Constructing the rough PPANs

The dynamic expression and assembly of all functional components in the genome of an organism are significantly influenced by the environment. In this study, we aimed at the reconstruction of the protein-protein association networks under TNFα stimulus at different time stages and the analysis of dynamic cross-talks to investigate the network characteristics of an endothelial inflammatory system. The proposed method of the PPAN construction is divided into four steps (see Figure 2). The rough PPAN responsive to TNFα stress is established in the first two steps, and the refinement is then performed in the last two steps.

Pruning the rough PPAN via a dynamic model

On the basis of the database information and the literature evidences, the rough PPAN, which consists of all possible static interactions among the proteins of interest, was constructed. Since the rough PPAN only outlined the possible protein interactions under all kinds of experimental conditions, these interactions were further pruned to indicate the effective protein interactions under TNFα stress. As the time profiles of microarrays may reflect the co-existence of two particular proteins, time-course microarray data were employed to assess the significance of protein-protein interactions at certain time. Here, a dynamic regulatory model and model selection method Akaike Information Criterion (AIC) [25] were used to prune the rough PPAN. The details of the pruning process are described in the following paragraph and in Supplementary Methods [Additional file 2].

Step 3

In this step, the protein association equation was used to describe the protein-protein associations between target proteins of interest and its possible interacting proteins of the human inflammatory system. For a target protein p in the rough PPAN, the stochastic dynamic model of the protein is as follows [26]

(1)

where y _p [t] represents the protein expression level at time t of the target protein p, b _pq denotes the association parameter of the q-th interactive protein to p-th target protein, y _q [t] represents the protein expression level of the q-th regulator protein interacting with the target protein p, α _p denotes the effect of translation from mRNA to protein, x _p [t] represents the mRNA expression level of the corresponding target protein p, β _p indicates the degradation effect of the protein and ω _p [t] is the stochastic noise. The biological meaning of equation 1 is that the protein expression of the target protein p at the next time t+1 is contributed by the concentration of protein p at the current time t, the effect of Q regulatory protein interactions, the translation effect from mRNA, the degradation effect of the present time, and some stochastic noises [26].

Cross-talk analysis by counting the CTRVs

To extract the significance from ever-changing associations and to determine if a protein is a possible cross-talk candidate, an original approach based on catalogues of pathway and dynamic associations in sequential time stages was proposed to compute the Cross-Talk Ranking Value (CTRV) for cross-talk analysis. We first clustered every protein (node) in the network into different pathways, and then calculated the number of associations which link outward to different pathways for each node. The numbers of associations in different time stages were summed up, resulting in the CTRVs. In general, if a protein has more associations to connect with several pathways, it would be considered to have more possibility as a cross-talk candidate. It should be noted that the protein associations, which link out as regulations to the other proteins and link in as regulations from other protein, are both important to the cross-talk analysis. A highly regulated protein always plays a critical role to receive, mediate or amplify signaling cascade, and a protein which intensively regulates others is usually characterized as an activator, inducer and transcription factor. Therefore, the proposed measurement of CTRV concentrates on counting the associations which link to different pathways for each protein, rather than takes account of every linkage as the ranking value, and the CTRVs of proteins are considered as a measurement to reflect the potential of a protein in connection with multiple signaling pathways. For example, protein A belongs to pathway A, and protein B belongs to pathway B. If all the proteins connected with protein A are within the pathway A, the numbers of connection for protein A will be considered as no change (see Figure 3A). If protein A connects with protein B but they belong to different pathways, then both ranking numbers of protein A and B will be added by one (see Figure 3B).

Because the CTRVs are counted based on the pathway catalogues, the way of pathway classification will be a critical step to determine the values of CTRVs. There are some proteins which have been proven to be involved in more than one pathway, but it is not appropriate to assign one protein to multiple pathway catalogues. The multi-assignment will decrease the values of CTRVs, which may cause the true cross-talk candidates to be neglected. To overcome this problem, every protein is only assigned to one pathway in this analysis. We assume that the active sequence under the TNFα stress is TNFα, IL-1, MyD88-dependent and finally MyD88-independent pathway. If there is a protein involved in more than one pathway, this protein will be assigned to the earliest activated pathway among them. Because the realistic situation for the activated sequence of pathways in vivo is unavailable, this hypothesis is based on the feedback signal from the known knowledge. In other words, TNFα stress will induce the gene expression and secretion of IL-1 cytokine [27], and upon binding of IL-1, the IL-1 receptor will associate with IL-1RAcP [28, 29], forming a functional signaling receptor complex to involve MyD88 to activate the related pathway [30] Nevertheless, there is a lack of evidence to reveal that the TNFα stimulus will induce the MyD88-independent pathway, so we assume that this pathway is activated last.

Construction of refined PPANs at different time stages of inflammatory system

The proposed method was used to investigate the refined PPANs at different time stages of inflammatory system under TNFα stress. The genome-wide microarray data downloaded from the Gene Expression Omnibus (GEO) database at the NCBI website (http://www.ncbi.nlm.nih.gov/geo/ accession number: GSE9055) were adopted in this study. HUVEC (human umbilical vein endothelial cells) were treated with 10 ng/ml TNFα and the samples were collected every 15 or 30 minutes (0~8 hrs, 25 time points) [31]. The data set of 25 time points is divided into 6 time stages (0~1, 1~2, 2~3, 3~4, 4~6, 6~8 hr), resulting in 6 subsets of data. For each time stage, the corresponding data is used to identify the parameters in equation 1 and to prune down the rough PPAN based on the identified parameters to obtain the refined PPAN of each time stage, respectively. Consequently, six refined PPANs are constructed for six time stages. These refined PPANs are rearranged and visualized by the Cytoscape tool [32] (see Figure 4). The numbers of nodes, edges and the highly connected hubs at different time stages are shown in Table 2.

Investigation of the TNFα signaling network

TNFα is a highly pleiotropic cytokine of inflammation that activates leukocytes and enhances adherence of neutrophils and monocytes to endothelium. As TNFα is synthesized by macrophages and other cells in response to pathogen-associated molecular patterns, inflammatory products, and other invasive stimuli, it mediates cellular responses through two distinct receptors, the p60 TNF receptor (TNFR1, p55) and the p80 TNF receptor (TNFR2, p75) [19]. These two receptors are present on the plasma membranes of virtually all cells except the erythrocyte, sharing structural homology in the extracellular TNFα-binding domains and exhibiting similar binding affinity for TNFα. However, they induce separate cytoplasmic signaling pathways following receptor-ligand binding. In order to investigate the TNF pathway clearly, TNFα-related proteins were extracted from the whole network, and the TNFα-related pathway is shown in Figure 5A. The inferred functional modules supported by literature evidences in the refined PPAN are further shown in Supplementary Table S2 [Additional file 3].

NFκB activation (TNFR1-TRADD-TRAF2-RIP) - One major capability of TNFα signaling pathway is of mediating the activation of inflammatory response transcription factor, NFκB. Upon activation of TNFR1 at the plasma membrane, the TNFR1 death domain (DD) serves as a docking site for the DD-containing adaptor protein TRADD through homotypic DD interactions [33]. TRADD then sequentially recruits TNF receptor-associated factor 2 (TRAF2) and the serine/threonine kinase RIP, which rapidly signals to NF-κB activation [33, 34]. The functional module including proteins TNFR1, TRADD, TRAF2, and RIP were successfully identified in the PPAN.

NFκB activation (TNAF5-RIP, MEKK3-IKKβ-TAK1) - Two other functional modules which associated with NFκB activation were also recognized. TRAF5 has been implicated in the TNF-induced NF-κB activation, as in contrast to the single TRAF2 or TRAF5 knockout cells, TRAF2/TRAF5 double-knockout cells show impaired NF-κB activation upon TNF stimulation [35]. Unlike TRAF2, TRAF5 only interacts with RIP, but not with TRADD in co-immunoprecipitation assays [35], which can also been seen in the PPAN. In addition, MEKK3 has been shown to play a critical role in TNF-induced NF-κB activation using MEKK3-deficient fibroblast cells [36]. MEKK3 was also demonstrated to directly phosphorylate IKK and the kinase activity was regulated by TAK1 [36, 37]. These functional interactions which result in NF-κB activation are observed in the refined PPAN.

IKK activation (RIP-IKKs) and protein recruitment (RIP-TAK1) - For the IKK activation, RIP responds to TNF and becomes K63-poly-ubiquitinated at lysine 377 in its intermediate domain. This is indispensable for IKK activation upon TNF stimulation, as mutation of lysine 377 abolishes the ability of RIP to rescue IKK activation in RIP-deficient cells [38]. RIP also plays a role in the recruitment of TAK1, as TAK1 fails to translocate to the TNFR1 complex upon TNF stimulation of RIP-deficient Jurkat cells [37].

Apoptosis (TRADD-RIP-FADD-TRAF2-CASP8) and protein kinase (TAK1-TAB1-TAB2) - Apoptosis is another critical function involved in the TNF pathway. TNFα binding will promote the complex forming of TNFR1 at the cell membrane. As TRADD, RIP and TRAF2 dissociate from TNFR1, and endosomal TNFR1 recruits the DD-containing adaptor protein FADD, which binds itself to caspase-8, a cytoplasmic complex forms and is implicated in signaling to apoptosis [39]. Moreover, the TAK1-TAB1-TAB2 complex is a protein kinase module which takes part in the TNFα signaling transduction and IKK activation. Activation of TAK1 leads to autophosphorylation of TAB1, whereas TAB2 becomes phosphorylated at the membrane, probably by an upstream protein kinase [40].

Investigation of the IL-1R and TLR-4 signaling networks

The IL-1R/TLR superfamily can be clustered into multiple receptors, which all play a crucial role in both innate and adaptive inflammatory systems [12]. Members of the IL-1R subfamily are characterized by Ig-like domain that binds to specific IL-1-related cytokines, which is a primary regulator of inflammatory and inflammatory responses. By means of type I receptor (IL-1R1), it activates specific protein kinases, including the NFκB inducing kinase (NIK) and three distinct mitogen-activated protein (MAP) kinase cascades. These kinases modulate a number of transcription factors including NFκB, AP1 and CREB, each of which regulates a plethora expression of immediate early genes central to the inflammatory response [41]. On the other hand, the TLR subfamily includes 13 members that contain leucine-rich repeat motifs in their extracellular domains, which recognize distinct pathogen-associated patterns such as LPS, microbial lipopeptides, viral double-stranded RNA and CpG DNA [42]. These receptors have been established to play an essential role in the activation of inflammation and induce the release of critical pro-inflammatory cytokines that are necessary to activate potent inflammatory responses [43]. The cytoplasmic portions of both IL1R- and TLR-family members share a common structural motif, the so-called TLR and IL-1R (TIR) homology domain at their cytoplasmic portion [44]. Like TNFRs, TIR-containing receptors do not have catalytic activity and use intracellular adaptors and signal-transducing molecules to activate effector pathways [45]. Homotypic TIR-TIR interactions with a limited set of TIR-containing adaptors explain why more than 15 different receptors trigger only a small number of signaling pathways [45]. Because of the largely common use of signaling modules, the IL1R- and TLR4-related pathways were integrated into the same diagram for investigation (see Figure 5B). The inferred functional modules supported by literature evidences in the refined PPAN are further shown in Supplementary Table S3 [Additional file 4].

Pathway adaptor (MyD88-TLR4-IL1, IL1-IL1R1-MyD88-TOLLIP-IRAK1) - MyD88 is the universal adaptor for TLRs and is also a member of the IL-1 receptor subfamily [30]. Upon binding of IL-1, the IL-1R1 will associate with IL-1 receptor accessory protein (IL-1RAcP), forming a functional signaling receptor complex [28]. Then TIR domain containing adaptor protein MyD88 is recruited to the receptor complex [29]. This leads to the translocation of IRAK1, together with the adaptor protein TOLLIP [46], into the IL-1R1 and then IRAK1 interacts with TRAF6 [47]. The functional modules which are responsible for adaptation are observed in the refined PPAN.

Protein kinase (TRAF6-IRAK1-IRAK4, TRAF6-IRAK1-TAK1-TAB1-TAB2) and IKK activation (TRAF6-IKKs) - After forming the pathway adaptor modules, IRAK4 is recruited to TRAF6 and activated by intramolecular autophosphorylation [48]. Activation of IRAK4 leads to phosphorylation of IRAK1, procuring full kinase activity [48, 49]. Then the IRAK-1-TRAF6 complex interacts with a pre-existing TAK1-TAB1-TAB2 membrane-bound complex [50], thus forming the protein kinase module. After that, the protein kinase module will translocate to the cytosol, whereas IRAK1 stays at the membrane and becomes polyubiquitinated. In the cytoplasm, TRAF6 interacts with the E2 ubiquitin-conjugating enzyme complex Ubc13/Uev1A [51]. In addition, lysine 124 in TRAF6 was identified as the main ubiquitin acceptor site for autoubiquitination, and mutation of this lysine leads to impaired TAK1, IKK and JNK activation [52, 53]. Oligomerization of TRAF6 might lead to auto-polyubiquitination of TRAF6, which is necessary for IL-1-and LPS-induced NF-κB activation, whereas TRAF6- induced poly-ubiquitination of NEMO (NF-κB essential modulator) might rather play a role in IL-1-induced JNK activation [12].

Cross-talk analysis of the refined PPANs

The biological significance of some highly ranked proteins we identified (Table 3) was investigated. Interleukin-1 receptor-activated kinase 1 (IRAK1, ranked No.1) is one of the key mediators in the signaling pathways of TLRs/IL-1Rs. IRAKs which initiate a cascade of signaling events eventually lead to induction of inflammatory target gene expression [54]. IRAK1 activation constitutes an important signaling module in both IL-1R and TLR signal transductions. Binding to myeloid differentiation primary response protein (MyD88, ranked No.5) brings IRAK1 and IRAK4 together at the receptor complex and facilitates the phosphorylation of IRAK1. In the downstream of MyD88, the important role of IRAK and TRAF6 in related pathways has also been confirmed in some knockout studies. Cells from IRAK-deficient mice were shown to be defective in their response to IL-1 and IL-18 [55]. Tumor necrosis factor receptor-associated factor 6 (TRAF6, ranked No.2) is a pivot signaling molecule regulating a diverse array of physiological processes including adaptive immunity, innate immunity and the development of several tissues. It is also essential for the signaling downstream of the IL-1R/TLR superfamily [56]. The crucial biological role of TRAF6 in the IL-1R/TLR signaling has been demonstrated by the targeted deletion of TRAF6 [57, 58]. Mitogen-activated protein kinase kinase kinase 14 (NIK, ranked No.3) is a member of the MAPKKK family that may either directly or indirectly phosphorylate or activate IKKα/β, leading to the phosphorylation and degradation of IκBα followed by NFκB activation [59]. NIK is also a common mediator of NF-κB activation by the TNF receptor family and shown to activate the downstream of TRAF-associating receptor signaling pathways, including TNFR, CD40, CD30 and LTβr [60, 61]. Tumor necrosis factor, alpha-induced protein 3 (TNFAIP3/A20, ranked No.4) is a protein which can be induced in many cell types and by a wide range of stimuli [62]. Although A20 was originally characterized as an inhibitor of TNF-induced apoptosis [63], it has been most intensively studied as an inhibitor of NF-κB activation. The use of A20-deficient mice and RNA interference technologies has revealed the crucial role of A20 in a variety of pathogen- and cytokine-induced signaling pathways. Mice lacking A20 are born at normal Mendelian ratios but die shortly after birth due to massive multi-organ inflammation, which is an indication of a key role for A20 in homeostasis of the host [64].

Although there are still many highly ranked proteins with critical roles in signal transduction like MyD88 and SIGIRR, it is not our intension to use an exhaustive attack method to prove them one by one. Instead, the global properties and robustness of the network architecture in the sequel will be investigated.

Dynamic progression of the PPANs

To determine the dynamic progression of PPANs at different time stages, we presented the time series PPANs from 0 to 3 hours in which the positions of nodes are rearranged based on approximately up/down-stream relations (see Figure 6, and the complete and pellucid time series diagrams from 0 to 8 hours are presented in Supplementary Figures [Additional file 5]).

In the first hour, there is a very obvious signal cascade which passes through TNFR1, TRADD, TRAF2, RIP, NIK, TAK1/TAB1/TAB2 complex and finally reaches the IKK complex (see Figure 6, 0~1 hour, red edges). It seems to be the rapidest way to activate the NF-κB transcription by TNFα induction. This well-characterized pathway contains NF-κB, JNK, p42/p44 mitogen-activated protein kinase (MAPK) and p38 MAPK [19]. Interestingly, NIK, which seems to be an important mediator between RIP and IKK family in our network diagram, was not previously considered to be a part of the TNF-induced NF-κB activation. However, Yin et al. found that NIK is required for NF-κB activation by LTβR [65]. In addition, MAP/ERK kinase kinase kinase 3 (MEKK3) is also involved in this pathway by RIP. Gene deletion studies have indicated that MEKK3 is required for IKK activation and functions downstream of RIP in TNF-induced NF-κB activation [66]. In the second hour, the IL-1R/TLR4 signaling pathways are sequentially turned on after the TNFR-related pathway (see Figure 6, 1~2 hour, red edges). This observation suggests the movement of autocrine signaling, in which a cell secretes a hormone or chemical messenger that binds to autocrine receptors on the same cell type, leading to changes in the cells. At this time point, the connections in the TNFR pathway become relatively less than those shown in the first hour and even display an inhibitory effect on this pathway. The reason for the rearrangement of protein associations might be that the cell's inflammatory mechanism tends to focus on some specific mechanisms which largely share common community to fight against the pathogens, rather than distributes resources to the overextended pathways. In the third hour, the TNFR-related pathway is triggered again. It is noticed that several negative regulators such as SOC1 (inhibitor of TIRAP (MAL) and p56), IRAK3 (inhibitor of IRAK1 and IRAK4) and A20 (inhibitor of TRAF6) are significantly expressed at this stage, reflecting the inhibitory effect of anti-inflammation (see Figure 6, 2~3 hour, purple edges). Apart from these three refined PPANs, the dynamic properties of another three residual networks of the late stages of immunity (3 to 4, 4 to 6 and 6 to 8 hours) are more like at steady state without significant perturbations (see Supplementary Figures [Additional file 5]).

Specific architecture in the signaling network

A cell's behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond and adapt to an ever-changing environment. In case of pathogen invading, the human inflammatory system is required to rapidly take appropriate response to eliminate or moderate the lethal factors without unnecessary wastage. Figure 7 displays the bow-tie structure extracted from the PPANs. The core elements in the bow-tie structure are the highly ranked proteins according to the CTRV ranking algorithm. As different receptors on the cell membrane are only able to recognize their specific pathogen-associated molecular patterns (PAMPs), these receptors need to form various functional modules by complex and dimer/trimer assembling for representing different signals of pathogens. Then these various types of signal would converge to a common cross-talk, that is, the core elements in the bow-tie structure. Therefore, the cross-talks may be considered as a robust and efficient signal processor on the pivotal position of signal transduction, which plays a role of rearranging the sinew and determines which necessary protective mechanisms or recruitments should be activated. Through the coordination of signal processor, inflammatory system organizes the order and balance in the cell and human body.

Oda and Kitano manually integrated 411 published literatures and presented a comprehensive map of TLRs and IL-1 receptor signaling networks under different stimulant conditions [67]. This map illustrates the possible existence of a main network subsystem that has a bow-tie structure in which MyD88 is a non-redundant core element, two collateral subsystems with small GTPase and phosphatidylinositol signaling, and MyD88-independent pathway [67]. In comparison of our ranking results with their signaling map, it reveals that the top ranked proteins such as IRAK1 (ranked No.1), TRAF6 (ranked No.2) and MyD88 (ranked No.5) in our study have also been considered the pivotal roles in the bow-tie core process. Specifically, the process mediates various types of stimulant signals and triggers the downstream activation of NF-κB and MAPK cascade, leading to the induction of many target genes such as cytokines. However, the map of Oda and Kitano only reflects the possible static connections without stimulus-specific response or temporal changes. In contrast, we integrated the gene expression patterns from time course data to infer the dynamic protein-protein interactions and networks. Consequently, our results may suggest a more significant and realistic bow-tie core network under a specific stimulus.

Possible existence of TLR4 endogenous ligand

Though the main focus of our study is the TNFRs that are different from the TLRs in Oda and Kitano [67], numerous similar functional modules are identified in this study. This observation reveals the characteristics of module community in the inflammatory system and the presence of active feedback signals from cytokines. It is proven that TNFα-induced cells will activate the transcriptional expression of several genes encode cytokines such as IL-1α, IL-1β and IL-6 [27]. These autocrine signals can act as the positive feedback to enhance the inflammatory responses by turning on other correlated inflammatory pathways, such as IL-1 and MyD88-dependent pathway of TLR4. Interestingly, in addition to the two pathways mentioned above, our TNFα-induced HUVEC model also exhibits the virtually complete activation of MyD88-independent pathway of TLR4 which theoretically may not be involved in the single TNFα-treated condition (see Figure 5B). It has been shown that increased expression and signaling by TLR4 may contribute to the activation of innate immunity in the injured myocardium [68]. Because no infection is evident in this model, our observation raises the intriguing possibility that TLR4 may also function during inflammation, possibly in response to an endogenous ligand. One candidate of this ligand is S100, a multigenic family of non-ubiquitous Ca²⁺-modulated proteins of the EF-hand type expressed in vertebrates exclusively [69]. It has been demonstrated that primary tumors secrete soluble factors, including VEGF-A, TGFβ and TNFα, which induce expression of S100 in the myeloid and endothelial cells within the lung prior to tumor metastasis [70]. Recently, the increased S100A8 and S100A9 levels were also detected in various human cancers, presenting abundant expression in neoplastic tumor cells as well as infiltrating immune cells [71]. Its expression and potential cytokine-like function in inflammation and in cancer suggests that S100A8/A9 may play a key role in inflammation-associated cancer. Another candidate is high-mobility group box 1 (HMGB1), which is one kind of damage-associated molecular patterns (DAMPs). HMGB1 is a nuclear protein expressed in nearly all cell types. In normal conditions, HMGB1 binds to DNA and facilitates gene transcription. Under stress conditions such as injury and infection, HMGB1 is released and promotes inflammation [72]. TLR4 has been identified as a receptor of HMGB1 as well as TLR2 and RAGE (receptor of advance glycation end product) [73]. As the mechanisms of promoting the release of HMGB1 and its activating signaling pathways remain to be completely elucidated, HMGB1 also appears to have several regenerative effects leading to tissue repair [72, 74]. Therefore, HMGB1 has potential significance in clinical medicine.

Negative feedback controls of the cross-talks

Inflammation is normally a protective response to destroy, dilute, or isolate an eliciting agent and to promote the repair of injured tissue. However, when inflammation is excessive or persistent, it may cause tissue injury or organ dysfunction and may contribute to the pathogenesis of disease. For this reason, at the anti-inflammation stage cells need to make use of the negative regulator proteins and cytokines to inhibit the function of some dominant cross-talks to recover from the dramatic activations in inflammation. This kind of negative feedback has also been proven to be related to some TNFα-mediated inflammatory diseases. For example, A20 has been identified as a negative regulator of the core cross-talk element TRAF6 [75], and several studies have shown that deficiencies in A20 are associated with some autoimmune diseases, including rheumatoid arthritis [76], systemic lupus erythematosus [77], and Crohn's disease [78]. These clues also reveal the fragility of the bow-tie structure. Because of the non-redundant property of core elements in the bow-tie structure, some targeted perturbations from environment and lethal pathogens might result in destructive consequences.

On the other hand, negative feedback controls may also play an important role to buffer the wide range of environment stimuli. Previous studies have indicated that proteasome inhibition can suppress TNFα-induced activation of adhesion molecules in endothelial cells in vitro [79, 80]. These studies showed that short-term treatment of endothelial cells with high doses of proteasome inhibitors results in strong inhibition of cytokine-induced expression by preventing nuclear translocation of NF-κB. Cheong et al. undertook an iterative computational and experimental investigation of the dynamic properties of TNFα-mediated activation of the transcription factor NF-κB [81]. They found that the temporal profile of the NF-κB activity is invariant to the TNFα dose from 0.1 to 10 ng/ml. These discoveries reflect the properties of robustness and protective mechanisms in the inflammatory system which might also be the effects of feedback controls to the cross-talks in the signaling network. As the environmental stresses trigger the appropriate responses to protect organisms themselves, it will help their survival. However, if the stresses suddenly perturb to an acute level and the inflammatory responses still take a correspondingly sharp response to excessively activate the downstream reactions, the protective mechanisms will instead injure the organisms. For this reason, there must be some cross-talks which buffer the perturbation from upstream signals and respond to the downstream negative feedback regulators to alleviate the reflecting scale.