The expression of novel membrane-type matrix metalloproteinase isoforms is required for normal development of zebrafish embryos.

Matrix metalloproteinases (MMPs) play important roles in the turnover of components of extracellular matrix (ECM) and in the processing of active and latent-signaling molecules bound to the ECM or associated with the cell surface. Through such actions, MMPs regulate a variety of cellular and developmental processes. Membrane-type matrix metalloproteinases (MT-MMPs) are of particular importance because they function in the immediate pericellular environment that modulates both cell-cell and cell-ECM interactions. In this study, we utilized zebrafish as a developmental model to study the role of MT-MMPs during early embryogenesis. We successfully isolated two isoforms of a MT-MMP homologue that are structurally similar to MT1-MMP. They have been named zebrafish MT-MMPalpha and beta. Zebrafish MT-MMPbeta is unique among vertebrate MT-MMPs in that it contains an Arg-Glu-Asp (RED) multiple-repeat motif in its linker region. Whole mount in situ analysis, RT-PCR, immunofluorescence, reporter analysis, Western blot analysis, and zymography indicated that MT-MMPalpha and beta were expressed through at least the first 72 h of development and that this expression was targeted to the cell surface. Functional studies using injection of either mRNA or morpholino antisense oligonucleotides resulted in a truncation of the cranial to caudal axis as monitored through 72 h post fertilization, indicating that zebrafish MT-MMPalpha and beta had an important role in embryonic development. Axis markers indicated that these effects likely involved processes occurring later than 10 h of embryogenesis.     

Matrix metalloproteinase 2 from human rheumatoid synovial fibroblasts. Purification and activation of the precursor and enzymic properties

Human rheumatoid synovial cells in culture secrete at least three related metalloproteinases that digest extracellular matrix macromolecules. One of them, termed matrix metalloproteinase 2 (MMP-2), has been purified as an inactive zymogen (proMMP-2). The final product is homogeneous on SDS/PAGE with Mr = 72,000 under reducing conditions. The NH2-terminal sequence of proMMP-2 is Ala-Pro-Ser-Pro-Ile-Ile-Lys-Phe-Pro-Gly-Asp-Val-Ala-Pro-Lys-Thr, which is identical to that of the so-called '72-kDa type IV collagenase/gelatinase'. The zymogen can be rapidly activated by 4-aminophenylmercuric acetate to an active form of MMP-2 with Mr = 67,000, and the new NH2-terminal generated is Tyr-Asn-Phe-Phe-Pro-Arg-Lys-Pro-Lys-Trp-Asp-Lys-Asn-Gln-Ile. However, following 4-aminophenylmercuric acetate activation, MMP-2 is gradually inactivated by autolysis. Nine endopeptidases (trypsin, chymotrypsin, plasmin, plasma kallikrein, thrombin, neutrophil elastase, cathepsin G, matrix metalloproteinase 3, and thermolysin) were tested for their abilities to activate proMMP-2, but none had this ability. This contrasts with the proteolytic activation of proMMP-1 (procollagenase) and proMMP-3 (prostromelysin). The optimal activity of MMP-2 against azocoll is around pH 8.5, but about 50% of activity is retained at pH 6.5. Enzymic activity is inhibited by EDTA, 1,10-phenanthroline or tissue inhibitor of metalloproteinases, but not by inhibitors of serine, cysteine or aspartic proteinases. MMP-2 digests gelatin, fibronectin, laminin, and collagen type V, and to a lesser extent type IV collagen, cartilage proteoglycan and elastin. Comparative studies on digestion of collagen types IV and V by MMP-2 and MMP-3 (stromelysin) indicate that MMP-3 degrades type IV collagen more readily than MMP-2, while MMP-2 digests type V collagen effectively. Biosynthetic studies of MMPs using cultured human rheumatoid synovial fibroblasts indicated that the production of both proMMP-1 and proMMP-3 is negligible but it is greatly enhanced by the treatment with rabbit-macrophage-conditioned medium, whereas the synthesis of proMMP-2 is constitutively expressed by these cells and is not significantly affected by the treatment. This suggests that the physiological and/or pathological role of MMP-2 and its site of action may be different from those of MMP-1 and MMP-3.     

Epithelial sodium channel (ENaC) is multi-ubiquitinated at the cell surface

MMP-2 (matrix metalloproteinase 2) contains a CBD (collagen-binding domain), which is essential for positioning gelatin substrate molecules relative to the catalytic site for cleavage. Deletion of the CBD or disruption of CBD-mediated gelatin binding inhibits gelatinolysis by MMP-2. To identify CBD-binding sites on type I collagen and collagen peptides with the capacity to compete CBD binding of gelatin and thereby inhibit gelatinolysis by MMP-2, we screened a one-bead one-peptide combinatorial peptide library with recombinant CBD as bait. Analyses of sequences from the CBD-binding peptides pointed to residues 715-721 in human alpha1(I) collagen chain as a binding site for CBD. A peptide (P713) including this collagen segment was synthesized for analyses. In SPR (surface plasmon resonance) assays, the CBD and MMP-2(E404A), a catalytically inactive MMP-2 mutant, both bound immobilized P713 in a concentration-dependent manner, but not a scrambled control peptide. Furthermore, P713 competed gelatin binding by the CBD and MMP-2(E404A). In control assays, neither of the non-collagen binding alkylated CBD or MMP-2 with deletion of CBD (MMP-2DeltaCBD) bound P713. Consistent with the exodomain functions of the CBD, P713 inhibited approximately 90% of the MMP-2 gelatin cleavage, but less than 20% of the MMP-2 activity on a peptide substrate (NFF-1) which does not require the CBD for cleavage. Confirming the specificity of the inhibition, P713 did not alter MMP-2DeltaCBD or MMP-8 activities. These experiments identified a CBD-binding site on type I collagen and demonstrated that a corresponding synthetic peptide can inhibit hydrolysis of type I and IV collagens by competing CBD-mediated gelatin binding to MMP-2.     

斑马鱼胚胎发育过程中TGF-1基因的表达特征分析

为研究转化生长因子 (Transforming growth factor , TGF)1对斑马鱼胚胎发育的调控作用, 通过NCBI获得TGF-1基因序列, TGF-1 cDNA全长1571 bp, 编码377个氨基酸。系统进化树分析发现, TGF-蛋白按照不同的类型严格聚类, 斑马鱼TGF-1与其他鱼类的TGF-1聚集到一个分支, 在进化中非常保守。对斑马鱼胚胎进行RT-PCR和Real-Time PCR检测显示, TGF-1基因为母源表达基因, 在分节期之前的表达水平比较低, 而从咽囊期开始持续高水平的表达。胚胎整体原位杂交发现, TGF-1基因在斑马鱼24 hpf 胚胎中开始有特异信号出现, TGF-1基因的表达主要分布在腮弓、侧线原基、耳囊、嗅觉基板、心脏和前肾等处, 表明TGF-1基因可能参与斑马鱼胚胎免疫调节、循环系统发育和侧线形成。用低氧处理斑马鱼胚胎, 发现低氧处理24h后斑马鱼胚胎发育延迟。利用Real-Time PCR和胚胎整体原位杂交检测发现, 低氧处理后发育延迟的斑马鱼胚胎中TGF-1 mRNA表达量较常氧组显著降低。以上结果表明, TGF-1基因参与斑马鱼胚胎发育调控, 并且可能与低氧处理后斑马鱼胚胎发育延迟有关。研究结果将为深入研究斑马鱼TGF-1基因的功能奠定基础。       

Pneumococcal zinc metalloproteinase ZmpC cleaves human matrix metalloproteinase 9 and is a virulence factor in experimental pneumonia

The ZmpC zinc metalloproteinase of Streptococcus pneumoniae, annotated in the type 4 genome as SP0071, was found to cleave human matrix metalloproteinase 9 (MMP-9). The previously described IgA protease activity was confirmed to be specifically linked to the IgA1-protease/SP1154 zinc metalloproteinase. MMP-9 is a protease cleaving extracellular matrix gelatin and collagen and is activated by proteolytic cleavage like most proteases. MMP-9 is a human protease and is involved in a variety of physiological and pathological matrix degrading processes, including tissue invasion of metastases and opening of the blood-brain barrier. While TIGR4 (serotype 4) and G54 (serotype 19) pneumococcal genome strains have a highly conserved copy of zmpC, the genome of R6 (a derivative of serotype 2 D39 strain) lacks zmpC. Both the analysis for zmpC presence and MMP-9 cleavage activity in various pneumococcal strains showed correlation of ZmpC with MMP-9 cleavage activity. When assaying clinical isolates of S. pneumoniae, the zmpC gene was not found in any of the nasal and conjunctival swab isolates, but it was present in 1 out of 13 meningitis isolates and in 6 out of 11 pneumonia isolates. In a murine pneumonia model, infection with a zmpC-mutant reduced mortality at 3-4 days post-infection by 75%, when compared with infection with wild-type strains. These data indicate that the ZmpC pneumococcal protease may play a role in pneumococcal virulence and pathogenicity in the lung.     

Hypoxia modulates the effects of transforming growth factor-beta isoforms on matrix-formation by primary human lung fibroblasts

Chronic hypoxia is implicated in lung fibrosis, which is characterized by enhanced deposition of extracellular matrix (ECM) molecules. Transforming growth factor-beta (TGF-beta) plays a key role in fibroblast homeostasis and is involved in disease states characterized by excessive fibrosis, such as pulmonary fibrosis. In this study, we investigated if hypoxia modulates the effects of TGF-beta on the expression of gelatinases: matrix metalloproteinase (MMP)-2 and MMP-9, interstitial collagenases: MMP-1 and MMP-13, tissue inhibitors of MMP (TIMP), collagen type I and interleukin-6 (IL-6). Primary human lung fibroblasts, established from tissue biopsies, were cultivated under normoxia or hypoxia in the presence of TGF-beta1, TGF-beta2 or TGF-beta3. Gelatinases were assessed by gelatin zymography and collagenases, TIMP, collagen type I and IL-6 by ELISA. Under normoxia fibroblasts secreted MMP-2, collagenases, TIMP, collagen type I and IL-6. TGF-betas significantly decreased MMP-1 and increased TIMP-1, IL-6 and collagen type I. Hypoxia significantly enhanced MMP-2, and collagenases. Compared to normoxia, the combination of TGF-beta and hypoxia reduced MMP-1, and further amplified the level of TIMP, IL-6, and collagen type I. Thus, in human lung fibroblasts hypoxia significantly increases the TGF-betas-induced secretion of collagen type I and may be associated to the accumulation of ECM observed in lung fibrosis.     

Diminished matrix metalloproteinase 2 (MMP-2) in ectomesenchyme-derived tissues of the Patch mutant mouse: regulation of MMP-2 by PDGF and effects on mesenchymal cell migration.

Platelet-derived growth factors (PDGF) regulate cell proliferation, survival, morphology, and migration, as well as deposition and turnover of the extracellular matrix. Important roles for the A form of PDGF (PDGF-A) during connective tissue morphogenesis have been highlighted by the murine Patch mutation, which includes a deletion of the alpha subunit of the PDGF receptor. Homozygous (Ph/Ph) embryos exhibit multiple connective tissue defects including cleft face (involving the first branchial arch and frontonasal processes), incomplete heart septation, and heart valve abnormalities before they die in utero. Analyses of the cell biology underlying the defects in Ph/Ph embryos have revealed a deficit in a matrix metalloproteinase (MMP-2) and one of its activators (MT-MMP) that are likely to be involved in cell migration and tissue remodeling, two processes necessary for normal cardiac and craniofacial development. Morphogenesis of these structures requires infiltration of ectomesenchymal precursors and their subsequent deposition and remodeling of extracellular matrix components. First branchial arch and heart tissue from E10.5 embryos were examined by gelatin zymography and RT-PCR in order to characterize the expression of MMPs in these tissues. Of the MMPs examined, only MMP-2 and one of its activators, MT-MMP, were expressed in the first arch and heart at this stage of development. Tissues from Ph/Ph embryos exhibited a significant decrease in both MMP-2 and MT-MMP compared to tissues from normal embryos of the same developmental stage. In order to assess whether this decrease affects the motile activity of mesenchymal cells, cell migration from Ph/Ph branchial arch explants was compared to migration from normal arch tissue and found to be significantly less. In addition, the migratory ability of branchial arch cells from normal explants could be reduced in a similar manner using a specific MMP inhibitor. Although it is still unclear whether the MMP-2 reduction is a direct result of the absence of response of Ph/Ph cells to PDGF-A treatment of normal branchial arch cells in vitro with recombinant PDGF-AA significantly upregulated MMP-2 protein. Together, these results suggest that PDGF-A regulates MMP-2 expression and activation during normal development and that faulty proteinase expression may be at least partially responsible for the developmental defects exhibited by Ph/Ph embryos.     

In situ localization of gelatinolytic activity in the extracellular matrix of metastases of colon cancer in rat liver using quenched fluorogenic DQ-gelatin.

Matrix metalloproteinases (MMPs) such as gelatinases are believed to play an important role in invasion and metastasis of cancer. In this study we investigated the possible role of MMP-2 and MMP-9 in an experimental model of colon cancer metastasis in rat liver. We demonstrated with gelatin zymography that the tumors contained MMP-2 and MMP-9, but only MMP-2 was present in the active form. Immunolocalization of MMP-2 showed that the protein was localized at basement membranes of colon cancer cells and in intratumor stroma, associated with extracellular matrix (ECM) components. However, zymography and immunohistochemistry (IHC) do not provide information on the localization of MMP activity. Therefore, we developed an in situ zymography technique using the quenched fluorogenic substrate DQ-gelatin in unfixed cryostat sections. The application of DQ-gelatin in combination with a gelled medium allows precise localization of gelatinolytic activity. Fluorescence due to gelatinolytic activity was found in the ECM of tumors and was localized similarly to both MMP-2 protein and collagen type IV, its natural substrate. The localization of MMP-2 activity and collagen type IV at similar sites suggests a role of MMP-2 in remodeling of ECM of stroma in colon cancer metastases in rat liver.     

Contributions of the MMP-2 collagen binding domain to gelatin cleavage. Substrate binding via the collagen binding domain is required for hydrolysis of gelatin but not short peptides.

Two matrix metalloproteinases, MMP-2 and MMP-9, contain each three fibronectin type II-like modules, which form their collagen binding domains (CBDs). The contributions of CBD substrate interactions to the catalytic activities of these gelatinases have attracted special interest. Recombinant (r) CBDs retain collagen binding properties and deletions of CBDs in these MMPs reduce activities on collagen and elastin. We have characterized further the requirement of the CBD for MMP-2 cleavage of gelatin. The analyses used intact rMMP-2 and rCBD to eliminate any confounding effects that might result from structural perturbations in rMMP-2 induced by deletion of the approximately 20 kDa internal CBD. In protein-protein binding assays, 2% DMSO disrupted gelatin interactions of both rCBD and rMMP-2. At this concentration, DMSO also reduced the gelatinolytic activity by approximately 70%, pointing to a central role of CBD-substrate interactions during MMP-2 cleavage of gelatin. Subsequently, soluble rCBD was determined to competitively inhibit gelatin binding of unmodified rMMP-2 to gelatin by 73% and to reduce the MMP-2 degradation of gelatin by 70-80%. The residual gelatin cleavage that was not inhibited even by molar excess rCBD could be accounted for by degradation of short substrate molecules. Indeed, rCBD inhibited rMMP-2 cleavage of an 11 amino acid collagen-like peptide substrate (NFF-1) by less than 10%. These observations were confirmed with enzyme extracts from experimental tumors in mice. In the presence of rCBD, approximately 65% of the MMP-derived gelatinolytic activity was eliminated. Together, these results demonstrate that the CBD is absolutely required for MMP-2 cleavage of full-length collagen alpha-chains, but not for short protein fragments such as those generated by hydrolysis of gelatin.     

Matrix metalloproteinases and tissue inhibitor of metalloproteinase-2 in fetal rabbit lung

Cell-extracellular matrix interaction and extracellular matrix remodeling are known to be important in fetal lung development. We investigated the localization of matrix metalloproteinases (MMPs) in fetal rabbit lungs. Immunohistochemistry for type IV collagen, MMP-1, MMP-2, MMP-9, membrane type (MT) 1 MMP, and tissue inhibitor of metalloproteinase (TIMP)-2 and in situ hybridization for MMP-9 mRNA were performed. Gelatin zymography and Western blotting for MT1-MMP in lung tissue homogenates were also studied. MMP-1 and MT1-MMP were detected in epithelial cells, and MMP-2 and TIMP-2 were detected in epithelial cells and some mesenchymal cells in each stage. MMP-9 was found in epithelial cells mainly in the late stage. Gelatin zymography revealed that the ratio of active MMP-2 to latent MMP-2 increased dramatically during the course of development. MT1-MMP was detected in tissue homogenates, especially predominant in the late stage. These findings suggest that MMPs and their inhibitors may contribute to the formation of airways and alveoli in fetal lung development and that activated MMP-2 of alveolar epithelial cells may function to provide an extremely wide alveolar surface.     

Cloning, expression and functional study of translation elongation factor 2 (EF-2) in zebrafish

We have identified translation elongation factor 2 (EF-2) in zebrafish (GenBank Accession No. AAQ91234). Analysis of the DNA sequence of zebrafish EF-2 shows that the 2826 bp cDNA spans an open reading frame between nucleotide 55 to 2631 and encodes a protein of 858 amino acids. Zebrafish EF-2 protein shares 92%, 93%, 93% and 92% identity with the corresponding amino acid sequence in human, mouse, Chinese hamster and Gallus EF-2, respectively. Whole-mount in situ hybridization showed that zebrafish EF-2 was a developmentally regulated gene and might play important roles during the early development of zebrafish embryos. Therefore, we further studied the function of EF-2 during early embryogenesis. Using morpholino antisense oligo knockdown assays, anti-MO injected embryos were found to display abnormal development. The yolk balls were larger than normal and the melanophores spreading on their bodies became fewer. Furthermore, their tails were incurvate and their lenses were much smaller than those of the normal embryos. However the EF-2 overexpression data showed that extra EF-2 protein had no obvious effect on zebrafish embryonic development.     

Identification of collagen binding domain residues that govern catalytic activities of matrix metalloproteinase-2 (MMP-2)

An innovative approach to enhance the selectivity of matrix metalloproteinase (MMP) inhibitors comprises targeting these inhibitors to catalytically required substrate binding sites (exosites) that are located outside the catalytic cleft. In MMP-2, positioning of collagen substrate molecules occurs via a unique fibronectin-like domain (CBD) that contains three distinct modular collagen binding sites. To characterize the contributions of these exosites to gelatinolysis by MMP-2, seven MMP-2 variants were generated with single, or concurrent double and triple alanine substitutions in the three fibronectin type II modules of the CBD. Circular dichroism spectroscopy verified that recombinant MMP-2 wild-type (WT) and variants had the same fold. Moreover, the MMP-2 WT and variants had the same activity on a short FRET peptide substrate that is hydrolyzed independently of CBD binding. Among single-point variants, substitution in the module 3 binding site had greatest impact on the affinity of MMP-2 for gelatin. Simultaneous substitutions in two or three CBD modules further reduced gelatin binding. The rates of gelatinolysis of MMP-2 variants were reduced by 20–40% following single-point substitutions, by 60–75% after double-point modifications, and by > 90% for triple-point variants. Intriguingly, the three CBD modules contributed differentially to cleavage of dissociated α-1(I) and α-2(I) collagen chains. Importantly, kinetic analyses (k_cat/K_m) revealed that catalysis of a triple-helical FRET peptide substrate by MMP-2 relied primarily on the module 3 binding site. Thus, we have identified three collagen binding site residues that are essential for gelatinolysis and constitute promising targets for selective inhibition of MMP-2.     

The Activity of Collagenase-1 Is Required for Keratinocyte Migration on a Type I Collagen Matrix

We have shown in a variety of human wounds that collagenase-1 (MMP-1), a matrix metalloproteinase that cleaves fibrillar type I collagen, is invariably expressed by basal keratinocytes migrating across the dermal matrix. Furthermore, we have demonstrated that MMP-1 expression is induced in primary keratinocytes by contact with native type I collagen and not by basement membrane proteins or by other components of the dermal or provisional (wound) matrix. Based on these observations, we hypothesized that the catalytic activity of MMP-1 is necessary for keratinocyte migration on type I collagen. To test this idea, we assessed keratinocyte motility on type I collagen using colony dispersion and colloidal gold migration assays. In both assays, primary human keratinocytes migrated efficiently on collagen. The specificity of MMP-1 in promoting cell movement was demonstrated in four distinct experiments. One, keratinocyte migration was completely blocked by peptide hydroxymates, which are potent inhibitors of the catalytic activity of MMPs. Two, HaCaTs, a line of human keratinocytes that do not express MMP-1 in response to collagen, did not migrate on a type I collagen matrix but moved efficiently on denatured type I collagen (gelatin). EGF, which induces MMP-I production by HaCaT cells, resulted in the ability of these cells to migrate across a type I collagen matrix. Three, keratinocytes did not migrate on mutant type I collagen lacking the collagenase cleavage site, even though this substrate induced MMP-1 expression. Four, cell migration on collagen was completely blocked by recombinant tissue inhibitor of metalloproteinase-1 (TIMP-1) and by affinity-purified anti–MMP-1 antiserum. In addition, the collagen-mediated induction of collagenase-1 and migration of primary keratinocytes on collagen was blocked by antibodies against the α2 integrin subunit but not by antibodies against the α1 or α3 subunits. We propose that interaction of the α2β1 integrin with dermal collagen mediates induction of collagenase-1 in keratinocytes at the onset of healing and that the activity of collagenase-1 is needed to initiate cell movement. Furthermore, we propose that cleavage of dermal collagen provides keratinocytes with a mechanism to maintain their directionality during reepithelialization.     

Tissue- and Cell-Specific Co-localization of Intracellular Gelatinolytic Activity and Matrix Metalloproteinase 2

Matrix metalloproteinase 2 (MMP-2) is a proteolytic enzyme that degrades extracellular matrix proteins. Recent studies indicate that MMP-2 also has a role in intracellular proteolysis during various pathological conditions, such as ischemic injuries in heart and brain and in tumor growth. The present study was performed to map the distribution of intracellular MMP-2 activity in various mouse tissues and cells under physiological conditions. Samples from normal brain, heart, lung, liver, spleen, pancreas, kidney, adrenal gland, thyroid gland, gonads, oral mucosa, salivary glands, esophagus, intestines, and skin were subjected to high-resolution in situ gelatin zymography and immunohistochemical staining. In hepatocytes, cardiac myocytes, kidney tubuli cells, epithelial cells in the oral mucosa as well as in excretory ducts of salivary glands, and adrenal cortical cells, we found strong intracellular gelatinolytic activity that was significantly reduced by the metalloprotease inhibitor EDTA but not by the cysteine protease inhibitor E-64. Furthermore, the gelatinolytic activity was co-localized with MMP-2. Western blotting and electron microscopy combined with immunogold labeling revealed the presence of MMP-2 in different intracellular compartments of isolated hepatocytes. Our results indicate that MMP-2 takes part in intracellular proteolysis in specific tissues and cells during physiological conditions.     

Effects of bovine spermatozoa preparation on embryonic development in vitro

Background

The changes occurring in the rodent uterus after parturition can be used as a model of extensive tissue remodeling. As the uterus returns to its prepregnancy state, the involuting uterus undergoes a rapid reduction in size primarily due to the degradation of the extracellular matrix, particularly collagen. Membrane type-I matrix metalloproteinase (MT1-MMP) is one of the major proteinases that degrades collagen and is the most abundant MMP form in the uterus. Matrix metalloproteinase-2(MMP-2) can degrade type I collagen, although its main function is to degrade type IV collagen found in the basement membrane. To understand the expression patterns of matrix metalloproteinases (MMPs) in the rat uterus, we analyzed their activities in postpartum uterine involution.

Methods

We performed gelatin zymography, northern blot analysis and immunohistochemistry to compare the expression levels of MT1-MMP, MMP-2, matrix metalloproteinase-9 (MMP-9) and the tissue inhibitors of MMPs-1 and 2 (TIMP-1 and TIMP-2) in the rat uterus 18 h, 36 h and 5 days after parturition with their expression levels during pregnancy (day 20).

Results

We found that both MT1-MMP and MMP-2 localized mainly in the cytoplasm of uterine interstitial cells. The expression levels of MT1-MMP and MMP-2 mRNAs and the catalytic activities of the expressed proteins significantly increased 18 h and 36 h after parturition, but at postpartum day 5, their mRNA expression levels and catalytic activities decreased markedly. The expression levels of MMP-9 increased 18 h and 36 h after parturition as determined by gelatin zymography including the expression levels of TIMP-1 and TIMP-2.

Conclusion

These expression patterns indicate that MT1-MMP, MMP-2, MMP-9, TIMP-1 and TIMP-2 may play key roles in uterine postpartum involution and subsequent functional regenerative processes.