terminal C2 domain, two to four WW domains, and a C‐terminal HECT domain.2+ stimulation,WW domain‐containing proteins not only play roles in signal transduction, but also participate in regulating protein post‐translational modifications. Certain WW domain‐containing proteins are involved in the UPS. Interestingly, all the WW domain‐containing proteins participate in the UPS belonging to the NEDD4 ubiquitin ligase subfamily,3Failure of protein degradation is the common cause of accumulation of the malfunctioned and/or oncogenic proteins. These aberrant protein aggregates may contribute to tumorigenesis, neuronal diseases. and other devastating disorders.The majority of the tumor cells are originated from the epithelial lineages.3.1The EGFR family of receptor tyrosine kinases (RTKs) plays an important role in epithelial cell homeostasis. The EGFR family includes EGFR/ErbB1/HER1, ErbB2/HER2, ErbB3/HER3, and ErbB4/HER4. Each protein has a distinct role in controlling cellular function. Abnormal EGFR signaling and EGFR amplification cause tumorigenesis and malignancy.s, and thereby lead to a reduced ubiquitination level and increased protein stability of ErbB4/HER4.NEDD4 binds ErbB4/HER4 through its second and third WW domains.C‐terminal PY motif in ErbB3/HER3 for ubiquitination and degradation . Only the isoforms containing the JM‐a domain can be recognized and cleaved by TACE. The m80 is further cleaved by γ‐secretase to produce a soluble 80‐kDa fragment, s80Taken together, WW domain‐containing E3 ubiquitin ligases play an indispensable role in controlling EGFR signaling and maintaining the balance between proliferation and anti‐proliferation function of EGFR. Loss of WW domain‐containing E3 ubiquitin ligases contributes to the imbalanced epithelial proliferation and tumorigenesis.3.2SMURF1 and NEDD4L are involved in the BMP and TGF‐β pathways. SMURF1 recognizes the phospho‐PY motif in Smad1/5 that are phosphorylated sequentially by CDK8/9 and GSK3 . The observations suggest that ITCH maintains the stability and anti‐tumor function of WWOX.In a proteomic screening, ITCH is shown to be a WWOX binding protein.Phosphorylation of a specific amino acid residue(s) outside the WW domain affects protein function and drives the progression of diseases such as cancer and neurodegeneration. For example, when tumor suppressor WWOX is optimally activated, the resulting pY33‐WWOX plays a homeostatic role in maintaining normal physiology and restricts tumor growth.P63 is a substrate for ITCH. Rossi et al 2006) demonstrated that WW domains in ITCH interact with PY motif in p63 and promote p63 ubiquitination and degradation in keratinocytes ‐induced death.In the Notch signaling, binding of the WW domains in WWP2 with the PY motif in Notch3 leads to ubiquitination and degradation of Notch3 protein Figure A. EctopiF Figure C. This i3.8Itch or Cyld gene develops inflammation in numerous tissues such as in lung and spleen.Cyld is susceptible to chemically induced tumorigenesis. In addition, both Itch‐ and Cyld‐deficient mice have a higher frequency in developing lung cancer metastasis. Thus, ITCH‐ and Cyld‐controlled ubiquitination are crucial for the regulation of inflammatory response and tumorigenesis.Switching at the ubiquitination site regulates protein activity. One example is that the switch of ubiquitination site at K63 to K48 in TAK1 terminates the TAK1 activity. ITCH and Cyld regulate this switch. The WW domains of ITCH bind the PY motif in Cyld.4Deficiency of a specific WW domain‐containing protein or alterations in the WW domains affects the binding with ligands. The consequence of aberrant signaling may link to the generation of neurological disorders or other diseases. For example, WWOX deficiency is known to cause severe neural disease, including ataxia, severe early‐onset epileptic encephalopathy, global developmental delay, acquired microcephaly, epilepsy, and early death.4.1C‐terminus of Cx43. MAPK signaling cascade induces phosphorylation of the serine residues at amino acids 279 and 282 in Cx43, which significantly increases the binding affinity of the tandemly aligned WW domains to the phosphor‐PY motif (similar to group IV WW domain substrate). Indeed, the second WW domain of NEDD4 acquires a significantly enhanced binding to the phospho‐PY motif.Connexin 43 (Cx43) is one of the components of gap junction. Loss of Cx43 causes neonatal lethality owing to the defects in the heart and nervous systems during development.C‐terminal PY motif or containing a disrupted consensus PY motif due to missense mutations, possesses an increased sodium channel activity and membrane retention that results in hypertension in Liddle syndrome.In addition to gap junctions, NEDD4 also regulates the amiloride‐sensitive epithelial sodium channel (ENaC) protein level and its activity. Mutant ENaC, lacking the N‐terminus and is significantly upregulated in the brain of PD patients. Loss of NEDD4 increases the susceptibility of neuronal cells to RTP801‐induced cytotoxicity.In Parkinson's disease (PD), reduced expression of NEDD4 in the nigral neurons from the PD brains has been documented.4.2v) are transmembrane proteins that regulate the flow of sodium ions and control the initiation of the action potential. These channels are abundant in nerve and muscle cells, in which ion flow and action potential are critical for sustaining cellular function. From sequence analysis, there are 7 Nav subunits among the 10 Nav having the PY motif at the C‐terminus.v1.5 has been studied extensively. NEDD4L interacts with the C‐terminal PY motif and promotes the ubiquitination and degradation of Nav1.5 in HEK293 cells.Voltage‐gated sodium channels . Interestingly, NEDD4L expression is downregulated after nerve injury and results in the accumulation of Nav1.7 and Nav1.8 in DRG, where enhanced sodium influx causes neuron excitability and hypersensitivity to pain.In addition to NaIn conclusion, both NEDD4 and NEDD4L play an important role in regulating the stability of membrane proteins, which mainly regulate the transportation of molecules between cell‐cell and ions from extracellular space to the cytosol. Deficiency in NEDD4 or NEDD4L contributes to the accumulation of ion channels in the membrane, and the enhanced ion flow causes neuronal diseases.4.3WWP1 regulates p53 family proteins such as p53 and p63. WWP1 expression inversely correlates with the p53 and p63 protein levels. A recent study reported that WWP1 ubiquitinates huntingtin (Htt), and that mutation and aggregation of Htt are associated with Huntington's disease (HD) progression.4.4HECW1 was first isolated from human neuroblastoma tissues, and this protein is abundant in neuronal tissues such as brain and spinal cord.4.5C‐terminal PY motifs of p73, and this interaction promotes p73 ubiquitination (Figure HECW2 specifically binds p73 but not p53.Loss of HECW2 decreases the activation of GDNF/Ret downstream Akt signaling in human Hirschsprung's disease.4.6C‐terminal domain and the central loop region of Ptch1 with its WW domains. ITCH promotes Ptch1 ubiquitination and degradation, thereby modulating the apoptotic function of Ptch1.Sonic Hedgehog signaling is important for brain development, whereas an increased activity of SHH signaling induces tumorigenesis.Moreover, SMURFs participate in the noncanonical Wnt signaling and are one of the components of the PCP complex. Upon stimulation of noncanonical Wnt ligand Wnt5A, SMURF2 forms a tripartite complex with phosphorylated Dvl2 and Par6. The PY motif in Dvl2 is required for the binding with WW domains in SMURF2. This SMURF2‐phospho‐Dvl2‐Par6 interacts with Pk1 and promotes Pk1 ubiquitination and degradation Figure B. These 5There is an inverse correlation between the progression of cancers and neurodegenerative diseases.Based on the biochemical evidence, PTEN and p53 interact with NEDD4, WWP1, WWP2, and HECW1, and the binding has been shown to be involved in neuronal cell death and diseases.6WW domains are highly conserved protein‐binding modules that interact with a distinct subset of proteins possessing proline‐rich sequences Table . CumulatWW domain‐containing proteins participate in many biological and cellular processes. Gene amplification, deletion, and mutation of WW domain‐containing proteins are frequently found in human cancers and neuronal diseases, again suggesting their important roles in disease development Table . The E3 Intriguingly, WW domain‐containing E3 ligases participate in many signal pathways in tumorigenesis and cell death. Selective inhibition of WW domain‐containing E3 ligase has been a novel strategy in the field of cancer therapy. For example, WWP1 has been found amplified in numerous tumors, while downregulation of WWP1 attenuates leukemic cell growth.The authors declare no conflict in interest associated with the article.SSH wrote the article, LJH revised the article, and NSC polished the scientific writing and made the final revision. All authors approved the article prior to submission.This review article does not involve in using animal or human subjects.


DO) on the efficiency is not yet adequately documented. The present research aims to fill this gap by highlighting the effects of DO on the specific denitrification rate (SDNR) and consequently on the efficiency of the process. SDNR at a temperature of 20 °C (SDNR20°C) is the parameter normally used for the sizing of the denitrification reactor in biological-activated sludge processes. A sensitivity analysis of SNDR20°C to DO variations is developed. For this purpose, two of the main empirical models illustrated in the scientific literature are taken into consideration, with the addition of a deterministic third model proposed by the authors and validated by recent experimentations on several full-scale plants. In the first two models, SDNR20°C is expressed as a function of the only variable food:microrganism ratio in denitrification (DENF:M), while in the third one, the dependence on DO is made explicit. The sensitivity analysis highlights all the significant dependence of SDNR20°C on DO characterized by a logarithmic decrease with a very pronounced gradient in correspondence with low DO concentrations. Moreover, the analysis demonstrates the relatively small influence of DENF:M on the SDNR20°C and on the correlation between SDNR20°C and DO. The results confirm the great importance of minimizing DO and limiting, as much as possible, the transport of oxygen in the denitrification reactor through the incoming flows and mainly the mixed liquor recycle. Solutions to achieve this result in full-scale plants are reported.The biological denitrification process is extensively discussed in scientific literature. The process requires anoxic conditions, but the influence of residual dissolved oxygen ( As is known, the nitrogen contained in wastewater can be removed with physicochemical or biological processes. The most known usage of physicochemical processes consists of the removal of ammonia from industrial wastewaters by stripping ,6,7,8,9.5) and for the nitrification of total Kjeldhal nitrogen (TKN) [Currently, biological pre-denitrification, in activated sludge processes, is the most widely used technology. As shown in en (TKN) ,24,25,26DO), hydrodynamic behavior of the reactor, the fluctuations of raw wastewater loads, and also the alternative organic matrices that can be used for the reduction of nitrates in case of particular industrial wastewaters.The pre-denitrification process is based on the activity of heterotrophic bacteria capable of reducing nitrates to nitrogen through the biochemical use of the biodegradable organic substrate present in the wastewater ,19. The T of the mixed liquor, (DENr)T (gNO3-N h−1 kgMLVSS−1), was calculated by the Arrhenius equation [DEN); θ = 1.07 [θ = 1.07 .In the past, the design of the biological pre-denitrification reactor was based on the knowledge of the denitrification rate at 20 °C, which was supposed to be characterized by a zero-order kinetics (for both nitrate and organic substrates). The denitrification rate at the real temperature equation :(1)(rDEN3-N and BOD5) and the DO is preferred.This criterion is still used nowadays, even if a more extended equation which also keeps in consideration the influence of both the substrates (NOSDNR) defined as follows:TSDNR is the specific denitrification rate at the temperature T (kgNO3-N·kgMLVSS−1·d−1);SDNR20°C is the specific denitrification rate at the temperature of 20 °C (kgNO3-N·kgMLVSS−1·d−1);Q·ΔN is the load of nitrogen removed in denitrification (kg·d−1);−3);MLVSS is the mixed liquor volatile suspended solids in denitrification (kgVSS·mT is the temperature of mixed liquor (°C).A more recent approach to the sizing of the denitrification reactor is based on the calculation of the specific denitrification rate  and assimilative denitrification (cell synthesis). Once the value of SDNR20°C is known, it is possible to calculate the volume of the denitrification reactor through the Equations (2) and (3).Indeed, the SDNR20°C, and most of them are empirical. These models express SDNR20°C as a function of variables and constants which theoretically should consider all the factors influencing the denitrification kinetics [Several models are proposed in the literature for the calculation of kinetics ,31,32,33DO inhibition on denitrification at DO concentrations of 0.20 mg/L. Other studies have evidenced the effect of DO inhibition [DO concentration as low as 0.09 mg/L with a correspondent 35% reduction of the denitrification rate. Moreover, the United States Environmental Protection Agency, EPA, has confirmed in its reports the denitrification rate with a dependency from DO [DO was demonstrated experimentally on pilot plants and full-scale plants [DO, at different concentrations, on the SDNR20 °C. The present research aims to fill this gap by highlighting the sensitivity of SDNR20°C toward DO in denitrification. For this purpose, three of the most effective calculation models proposed by the scientific literature have been used. Two of these models are empirical and still widely used in plant design today. The third model is more recent and noteworthy as, for the first time, it makes the dependence on DO explicit.As is known, the biological denitrification process requires anoxic conditions. The influence of dissolved oxygen on the efficiency of the denitrification process has been reported by several studies. Already in 1972, Dawson and Murphy  had founhibition ,36,37,38 from DO ,40. Latee plants ,42. DespSDNR20°C models on which the sensitivity analysis is based are illustrated below:SDNR20°C with only the sludge loading in DEN (DENF:M). It was largely used for the sizing of denitrification reactors. This model does not make explicit the influence of residual DO in denitrification; as such, it does not consider the DO as a limiting factor of denitrification kinetic at the relatively small DO concentrations (about 0.25–0.40 mg L−1) that occur on well-designed and well-managed full-scale plants.Model I: It is described in Tchobanoglous . It is vbF to the DENF:M in order to take into account the deviation of the active fraction of biomass in the mixed liquor from the reference value of 0.3.Model II: The US EPA  proposedbF depends on the solid retention time (SRT).The correction factor bF = Active fraction of MLVSS;HY = Heterotrophic biomass synthesis yield, 0.47 g VSS/g BOD5;Tb = Endogenous decay rate at temperature T of mixed liquor, g VSS/g VSS d;b20 = Endogenous decay rate at 20 °C = 0.10 g VSS/g VSS d;IY = Inert VSS fraction in the influent, g VSS inert/g BOD5.IY can greatly influence the active biomass fraction of the MLVSS. Values for IY generally fall in the range 0.10–0.30 for plants with primary treatment and 0.30–0.50 for plants without primary treatment [The influent inert fraction reatment .SRT = 20, the factor is bF = 0.35.In plants with high efficiency for both nitrification and denitrification, the solid retention time can be assumed to be in the range of 18–20 days ,44. WithDO as well as of the DENF:M. The model was first validated by a pilot plant experimentation  and subsequently by testing eight full-scale installations of different capacity  [O DOK′ inhibition constant = 0.18 mgO2 L−1;BODη = 0.85–0.95 depending on the values assumed by DENF:M.Model III: This model was developed by the authors on a deterministic basis . It is c inhab.) . Please The three SDNR20°C at any DO and DENF:M values. At the same time, it is correct to note that the model has shown a modest reduction in its reliability for small capacity plants . This effect is probably determined by the greater fluctuations of the organic load fed to the plants, such as to determine a significant instability of the BOD5/NO3-N ratio in denitrification, compared to the optimal value of BOD5/NO3-N = 4. SDNR20°C proved a very strong sensitivity to DO, mainly in correspondence of low DO concentrations .The experimental results obtained on the full-scale plants experimentations demonstrated the ability of the model to calculate the DO for the three models. The examination of Model III was then deepened by representing it for a wide range of DO values. Finally, the derivative δ/δ DO of this model was also checked, in order to have a direct observation of the response of DO.The sensitivity analysis was conducted through the graphical representation of the correlation between SDNR20°C as a function of DO in the denitrification reactor, according to the three models under study. The DENF:M is set to 0.3 kgBOD5·kgMLVSS−1·d−1, a typical operating value of many full-scale plants. As Models I and II are constructed independently from DO, they are represented by a horizontal straight line. Instead, Model III shows a typically logarithmic trend, with a very strong gradient especially at low DO values (DO < 0.2–0.3 mg L−1). Then, the gradient tends progressively to reduce as DO increases. The inhibition effect exerted by DO is strongly conditioned by the phenomenon of oxygen transport from the core of the mixed liquor toward the inside of the activated sludge flocs. In the presence of small concentrations of DO, this phenomenon of penetration is strongly slowed down, so as to favor the creation of anoxic macrozones where the activity of denitrifying heterotrophic bacteria develops. In this sense, the great variability of SDNR20°C at different concentrations of DO is partly explained.DO (about 0.3–0.4 mg L−1) within which the values of SDNR20°C are quite comparable. This range is better quantifiable in the graph of SDNR20°C values of Model III from those of Models I and II.As can be observed, the difference between the models is considerable, but in reality, there is a range of DO concentration is calculated as the percentage difference between SDNR20°C of Model III and that of Models I and II. The examination of the graph allows us to observe that the deviation of ±5% corresponds to the range DO = 0.28–0.36 mg L−1 for Model II and DO = 0.31–0.40 mg L−1 for Model I.The deviation at any specific DO concentrations between 0.3 mg and 0.4 mg L−1 are very frequently found. Thus, within this range, the practical result produced by the three models is, in a first approximation, fairly well comparable. At the same time, it should be noted that there are well-designed and well-operated plants in which the DO is maintained at values slightly below 0.3 mg L−1, and at the same time, there are plants in which the DO is found at values appreciably higher than 0.4 mg L−1. In both cases, Models I and II lose their representativeness, while the same is preserved by Model III. SDNR20°C as a function of DO, according to Models II and III (Model I is not shown for a better graphic representation) at three different values of DENF:M. DO = 0.27–0.37 mg L−1. These data are further confirmation that the comparability of the three models exists, as a first approximation, within this specific range.In fact, in pre-denitrification reactors of full-scale plants, DO in the expressions of SDNR20°C, as it is made in Model III.What is illustrated above highlights how relevant it is to include the DO on SDNR20°C is well shown in SDNR20°C of Model III as a function of the DO at three different values of DENF:M. The specificity of this figure consists in the wide range of DO considered, from DO = 0 mg L−1 to DO = 1.2 mg L−1. At DO = 0 mg L−1, all the curves converge to the ideal value SDNR20°C = 0.864 kgNO3-N·kgMLVSS−1·d−1. By contrast, at high concentrations of DO, the curves tend to gradually flatten, making the variations of SDNR20°C less and less noticeable. The initial strong gradient leads to an about 45% reduction in SDNR20°C by increasing the dissolved oxygen from DO = 0 mg L−1 to DO = 0.2 mg L−1. A further increase in DO to 0.4 results in a further 18% reduction of SDNR20°C. At higher DO values (DO > 1 mg L−1), the SDNR20°C tends to be determined more and more by only cellular synthesis. The graph also shows how, although appreciable, the incidence of DENF:M is relatively limited.The strong influence of DO. The derivative expresses the response of SDNR20°C to the variation of each specific DO value. As such, it expresses the sensitivity better than any other parameter. The curves show a very high sensitivity of SDNR20°C to DO, mainly at low DO concentrations (DO approximately < 0.3 mg L−1). The sensitivity then tends to decrease with a progressively less pronounced gradient with increasing DO values (above 0.4–0.5 mg L−1). It is useful to consider that DO greater than 0.5–0.6 mg L−1 is rarely found on well-designed and operated full-scale plants. This figure, even more so than the previous one, shows that the variations of DENF:M are of little relevance and do not appreciably influence this sensitivity analysis.A full confirmation of the above evaluations can be seen in DO in the denitrification reactor, and this should already be done at the plant design stage. Among the measures that can be adopted, the following can be mentioned:DO and consequently on the denitrification efficiency. A set of four reactors demonstrates greater oxygen consumption capability  than a single complete mixing reactor . It is therefore necessary to provide configurations of the denitrification reactor tending as much as possible to the plug-flow [An appropriate hydrodynamic configuration for the denitrification reactor. In fact, the results of specific experimentations highlight the influence of the hydrodynamic model of the anoxic reactor on the residual lug-flow .DO. The reduction of the dissolved oxygen in the post-anoxic reactor is influenced by the retention time and the sludge loading of the biological process. It was observed that, with F:M = 0.130 kg BOD5∙d−1∙kg MLVSS−1 (referring to the volumes of denitrification plus oxidation-nitrification) and 1.5 h of retention time, it is possible to obtain the reduction of the dissolved oxygen in the post-anoxic reactor to the average concentration of 0.31 mg L−1, such as to determine an average concentration down to 0.11 mg L−1 in the pre-denitrification reactor. The consumption of DO in the post-anoxic reactor is due to the bio-assimilation of the residual BOD and the bio-oxidation of the endogenous carbon.A post-anoxic reactor (after the pre-denitrification and oxidation-nitrification steps) proved to be very effective in improving the efficiency of nitrogen removal . In factDO in the inlet flows to the denitrification reactor  using closed pipes instead of open channels [The limitation of channels ,48.2+ in denitrification (or in the post-anoxic reactor), which easily oxidizes to Fe3+, by consuming DO. A specific experimentation proved that dosages of 6 mg L−1 Fe2+ can lower the average DO concentration from 0.45 mg L−1 to 0.28 mg L−1, consequently increasing the denitrification efficiency. In addition, ferrous ion has been found to act as a catalyst for the reduction of nitrates [The dosage of a reducing agent such as Fenitrates ,50,51.Overall, the results of the present sensitivity analysis highlight the need to limit, as much as possible, the concentration of −3 [The careful choice of the mixed liquor stirring system (and of the relative power) in the denitrification reactor to avoid excessive surface turbulence with consequent excessive dissolution of atmospheric oxygen. In general, completely submerged agitators equipped with a power regulator are preferred. The specific power input must be limited to the minimum necessary to keep activated sludge in suspension, and it generally ranges from 8 to 12 W m−3 ,39.The coverage of the reactor surface with floating plastic elements in order to limit the exchange of oxygen with the overlying atmosphere.This solution can be of particular interest in cases where the sewage treatment includes the removal of phosphorus, which would be precipitated as ferric orthophosphate ,53.The SDNR20°C on dissolved oxygen (DO) in biological denitrification. Therefore, every reliable computational model should include this dependency. According to the following model proposed by the authors and validated by numerous experimentations on pilot plants and full-scale plants, the sensitivity proves to be particularly relevant at low values of DO.SDNR20°C = specific denitrification rate at 20 °C (kg NO3-N·kg MLVSS−1·d−1);TSDNR = specific denitrification rate at the real temperature T (°C) of the mixed liquor (kg NO3-N·kg MLVSS−1·d−1);DENF:M = food:microrganism ratio in denitrification (kg BOD5·kg MLVSS−1);OK’ = 0.18 mgO2 L−1;BODη = 0.85–0.95 depending on the values assumed by DENF:M;θ = 1.026–1.07 temperature coefficient.The sensitivity analysis highlights the strong dependence of the SDNR20°C while increasing the initial concentration DO = 0 mg L−1 up to DO = 0.2 mg L−1. A further increase to 0.4 mg L−1 determines an additional 18% decrease in SDNR20°C. The influence of the DENF:M on this sensitivity analysis appears very modest. In full-scale plants, the residual concentration of DO in denitrification is frequently found in the range of 0.3–0.4 mg L−1. In some cases, this range is increased to 0.5–0.6 mg L−1, thus often leading to a reduced efficiency of biological denitrification. In particularly favorable cases, DO is found in the range of 0.2–0.3 mg L−1, which allows a better denitrification performance.In particular, the strong initial gradient leads to a reduction of about 45% of the DO as much as possible. The main measures are summarized below:Designing the denitrification reactor with a hydrodynamic configuration closer to plug-flow than to complete mixing;Minimizing the transport of oxygen with the flows entering the reactor: use of pipes instead of open channels; tapered aeration in oxidation-nitrification or even the addition of a real post-anoxic reactor;2+  has proven to be effective;Dosage in denitrification  of an easily oxidizable reagent by dissolved oxygen: FeMinimizing the surface oxygen exchange by the careful choice of the agitation system.The objectives of a good design of the denitrification reactor must include several measures capable of limiting the SDNR with respect to DENF:M and to the temperature.Future research developments in this field are expected, in particular regarding the sensitivity of


Convective organization has the potential to impact the strength of precipitation extremes, but numerical models disagree about this influence. This study uses satellite observations to investigate the link between the mesoscale organization of deep convection and precipitation extremes in the Tropics. Extremes in domain‐averaged precipitation are found mostly over the western Pacific and Indian Ocean warm pools, and they primarily depend on the number of deep convective entities within the domain. On the other hand, extremes in local precipitation are found primarily over land, and they increase with the degree of convective organization. Therefore, this observational study shows evidence for a modulation of the strength of tropical precipitation extremes by the spatial organization of deep convection, especially over land. The link between tropical precipitation extremes and the mesoscale organization of deep convection is investigated using satellite dataThe strength of local precipitation extremes exhibits a strong dependence on convective organizationLocal precipitation extremes primarily result from changes in the fractional area of heavy precipitation Mesoscale organization and large cloud clusters, that occur on scales of hundred to thousand kilometers Houze, , includeDuring the last decade, many modeling studies have investigated the physical mechanisms and the impact of convective aggregation on climate  10° × 10° domains within the tropical belt.2.1The precipitation data are derived from the version 6 of the Tropical Rainfall Measuring Mission (TRMM) 3B42 product for the period 1998 to 2010 .Ar) and non‐precipitating (An=1−Ar) fractional areas , and the precipitating area is further decomposed into weakly (Aw) and strongly (As) precipitating areas, whose ratio relative to Ar is referred to as aw and as. Each of these areas is characterized by a precipitation intensity , so that the domain‐averaged precipitation (Pt) can be expressed asThen, we characterize the precipitation field within each 10° × 10° domain as represented schematically in Figure −1. To test the robustness of our results to this threshold, we also considered alternative values ; similar results are obtained for all threshold values greater than 1 mm hr−1.The distinction between weakly and strongly precipitating areas is done by considering a threshold value of 2 mm hrPr is defined as the average value of pixels having values greater than 0 mm hr−1, while Pt is defined as the average value of all grid points (both precipitating and non‐precipitating) within the 10° × 10° area. In the following, we will refer to Pt and Pr as domain‐scale and local‐scale precipitation, respectively. Figure Pt and Pr values obtained for all the domains satisfying the quality criteria discussed above. Over most of the domains, Pt and Pr are lower than 1 mm hr−1 and 4 mm hr−1, respectively  TRMM pixels of 0.25° × 0.25°. 2.2Pt and Pr are calculated for each 10° × 10° domain, and then we aggregate all values in space (20°S to 20°N) and time (1998 to 2010). Precipitation extremes are then defined as the 99th percentile value of this ensemble. The 99th percentile values of Pt and Pr, referred to as Pt°99 and Pr°99, respectively, are equal to 1.18 and 4.25 mm hr−1, respectively. All cases corresponding to Pt ≥ Pt°99 (or Pr ≥ Pr°99) are considered as extremes of domain‐scale precipitation , and they are referred to as Pt99 and Pr99, respectively.All precipitation diagnostics Pt99 and Pr99, respectively. The frequency of Pt99 extremes exceeds 1% over 40% of the tropical oceans and over 27% of tropical land. Most of the Pt99 events occur over the warm pools of the tropical western Pacific and Indian oceans  data derived from geostationary satellites  by applying an exponential‐distance decay over a 0.7° × 0.7° area (10 × 10 GridSat pixels). Then, every time the smoothed Tb value at one particular pixel corresponds to the lowest value of the 3 × 3 pixels area centered around it, this pixel is considered as a local minimum of Tb. If this local minimum is lower than 240 K, it is considered as a deep convective centroid .This method differs from that used in many previous studies of convective aggregation  than 0.5 correspond to a clustered (regular) distribution of deep convective entities, while Iorg=0.5 corresponds to a randomly distributed convection.Once all the convective centroids are identified within a given domain, the distances among nearest‐neighbor (NN) centroids are calculated. Then we characterize the spatial distribution of deep convective centroids by using the N and Iorg are calculated for each 10° × 10° domain of 20°S to 20°N, every 3 hr for the period of 1998 to 2010. The domains for which N is smaller than 20 are excluded from the statistics to remove cases which are close to clear‐sky conditions and to allow for reliable Iorg estimates. Applying this rule reduces further the number of 10° × 10° domains considered in the analysis by 31% .Both 3N) and the degree of mesoscale organization (Iorg) within 10° × 10° domains are presented in Figure The relationships between precipitation, precipitation extremes, the number of convective centroids . However, a simple scaling analysis based on equation Pt with N is mostly due to the increase of Ar (Pr∂Ar∂N is 4 times larger than Ar∂Pr∂N). Note that because of the dominance of the non‐precipitating area in 10° × 10° domains, Pt is much smaller than Pr, sometimes by an order of magnitude. We also note that the precipitation intensity of Pr saturates for large N  can correspond to vastly different organizations of convection within the domain.We now consider the influence on these relationships of the spatial organization of convection, as characterized by  systems . HoweverIorg. Figures Pt) and at the scale of the precipitating area (Pr). 75% of the decrease of Pt with increasing clustering is due to the shrinking of the precipitating area Ar and 25% due to a weakening of the local precipitation intensity associated with a decreased proportion of heavy precipitation within this area  is because the large nonprecipitating area (An=1−Ar) has a stronger weight in Pt than the small portion of the domain covered by intensive rain rate.Note that the fractional area covered by heavy precipitation increases with  Figures c and 4d.4N) and to the spatial organization of deep convection (Iorg) at the scale of 10° × 10° domains in the tropics.This study analyzes how mean precipitation and extreme precipitation relate to the number of deep convective entities , which occur mostly over the ocean warm pools , which occur mostly over land  is inversely related to the number of convective centroids (N), which is itself closely related to the total area of the domain covered by deep convection. This is consistent with idealized radiative‐convective equilibrium simulations showing that the area covered by deep convective clouds is reduced when the mesoscale organization of convection increases  when convective organization is stronger (Figure Regarding extreme precipitation, our observation that extremes in the domain‐averaged precipitation does not depend strongly on convective organization Figure c is consr Figure d, which r Figure  and Pendr Figure . In thisr Figure d. This er Figure .Many studies indicate that extreme precipitation can cause huge threats to the economy, agriculture, infrastructure, and human lives (Spekkers et al., Supporting Information S1Click here for additional data file.


Rhodopseudomonas palustris PS3 is one of the purple phototrophic non-sulfur bacteria (PNSB), which have plant growth-promoting effects on various plants. To expand the scale of PS3 fermentation in a time- and cost-effective fashion, the purpose of this work was to evaluate the use of low-cost materials as culture media and to optimize the culture conditions via response surface methodology. Corn steep liquor (CSL) and molasses were identified as potential materials to replace the nitrogen and carbon sources, respectively, in the conventional growth medium. The optimum culture conditions identified through central composite design were CSL, 39.41 mL/L; molasses, 32.35 g/L; temperature, 37.9°C; pH, 7.0; and DO 30%. Under the optimized conditions, the biomass yield reached 2.18 ± 0.01 g/L at 24 hours, which was 7.8-fold higher than that under the original medium (0.28 ± 0.01 g/L). The correlation between the predicted and experimental values of the model was over 98%, which verified the validity of the response models. Furthermore, we verified the effectiveness of the R. palustris PS3 inoculant grown under the newly developed culture conditions for plant growth promotion. This study provides a potential strategy for improving the fermentation of R. palustris PS3 in low-cost media for large-scale industrial production. Rhodopseudomonas palustris is one of the purple phototrophic non-sulfur bacteria (PSNB). Since it can process nutrients through various metabolic pathways, such as photosynthetic, photoheterotrophic, chemoheterotrophic and chemoautotrophic pathways, R. palustris can inhabit a variety of environments [R. palustris contains many useful characteristics and is broadly used in industry for bioremediation, sewage treatment, removal of phytotoxic compounds, etc. [R. palustris has also been reported to act as a promising biofertilizer for promoting crop yield and improving soil fertility [R. palustris strain, called as the PS3, from Taiwanese paddy soil that not only had beneficial effects on plant growth but also enhanced the efficiency of the uptake of the applied fertilizer nutrients [ronments . It is ads, etc. , 3. Thisds, etc. , 4–7. R.ertility –10. Prevutrients , 11. AccFor the purpose of the commercialization or the large-scale field application of the selected microbes, fermentation production is an essential prerequisite. The yield per unit biomass of the mass production is influenced by several factors, such as the medium composition , the culture conditions  and the mode of fermentation  . The scaResponse surface methodology (RSM), also called the Box–Wilson methodology, is a useful tool to optimize the factors of fermentation processes by applying mathematics and statistics . This teR. palustris fermentation [R. palustris strain DH with the original van Niel medium for 7 days, and the derived biomass was ~0.3 g/L. Carlozzi and Sacchi [R. palustris strain 42OL in a modified van Niel medium to which sodium acetate was added, and the derived biomass was 1.42 g/L/d. Chang et al [R. palustris strain YSC3 was 0.36 g/L after 2 days of incubation. However, the use of these media may be uneconomical for industrial application due to their high cost and long incubation time. The cost is primarily due to expensive nitrogen sources, such as yeast extract and peptone. On the other hand, some media have low-cost sources; for example, Xu et al [Stevia residue extractions supplied with NH4Cl as a medium to culture R. palustris, and the highest obtained biomass was 1.5 (OD660)  after 96 hours of cultivation. Kornochalert et al [R. palustris in latex rubber sheet wastewater supplied with pineapple extract after 96 hours of fermentation. In our previous study, we used a modified van Niel medium with malate and yeast extract as the carbon and nitrogen sources for the fermentation of R. palustris PS3, and the biomass was 0.07 g/L after 24 hours of cultivation. Although this broth showed promising plant growth-promoting effects on several crops [R. palustris PS3 that is cost-effective, results in high biomass yield, and has a short fermentation time. We evaluated some agro-industrial by-products, including corn steep liquor (CSL), beetroot extract (BRE), soybean flour (SF), soybean protein isolate (SPI), molasses and corn starch, for use as substrates for R. palustris PS3 cultivation in terms of cost reduction and tested them with RSM to obtain the optimal fermentation conditions. Furthermore, we inoculated the newly developed fermentation broth into plants to verify its plant growth-promoting effect.The van Niel medium and modified van Niel medium have been designed for entation , 27. Du entation  cultivatd Sacchi  incubateng et al  modifiedXu et al  used Steal crops , 11, 32,R. palustris PS3 was isolated from Taiwanese paddy soil and showed promising beneficial effects on plant growth in our previous studies [2PO4 1.0 g/L, NH4Cl 1.0 g/L, MgSO4•7H2O 0.2 g/L, FeSO4•7H2O 0.01 g/L, CaCl2 0.02 g/L, MnCl2•4H2O 0.002 g/L, Na2MoO4•2H2O 0.001 g/L, yeast extract 0.5 g/L, and malate 5.0 g/L, pH = 7.0. After 24 hours incubation, 2 mL of the above bacterial broth was incubated in a 250 mL Erlenmeyer flask containing 50 mL PNSB medium and then cultured at 37°C with shaking at 200 rpm. After 24 hours incubation, the bacterial broth was diluted with fresh PNSB medium and adjusted to an optical density approximately equal to OD600 = 1.0. This diluted bacterial broth was used as a seed culture for further experiments. studies , 11. Thi studies   , beetroot extract (BRE) , soybean flour (SF), soybean protein isolate (SPI) and NH4NO3) and carbon  and corn starch ) sources were used to optimize the composition of the PNSB medium. The initial concentrations of the individual carbon and nitrogen sources followed those in the PNSB medium described above and were sterilized separately by autoclave. For preliminary screening of alternative nitrogen sources, a final concentration of 1.5 g/L of each nitrogen-containing candidate material was introduced to substitute NH4Cl (1.0 g/L) as well as yeast extract (0.5 g/L) in the presence of 5.0 g/L malate (carbon source). For preliminary screening of alternative carbon sources, a final concentration of 5.0 g/L of each carbon-containing candidate material was introduced to substitute malate (5.0 g/L) in the presence of CSL (1.5 g/L) as the selected nitrogen source.Different nitrogen  into 50 mL of the respective modified media in a 250 mL Erlenmeyer flask, and then cultured at 37°C with shaking at 200 rpm.For the experiments, the seed culture mentioned above was centrifuged at 3,000 rpm for 5 min at 4°C and then suspended in phosphate buffer solution (PBS). The final OD600 was multiplied by the dilution times. Biomass (grams per liter) was assayed from the OD600 value by using a calibration standard curve. Viable counts were determined by the plate counting method.The population of PS3 cells was estimated by a standard plate count method. Enrichment culture broth was serially diluted by fresh PNSB medium, and spread onto PNSB agar plate. Incubated the plate at 37°C in the dark and then calculated the number of colony forming unit (CFU) per milliliter. On the other hand, the cell concentration was also measured by optical density with a spectrophotometer at 600 nm. The bacterial culture broth was diluted in distilled water to obtain an optical density less than 0.6, and the OD4−1 (four factors) fractional factorial design (FFD) using R software with the package “rsm”. Then, the design was augmented by eight axial points and four replications of the center points. This design resulted in a total of 20 experiments [xi is the coded variable of the factor, Ei is study value of variable, E0 is the real value of the variable at the center point, and ΔEi is the step-altered value, which represents the difference from the real value in the higher or lower value from the real value at the central point. In present study, the ΔEi for CSL, molasses, temperature and pH value are 5 mL/L, 4 g/L, 1.5°C and 0.3, respectively. The various factors and levels for the CCD are shown in Y is the predicted response, β0 is the intercept, and βi, βii and βij are the linear, quadratic and cross-interaction regression constant coefficients, respectively. xi and xj are the coded independent variables for factors. The quality of the fitting of the second-order equation model to the data was described by the coefficient of determination R-squared, and the statistical significance was evaluated by the F-test. The significance of the regression coefficients was analyzed by a t-test. The computer software used was R, version 3.6.2 [Based on the results of factor screening, the following independent variables, including the medium components (molasses and CSL) as well as the fermentation conditions (temperature and pH), were selected for optimization by central composite design (CCD). The CCD consists of three parts: a factorial design, a central points, and axial points . In ordeeriments . The diseriments . Before on 3.6.2 .e experimental trials. We inoculated 300 mL of bacterial culture into 3 L of fresh medium. The conditions for molasses, CSL, temperature and pH value were set according to the experimental design matrix corresponding to the CCD described. The pH value of the cultures was controlled by pH-stat and automatically adjusted with 2 N NaOH and 2 N HCl.To perform the response surface methodology assay, a 5-L stirred tank bioreactor  was used to carry out all of the batch-culturBrassica rapa L. spp. pekinensis cv. “Michelle”) were purchased from Formosa Farming Materials Co., Ltd. . The seeds were immersed in 70% alcohol for 3 min and then in 3% hydrogen peroxide solution for 7 min for surface sterilization, followed by a thorough washing with sterile distilled water. These seeds were germinated for 1 day at 25°C in the dark. For hydroponic cultivation, well-germinated seeds were transferred to completely wet cotton and cultivated under continuous (24-h photoperiod) light-emitting diode (LED) light (~210 μmol m-2s-1). After one week, the seedlings were transferred to hydroponic tanks (35 L) in a plant factory facility . Twenty-four seedlings were cultivated in each tank, and each tank was equipped with an air pump to homogenize the solution and maintain the dissolved oxygen. Hoagland’s solution 2•4H2O) was used as a nutrient sources [-1. The initial pH value of the hydroponic nutrient solution was adjusted by H3PO4 and 2N KOH to 7.0. The cultivation environment was set at 25°C, 70% humidity, and 210 μmol.m-2.s-1 light intensity for 16 hours. We poured 250 mL of the liquid culture  into the tank, resulting in a final bacterial concentration of 106 CFU/mL. After seven days post inoculation (7 dpi), another 250 mL of the liquid culture was applied to each tank. Seventeen days after planting (DAP), the Chinese cabbages were harvested, and the fresh and dry weights were measured. For soil cultivation, well-germinated seeds were transferred to cultivatable soil under controlled illumination with a 16-hour photoperiod (~210 μmol m-2s-1). After one week, the seedlings were transferred to pots containing approximately 300 g cultivatable soil. The cultivation environment was set to be consistent with that under hydroponic cultivation. Two milliliters of the respective culture broth  and 0.05g chemical fertilizer were added into each pot once a week as described previously [Chinese cabbage seeds  were performed with R version 3.6.2 . Fisher’optimization strategy) was used. We selected corn steep liquor (CSL), beetroot extract, soybean flour (SF), soybean protein isolate (SPI), and NH4NO3 as the individual nitrogen sources and malate, sodium acetate, glucose, fructose, molasses, and corn starch as the individual carbon sources. These materials are common, low-cost agro-industrial byproducts and are the most common nutrient sources in industrial fermentations [R. palustris PS3 strain. In the presence of 5 g/L malate as single carbon source, the highest turbidity (OD600) was observed when using SF or SPI as the sole nitrogen source, followed by that of the strain incubated with CSL, BRE and PNSB and that from fermentation in NH4NO3 (600) and colony-forming unit (CFUs) counts. As shown in S1 Fig in 600 and CFUs values were positively correlated during the fermentation progress (24 hr). As shown in R. palustris PS3 was 1.14 ± 0.72 × 109 CFU/mL, which was comparable to that with the original nitrogen source (NH4Cl and yeast extract in PNSB medium) and higher than with the other nitrogen sources. Although the soybean flour (SF) and soybean protein isolate (SPI) also showed high OD600 values, their CFUs were dramatically lower than the others. This implied that the turbidities (OD600) of these two microbial samples did not reflect the number of viable cells produced (CFU). This inconsistency may be attributed to their poor solubility in the individual media, which interfered with the turbidity readout. Accordingly, CSL is considered a potential nitrogen source for the production of R. palustris PS3. After 1.5 mL/L CSL was determined as the nitrogen source for the modified medium, we further screened appropriate carbon sources. We found that molasses and sodium acetate significantly increased the biomass of R. palustris PS3 compared with those under the other carbon sources , 0.58188 (molasses), 0.00438 (dissolved oxygen), 0.34688 (temperature) and -0.08312 (pH), respectively . Therefore, we set the dissolved oxygen as constant at 30% for the subsequent experiments. To further identify the appropriate range of variables for RSM, we conducted the steepest ascent path method to clarify the levels of factors. The steepest ascent path was designed according to S2 Eq in R. palustris PS3 dramatically decreased and was even lower than the original biomass.All of the experiments in FFD were performed in the 5 L desktop bioreactor. The factor screening process and the experimental design for the range and levels of test variables, as well as results for the FFD are shown in S2 Table in R. palustris PS3 growth. We conducted a four-coded-level central composite design (CCD) to optimize the levels of these variables. The corresponding experimental results of the CCD design are shown in R. palustris PS3 is shown in According to the results of the factorial design experiment . However, the molasses term and other interaction terms were not significant at the 5% level. Moreover, other interaction terms between molasses, temperature and pH value were omitted from the predicted model. The coefficient and adjusted coefficient of determination, R2, for the regression model fit were calculated to be 0.9962 and 0.9896, respectively. This means that more than 98% of the variability of the regression model could be explained by the regression equation. The response-surface full quadratic model of biomass for R. palustris PS3 was also tested by ANOVA. The F value of the model was 151.99, and the p value was less than 0.0001 (2.84×10−7), indicating that the model was highly significant . The plots showed the effect of two variables on the response while the other factors were set at the “zero” level; the levels tested were 40 mL/L CSL, 35 g/L molasses, 38.5°C temperature and 6.9 pH . These canalyses , i.e., bR. palustris PS3, confirmation fermentation with the predicted optimal culture conditions  was performed. As shown in R. palustris PS3 was 2.18 ± 0.01 g/L, which was approximately 7.8 times higher than that obtained in the original PNSB medium (0.28 ± 0.01g/L). The validated biomass production showed a high correlation (95%) with the predicted biomass from the response model. This result suggests that the proposed model R. palustris PS3 biomass production. The estimated cost of this newly developed medium was about 0.16 US$/L, which was approximately 30% of the original PNSB medium (0.53 US$/L). The detailed material cost of each component in respective medium was shown in S5 Table in To verify the predicted biomass production of R. palustris PS3 produced under the newly developed culture conditions had beneficial effects on plant growth.To confirm the plant growth-promoting effect of PS3 with the newly developed fermentation broth, we cultivated Chinese cabbage in either hydroponic or soil system with different treatments. As shown in S6 Table in R. palustris PS3 has been shown to have beneficial effects on several crops [R. palustris PS3 biomass production (2.18 ± 0.01 g/L at 24 hours fermentation) that was 7.8-fold higher than that with the original PNSB medium (0.28 ± 0.01g/L at 24 hours fermentation). Accordingly, this optimal fermentation condition for R. palustris PS3 is not only highly productive but also cost- and time-effective. It has been indicated that the sources of nitrogen and carbon play a critical role in the production of microbial secondary metabolites [al crops , 11, 32.abolites , 38. Varabolites –41. TherR. palustris is already known as the most metabolically versatile bacteria, which was able to catabolize various carbon and nitrogen sources, such as glucose, fructose, malic acid, acetic acid, ammonium nitrate, glutamine, yeast extract and so on [R. palustris PS3 and found that a variety of nitrogen and carbon sources could be utilized , was significantly higher than that of PS3 cultured with a sole nitrogen source   . These c NH4NO3) . We deduR. palustris biomass production is stimulated by the co-utilization of multiple carbon sources [E. coli was higher with a combination of two substrates  than with a single substrate  [Lactobacillus brevis subsp. lindneri CB1 cultivated with maltose and citrate mixtures resulted in a faster cell growth rate than that of the strain cultivated with maltose alone, and the growth rate and viable counts (OD620) derived from the former media were 1.8-fold and 1.2-fold higher, respectively [B. subtilis 168 increased 1.25-fold when cultured in medium containing glucose and malate mixtures [R. palustris can readily utilize organic acids as carbon sources [R. palustris co-metabolized several of the carbon sources in molasses, although further experimentation is needed.For carbon sources, as shown in  sources . Similarctively) . Lactobaectively . Comparimixtures . It is a sources . Since o sources , it is pR. palustris PS3 biomass production was explained by mathematical models and ANOVA. The linear regression model and ANOVA in FFD suggested that increasing the concentration of molasses could increase biomass production  [R. palustris PS3 biomass production  [2 concentration and is only carried out under microaerobic conditions. Thus, under the aerobic culture conditions of this study, BNF did not occur. Accordingly, supplementation with exogenous nitrogen in the culture medium was necessary.In contrast, the factors CSL, temperature and pH value significantly influenced the growth of tris PS3 . It was tris PS3 . Not sur was 7.0 . This re was 7.0 . Interesg (30°C) . We infeoduction . Howeveroduction . In the oduction . Regardion (BNF) . HoweverBacillus spp. Azospirillum spp. or Azotobacter spp.) showed a negative influence on seed germination in vitro [Molasses and CSL can be applied individually as fertilizers in agriculture. For example, it has been found that the soil quality was remarkably improved by the application of molasses , 59. Thein vitro . In thisR. palustris PS3 were elicited by viable cells or conferred by organic compounds from the PNSB medium or dead/ decaying cells, the 65°C heat-killed bacterial suspension was applied to replace the vegetative R. palustris cells. The results showed that neither medium nor dead R. palustris cells was able to promote plant growth [R. palustris PS3. Notably, it was also demonstrated that not only the population (i.e viability) but also the metabolic activity  of PS3 cells is crucial for the plant beneficial traits [R. palustris strains in plant-growth promotion. PS3 and YSC3 exhibited a very close phylogenetic relationship and shared several conserved regions and genetic arrangements in their chromosomes. Although these strains have many plant growth-promoting (PGP) genes in common, only PS3 exhibited beneficial traits. We noticed that the transcripts of genes associated with bacterial colonization and biofilm formation in response to root exudates were higher in PS3 than those in YSC3 strain [Furthermore, it is notable that PS3 fermentation broth obtained from newly developed medium that is consistent with PS3 cultured in modified PNSB, it shown the plant growth promotion effect . In our t growth . These rl traits ). On thel traits , we carr3 strain . These dR. palustris PS3 biomass production with an alternative, low-cost medium containing agricultural byproducts. CSL and molasses were identified as potential nitrogen and carbon sources for R. palustris fermentation. The utilization of CSL and molasses as raw materials for R. palustris fermentation can aid in reducing agro-industrial waste. The response surface methodology revealed the factors that greatly influence R. palustris PS3 growth, namely, CLS, temperature and pH value. R. palustris PS3 biomass production increased significantly, by 7.8-fold, from 0.28 ± 0.01 g/L to 2.18 ± 0.01 g/L, compared to that under the basal medium/conditions when the strain was cultivated in the optimal culture conditions  developed by statistical experimental methods. The in planta experiments verified that the newly developed fermentation broth retained the plant growth-promoting functions of R. palustris PS3. Compared with those in previous studies, our newly developed fermentation process could successfully produce high levels of R. palustris in a shorter time. This study described the prospective uses of agro-industrial techniques for R. palustris biofertilizer production.This paper presented an experimental design for the optimization of S1 File(DOCX)Click here for additional data file.


The panel of fluid- and imaging-based biomarkers available for neurodegenerative disease research is growing and has the potential to close important gaps in research and the clinic. With this growth and increasing use, appropriate implementation and interpretation are paramount. Various biomarkers feature nuanced differences in strengths, limitations, and biases that must be considered when investigating disease etiology and clinical utility. For example, neuropathological investigations of Alzheimer’s disease pathogenesis can fall in disagreement with conclusions reached by biomarker-based investigations. Considering the varied strengths, limitations, and biases of different research methodologies and approaches may help harmonize disciplines within the neurodegenerative disease field.Alzheimer’s Research and Therapy, we present the result of a discussion from the 2019 Biomarkers in Neurodegenerative Diseases course at the University College London. Here, we discuss themes of biomarker use in neurodegenerative disease research, commenting on appropriate use, interpretation, and considerations for implementation across different neurodegenerative diseases. We also draw attention to areas where biomarker use can be combined with other disciplines to understand issues of pathophysiology and etiology underlying dementia. Lastly, we highlight novel modalities that have been proposed in the landscape of neurodegenerative disease research and care.Along with separate review articles covering fluid and imaging biomarkers in this issue of  With 50 million individuals affected worldwide, neurodegenerative diseases remain without disease-modifying treatments. Neuropathological investigations are critical for closing intellectual gaps regarding pathophysiologic mechanisms, as postmortem examination serves as a gold standard and provides adequate resolution to observe the elements of pathophysiological cascades. However, they are limited to cross-sectional assessment. The use of antemortem biomarkers renders possible the detection of hallmarks longitudinally, throughout disease stages. Even in situations where conclusions drawn from antemortem biomarkers might differ from postmortem observations, antemortem biomarkers still offer utility. Here, we will illustrate ways that evidence can be weighed to understand neurodegenerative diseases holistically, focusing on methodology and the limitations and strengths of different modalities.Despite sometimes indirect associations with lesions, neuropathologically validated biomarkers can be used to assess disease course, particularly as degeneration relates to clinical manifestations. For trials, biomarkers are of paramount importance. They are key for efficiently identifying and tracking cohorts by defining inclusion criteria and outcome variables . As showAlzheimer’s Research and Therapy, separate articles will discuss fluid  and imaging  biomarkers for neurodegenerative diseases. Priming this, it is important to consider how one assesses the utility and biases of different modalities. We will discuss ways that biomarkers are utilized in neurodegenerative disease research and care, commenting on appropriate use, interpretation, and implementation. Finally, we will consider where major knowledge gaps lie and how novel biomarkers may fill them. This review will primarily focus on Alzheimer’s disease, due to a significant deficit in biomarkers useful for other neurodegenerative diseases; however, we will comment on emerging techniques for other diseases. Many of the themes discussed here on utility can be readily applied across neurodegenerative diseases.There are numerous biomarkers for neurodegenerative diseases readily available or under development Tables , 3 and 4Neurodegenerative diseases represent the confluence of a range of pathophysiologic cascades with associated clinical spectra. While typically defined by proteinopathic hallmarks, it is unclear whether these hallmarks are driving the disease or are themselves consequences of other underlying processes. AD, frontotemporal lobar degeneration (FTLD), and Parkinson’s disease are the most common neurodegenerative diseases. Overlapping diseases, otherwise known as co-pathologies, are frequent and have complex contributions to clinical phenotypes .APOE-ε4 allele and TREM2 mutations .–17.APOE-Synucleinopathies are the second most common neurodegenerative disease . The mosFTLD is nearly as prevalent as early-onset AD in dementia cases below the age of 65 with an incidence of 1.6–4.1/100,000 individuals annually in the USA and Europe , 24. FTLHuntington’s disease (HD) is a rare, autosomal dominant disease with an incidence of 0.16–0.94/100,000 individuals annually . The agePRNP gene [Prion diseases are characterized by spongiform encephalopathy with underlying neuronal loss, gliosis, and aggregation of the prion protein (PrP) encoded by the RNP gene . PrP disRNP gene . With a RNP gene . RelevanRNP gene .Decades of neuropathological studies augmented by novel biomedical tools have revealed that many complex, interrelated mechanisms underlie neurodegenerative diseases. A principle limitation of the cross-sectional nature of neuropathology is difficulty in assessing temporal relationships. Neuropathological investigations typically only observe end-stages; however, existing population-based cohorts can capture the full range of disease progression . DetectiGiven the clear etiology and sometimes predictable age of onset, several studies have focused on hereditary neurodegenerative diseases to investigate early disease stages. For example, positron emission tomography (PET) imaging studies of familial AD cases have suggested that brain Aβ deposition begins up to 20 years before clinical symptoms, while cortical tau deposition arises roughly 6 years before onset , 40. SimCuriously, conclusions from in vivo studies of the relative onset of Aβ and tau lesions in AD often conflict with investigations using large postmortem case series that indicate that tau lesions occur prior to Aβ deposition in the brain , 7. ThisInformation gleaned from longitudinal studies has been used to construct models of multiple biomarkers. The widely recognized “Jack curves” , for exa. Of note, lipid peroxidation and metabolism have been implicated in neurodegenerative diseases [. Similarly, robust fluid biomarkers of blood-brain barrier function have been lacking, with several under development.When combining biomarkers in a study, it is also important to account for differences in how they represent respective disease hallmarks. Importantly, the biomarkers must have a comparable target engagement with their respective hallmarks or, at the least, empirical measures of target engagement to adjust for different sensitivities. For fluid biomarkers, the kinetics of how biomarkers appear in the fluid samples  may differ and must be accounted for. While expensive and labor-intensive, kinetics can be measured through in vivo labeling techniques  that tradiseases , yet curn = 161) while a population-based autopsy study [n = 455) as Braak stage 0. Depending on the thresholds used, tau PET recapitulates the histological progression of tau lesions seen at autopsy; however, the thresholds set may render the tau PET “Braak stage” an underestimate of the true Braak stage at autopsy, particularly at early stages, as seen in these studies [11C-PiB and other ligands targeting Aβ can detect early, neocortical involvement of plaques [Idiosyncratic properties of pathophysiological processes can manifest misleading results in biomarker-based studies of pathophysiology. For PET, there is a heterogeneous uptake of different ligands throughout the brain, and differences in this uptake, off-target binding, and imaging sensitivity should be accounted for. In AD, early tau lesions begin in the brainstem nuclei followed by limbic involvement, whereas Aβ lesions begin in the neocortical regions , 8, 49.  studies , 57. Add studies , 59. By  plaques , making Other biological factors, including the significant impact of low-abundance hallmarks such as mutant huntingtin, synaptic proteins, and neurogranin should also be considered, as their low abundance may lead to underestimation of the roles these hallmarks play using event-based modeling approaches. To illustrate, differences in relative abundances of tau versus Aβ lesions, due to tau tangles accumulating within cells and Aβ occurring extracellularly, make the relative determination of proteinopathy onset difficult in vivo. The strengths of Aβ biomarkers may outweigh the weaknesses of tau biomarkers, potentially overrepresenting the relative involvement of Aβ versus tau lesions at different AD stages, especially in early stages. The development of biomarkers and studies with multidisciplinary, postmortem observations are needed to reconcile these issues.Biomarkers are invaluable for elucidating pathophysiology with appropriate caution. Specific biological questions may call for different implementations of biomarkers, and establishing universal guidelines for their research use would be presumptuous. Biomarker status may be sensitive and specific to certain neuropathological diagnoses; however, one should not assume that clinical utility implies broad-sweeping research utility or vice versa. In vivo, labeling approaches and high-resolution biomarker-neuropathology correlations are critical for assessing the validity of individual biomarkers as they relate to underlying lesions . Unless Rigorous validations of biomarkers through methods such as kinetics quantification  or postmThe 2018 NIA-AA guidelines for an in vivo research definition of AD set an outline for clinical trials based on a biomarker definition of AD [Aβ and tau PET imaging could serve as useful outcomes in clinical trials due to their ability to detect regional changes in vivo preceding significant atrophy , 62. TheSimilarly, therapeutic development for HD serves to benefit from biomarker development. Despite the existence of a highly specific and sensitive genetic marker , 65, it Novel ultrasensitive immunoassays make blood biomarkers promising for the future as less invasive, cost-effective screening instruments . In AD, In individuals with suspected neurodegenerative diseases that lack known monogenic etiologies, biomarkers are currently used on an exclusionary basis to rule out other diseases and may be used to support a specific diagnosis of a neurodegenerative disease. Other biomarkers are in the pipeline for clinical validation and determination of clinical value.18F-FDG PET can also be used to identify the affected brain regions and networks [For example, structural MRI can be used to exclude space-occupying lesions and assess patterns of atrophy that aids diagnoses made by neurological assessment. Functional MRI and networks , 79, 80.networks . A summaFollowing the discovery and validation phases of biomarker development, standardization and clinical utility are key steps for clinical implementation. In these phases of biomarker development, key questions regarding optimal procedures, reproducibility, and elucidation of the biological relevance can be assessed. Further, these phases will determine the sensitivity and specificity of each biomarker to a given disease. For example, plasma NfL well represents the underlying neurodegeneration , but theA further criterion for establishing biomarkers in clinical practice, even when biologically meaningful, is the utility for patient management which can determine financial coverage for the test. An ongoing study in the USA is examining how Aβ PET results influence patient management . PrelimiIn addition to the array of targets that can be detected by standard fluid and imaging biomarkers, other features of neurodegenerative diseases have been proposed as viable biomarkers of disease progression. One technique, the Multimer Detection System-Oligomeric Aβ, examines the tendency of plasma proteins to oligomerize, circumventing issues in measuring concentrations of Aβ itself . AnotherIn combination with basic science and neuropathologic examination, biomarkers are invaluable for building a narrative on pathophysiology, clinical etiology, and strategies for interventions. As there are numerous ways biomarkers may be informative, caution must be exercised to ensure appropriate interpretation given the varied limitations of different modalities. Importantly, a significant gap remains for biomarker availability in non-AD neurodegenerative diseases. As the field works towards therapies for dementias, there continues to be a grave need for novel biomarkers, improved development of existing tools, standardization, and improved accessibility for clinical and research communities.