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The Wnt signaling pathway has been implicated in regulation of hematopoiesis through a plethora of studies from many different laboratories. However, different inducible gain- and loss-of-function approaches retrieved controversial and sometimes contradictory results. Different levels of activation of the pathway, dosages of Wnt signaling required, and the interference by other signals in the context of Wnt activation collectively explain these controversies. Gain-of-function or in vitro exposure to WNT proteins and more specifically WNT3a was shown to enhance hematopoietic stem cell (HSC) activity, but its exact role was still not completely understood. In a recent study we analyzed the hematopoietic system of mice deficient for this specific Wnt gene. Wnt3a deficiency results in early embryonic lethality around embryonic day 12.5 (E12.5), precluding analysis in adult mice, but allowing hematopoiesis to be studied in fetal liver (FL) and in the just colonized thymic rudiment. Notably, we showed that long-term HSCs and multipotent progenitors are reduced in FL and have severely reduced long-term reconstitution capacity as observed in serial transplantation assays. Of interest, deficiency in Wnt3a leads to complete abolition of canonical Wnt signaling in FL hematopoietic stem and progenitor cells. This HSC deficiency is not explained by altered cell cycle or survival and is irreversible, since it cannot be restored by transplantation into Wnt3a-competent mice. In addition, Wnt3a deficiency differentially affects myeloid and B-lymphoid lineages, with myeloid cells being affected at the progenitor level, while B lymphopoiesis is apparently unaffected. Immature thymocytes, however, were reduced in cell numbers due to lack of Wnt3a production by the thymic microenvironment. Our results show that while in the thymus Wnt3a provides cytokine-like, proliferative stimuli to developing thymocyte Wnt3a regulates cell fate decisions of FL HSC in a nonredundant way.

Infection of an individual (aged 20-30 years) by a virus will cause a response from the T (thymus derived) lymphocytes of which there are approximately 3 x 10(11). If the individual has not met the virus before, the response will come from the naive T cell subset (50 +/- 10% of the total T cell pool at this age) containing recent thymic emigrants produced from the thymus at approximately 10(8) per day. Their antigen-specific receptor has a defined specificity governed by the conformation of its two chains (alpha and beta), and the repertoire of specificities is somewhere in the region of 2 x 10(7) to 10(8). A successful response leads to clonal expansion and the generation of memory T cells to the infecting agent.

We used c-Fos-deficient activated T cells from the spleen and c-Fos-deficient thymocytes to address the capacity of these cells to undergo apoptosis in response to various stimuli. To determine the role of c-Fos in apoptosis regulation in thymocytes, we challenged thymocytes from wild-type and c-Fos-deficient mice with either TPA or the glucocorticoid dexamethasone. After various time points cells were stained according to the Nicoletti method and analyzed by FACS. Thymocytes from both genotypes exhibited similar efficiency of apoptosis in response to treatment with TPA or dexamethasone. Our data provide clear evidence that c-Fos is not required for apoptosis regulation in activated T cells as well as in thymocytes.

The monogenic autoimmune syndrome, APS-1 (autoimmune polyglandular syndrome type 1), is characterized by the loss of self-tolerance to multiple organs. Although mutations in the AIRE (autoimmune regulator) gene are responsible for the APS-1, the function of AIRE is not known. AIRE may determine thymic induction of tolerance to self-antigens in multiple organs. To study the function of AIRE in induction of self-tolerance, an in vitro negative selection system was made using 10(6) DO11.10 TCR transgenic thymocytes, 10(5) antigen-presenting cells (APC), and the different constructs of ovalbumin (OVA). In this system, the addition of the immunodominant epitopes of OVA peptide, the antigenic ligand for the DO11.10, made the thymocytes apoptotic and negatively selected. Overexpression of the AIRE gene in APC using retroviral transduction did not cause more thymocytes to become apoptotic. However, the suppression of the expression of AIRE in APC using the dominant-negative gene made the recovery rates of the thymocytes higher than those with the expression of LacZ as a control, and consequently inducing loss of self-tolerance. From these studies, it might be possible to suggest that the AIRE gene might regulate thymic induction of the negative selection process. The target genes for transcriptional regulation by AIRE have been investigated to study the influence of AIRE expression on other proteins in antigen presentation. The expression level of B7.1 was higher in APC expressing the dominant-negative form of AIRE. The target gene regulated by AIRE in transcription will be screened using cDNA microarray.

We have studied responses in thymoma patients to interferon-alpha and to the acetylcholine receptor (AChR) in early-onset myasthenia gravis (EOMG), seeking clues to autoimmunizing mechanisms. Our new evidence implicates a two-step process: (step 1) professional antigen-presenting cells and thymic epithelial cells prime AChR-specific T cells; then (step 2) thymic myoid cells subsequently provoke germinal center formation in EOMG. Our unifying hypothesis proposes that AChR epitopes expressed by neoplastic or hyperplastic thymic epithelial cells aberrantly prime helper T cells, whether generated locally or infiltrating from the circulation. These helper T cells then induce antibody responses against linear epitopes that cross-react with whole AChR and attack myoid cells in the EOMG thymus. The resulting antigen-antibody complexes and the recruitment of professional antigen-presenting cells increase the exposure of thymic cells to the infiltrates and provoke local germinal center formation and determinant spreading. Both these and the consequently enhanced heterogeneity and pathogenicity of the autoantibodies should be minimized by early thymectomy.

In mammals, the thymus is the primary central organ of the lymphoid system; after birth, it progressively diminishes in size, undergoing gradual atrophy. Physiological maturation and/or involution of the thymus may be accelerated by endogenous or exogenous factors. Exposure to extremely low frequency EMF seems to interfere with thymic cell death. Data suggest that, in the rat model, a prolonged exposure to 50 Hz electric and magnetic fields, independently from field strength, seems to affect thymic cell death and possibly thymic physiology, since alterations in the balance of cell death and other parameters such as mitoses might interfere with the positive and negative selection of thymocytes and with the immunosurveillance properties of the thymus.

Intrathymic T-cell differentiation is essentially driven by the thymic microenvironment, a tridimensional network formed by thymic epithelial cells and to a lesser extent, dendritic cells, macrophages, fibroblasts, and extracellular matrix components. Thymocyte migration throughout the thymus is partially dependent on extracellular-matrix (ECM)-mediated interactions. Herein we investigated the putative role of growth hormone (GH) upon events related to intrathymic T-cell migration. We demonstrated that GH upregulates the expression of ECM ligands and receptors in distinct preparations of cultured thymic epithelial cells TECs). We also showed that adhesion of thymocytes to thymic epithelial cells was significantly increased by GH treatment, an effect that could be consistently abrogated when TECs were treated to antifibronectin, anti-VLA5, antilaminin, or anti-VLA6 antibodies before addition of thymocytes to the cultures. We also studied thymic nurse cells (TNCs), lymphoepithelial complexes that can be isolated ex vivo from the thymus. In this system, we had previously demonstrated that ECM ligands and receptors control both inward and outward thymocyte traffic. We then showed that GH enhances thymocyte release from TNCs, as well as the reconstitution of these lymphoepithelial complexes. Lastly, we evaluated the in vivo influence of GH on thymocyte exit. This was done by means of intrathymic injection of GH plus fluorescein isothiocyanate (FITC), and further analysis of recent thymic emigrants (FITC+ cells) in peripheral lymphoid organs, as defined by CD4/CD8-based cytofluorometric phenotyping. The proportions of FITC+ T cells appeared augmented in lymph nodes in GH-treated mice, as compared to controls. Taken together, these data indicate that GH stimulates intrathymic T-cell traffic, an effect that is at least partially mediated by extracellular matrix-mediated interactions.

The numerous relationships existing between the nervous and the immune systems suggest that the neural networks present in the intrathymic microenvironment may influence T-cell development. We previously reported that thymic neural-crest-derived stromal cells are involved in a neural differentiation pathway and are able to produce neurotrophic factors and neurokines that are in turn able to increase and/or modulate thymic-stromal cell neuronal phenotype. We also showed that EGF promotes a neural phenotype in thymic epithelial cells by enhancing the expression of neuronal-specific markers, neurotransmitters, and neuropoietic cytokines, such as IL-6 and CNTF. More recently we showed that the effect of EGF in directing thymic epithelial cells toward a neural-oriented cell fate is mediated by modulating the expression of genes directly involved in neurotypic differentiation (i.e., thrombospondin-1). EGF-induced regulation of stromal cells may also affect T-cell differentiation, as we observed that an EGF-pretreatment reduces the ability of thymic epithelial cells to sustain thymocyte differentiation in vitro. Finally, we demonstrated that a complex network involving the neurotrophin BDNF and its specific receptors may have a role in sustaining thymocyte precursor survival and supporting the thymocyte differentiation process. All together, our results suggest that the thymus may be the site of integration of different neuroimmune networks that are potentially involved in the regulation of thymocyte survival and/or differentiation.

A decline in plasma concentrations of both growth hormone and IGF-I occurs during aging of humans and rodents, and this is accompanied by involution of the thymus gland. Exogenous growth hormone induces the synthesis of IGF-I, which acts on bone marrow-derived hematopoietic progenitors of the myeloid and lymphoid lineages to promote their replication and survival. The increase in survival of these cells is caused by the ability of IGF-I to inhibit their apoptotic death. In contrast to the multipotential colony-stimulating-factor IL-3, inhibition of apoptosis by IGF-I requires the activation of the critical intracellular effector PI 3-kinase. These data establish that hematopoietic progenitors can use more than one intracellular signaling pathway in order to maintain their survival. The data also extend the original hypothesis that IGF-I shares with the colony-stimulating factors the properties of promoting DNA synthesis and inhibiting programmed cell death. Collectively, these data establish that hematopoietic progenitor cells are important targets for IGF-I, and this is likely to be important in understanding thymic aging.

In the course of our studies, we have shown the presence of calcitonin gene related peptide (CGRP) by immunocytochemistry in cell bodies and nerve fibers of the murine thymus and in a sparse innervation of the spleen. Receptors for CGRP have been characterized within these glands, and their activation by physiological levels of CGRP was found to suppress Con A-stimulated proliferation of thymocytes and splenic T cells as well as antigen-specific T-cell proliferation. This suppression is blocked by the antagonist for CGRP (CGRP 8-37). Within the thymus cultures, the antagonist CGRP (8-37) alone enhanced proliferation of thymocytes during Con A stimulation, most likely by inhibiting the endogenous release of CGRP into the culture medium by resident thymocytes. Some of the CGRP-induced suppression of mitogenic stimulation of thymocytes, but not of splenocytes, was due to apoptosis. The antagonist, CGRP(8-37), did not block apoptosis caused by Con A or CGRP but rather enhanced it. Flow cytometric analysis of CGRP-treated cultures using antibodies to cluster determinates (CD) showed that the majority of thymocytes undergoing apoptosis induced by CGRP were of the CD4/CD8 double-positive type. These data indicate that apoptosis in the thymocytes is mediated by a CGRP receptor not sensitive to the antagonist CGRP(8-37). Because proliferation of thymocytes and splenocytes induced by Con A is blocked by this antagonist and splenocytes are refractory to CGRP induced apoptosis, CGRP appears to mediate at least two separate functions on subpopulations of thymocytes and T cells via two different CGRP receptors within the gland. These effects of a neuropeptide exemplify the phenomenon of differential regional regulation of immunity by the autonomic and neuroendocrine systems.

Thymocytes undergo a complex process of differentiation, largely dependent on interactions with the thymic microenvironment, a tridimensional cellular network formed by epithelial cells, macrophages, dendritic cells, and fibroblasts. One key cellular interaction involves the TCR-CD3 complex expressed by thymocytes with MHC-peptide complexes present on microenvironmental cells. Additionally, thymic epithelial cells (TEC) interact with thymocytes via soluble polypeptides such as thymic hormones and interleukins, as well as through extracellular matrix (ECM) ligands and receptors. Such types of heterotypic interactions are under neuroendocrine control. For example, thymic endocrine function, represented by thymulin production, is up-regulated, both in vivo and in vitro, by thyroid and pituitary hormones, including prolactin and growth hormone. We also showed that these peptides enhance the expression of ECM ligands and receptors, as well as the degree of TEC-thymocyte adhesion. In addition, we studied the thymic nurse cell complex, used herein as an in vitro model for ECM-mediated intrathymic T-cell migration. We observed that T-cell migration is also hormonally regulated as ascertained by the thymocyte entrance into and exit from these lymphoepithelial complexes. Taken together these data clearly illustrate the concept that neuroendocrine circuits exert a pleiotropic control on thymus physiology. Lastly, the intrathymic production of classic hormones such as prolactin and growth hormone suggests that, in addition to endocrine circuits, paracrine and autocrine interactions mediated by these peptides and their respective receptors may exist in the thymus, thus influencing both lymphoid and microenvironmental compartments of the organ.

Thymic epithelial and nurse cells from different species express a repertoire of neuroendocrine polypeptide precursors. This repertoire exerts a dual role in T-lymphocyte selection according to their status either as cryptocrine signals or as neuroendocrine self-antigens of the peptide sequences that are processed from those precursors then presented to pre-T cells. Thymic neuroendocrine self-antigens correspond to peptide sequences highly conserved throughout evolution of their family. Though thymic MHC class I molecules are involved in the processing of thymic neuroendocrine self-antigens, preliminary data show that their presentation to pre-T cells is not allelically restricted. Thymic T-cell education in neuroendocrine families also implies that the structure of a given family may be presented to pre-T cells. Our studies have evidenced the homology between thymic neuroendocrine-related self-antigens and dominant T-cell epitopes of peripheral neuroendocrine signals (neuroendocrine autoantigens). The biochemical difference between neuroendocrine autoantigens and homologous thymic self-antigens might explain the opposite immune responses evoked by those two types of antigens (activation and memory induction vs. tolerogenic effect). Altogether, these studies support the therapeutic use of thymic neuroendocrine self-antigens in reprogramming the immunological self-tolerance that is broken in autoimmune endocrine diseases like insulin-dependent diabetes type I. As recently stated by P. M. Allen in an important review, the fate of developing T lymphocytes in the thymus is influenced by the numerous types of peptidic interactions within the thymic cellular environment. To define the precise nature of thymic cells and naturally occurring biochemical peptide signals involved in positive and negative selection of immature T cells has become a prominent objective for the future research efforts in thymic physiology. This paper will try to show how thymic neuroendocrine-related peptides synthesized and processed within the thymic microenvironment indeed can play a role both in the development of the peripheral T-cell repertoire and in the death of randomly rearranged, self-reactive T cells.

The thymus involutes relatively early in life; cellular immune deficiencies of aging correspond to decline in function of the hypothalamic-pituitary-endocrine axis. Recent studies point to important roles for the pituitary, the pineal, and the autonomic nervous system as well as the thyroid, gonads and adrenals in the thymus integrity and function. Thymic function at the local level requires complex cellular interactions among thymic stromal cells and developing thymocytes involving paracrine and autocrine mediators including interleukins (ILs) 1, 2, 6, 7, 8, colony-stimulating factors (CSFs), interferon-gamma, thymosin alpha 1, and zinc-thymulin. An important endocrine function of the thymus is to package zinc in zinc-thymulin for delivery to the periphery. Thymic involution has been treated with interleukins, thymic hormones, growth hormone, prolactin, melatonin, zinc, and others. Our work to reverse thymic involution in hydrocortisone-treated, aged mice with interleukins, thymosin alpha 1, and zinc will be reviewed. Recent efforts to treat successfully immune deficiency in aged and cancer-bearing humans will be presented.

Calcitonin gene-related peptide has been identified by immunocytochemistry within the thymus of fetal through aged adult mice. Calcitonin gene-related peptide positive nerves are observed from embryonic day 17 throughout the lifespan of the mouse. A sparse cell population positive for CGRP is first observed during the late embryonic period at the corticomedullary boundary and the medulla, and it becomes more densely distributed in this region in the adult. In the thymus of the aged mouse the number of CGRP-positive cells diminishes. Pharmacologic studies demonstrated that fresh thymocytes display a receptor Kd for CGRP of 1.17 +/- 0.06 x 10(-10)M and a Bmax of 12.7 +/- 4.7 fmol/mg protein. Functional studies indicate that CGRP is a potent inhibitor of mitogen and antigen-stimulated proliferation of T cells and that it inhibits IL-2 production in cloned splenic T cells. Recent studies suggest that endogenous CGRP may serve as a natural inhibitor of inappropriate induction of mature, antigen-sensitive cells in the thymus as well as play a role in thymocyte education. These findings are discussed in terms of the distribution of CGRP cells and nerve terminals within the thymus and their relationship to positive and negative selection of the T-cell repertoire.

The thymus produces several putative thymic hormones: thymosin alpha 1, thymulin, and thymopoietin, which have been reported to circulate and to act on both prothymocytes and mature T cells in the periphery, thus maintaining their commitment to the T cell system. These endocrine influences decline with age and are associated with "thymic menopause" and cellular immune senescence, which contribute to the development of diseases in the aged. Thymus endocrinology is characterized by the action of many hormones and hormone-like substances on the cellular components of the thymus, including thymocytes, thymic epithelial cells, and thymic stromal cells. The intrathymic environment is characterized by a complex network of paracrine, autocrine, and endocrine signals involving both interleukins and thymic peptides, which can be envisioned to operate in a synergistic network to carry the evolving T cell through its stepwise development to a mature T cell. Extrathymic influences regulating the secretory function of thymic epithelial cells and the stepwise evolution of T cells can be ascribed to circulating interleukins, mainly IL1 and IL2, derived from activation and secretion of leukocytes in the periphery. These interleukins act in a synergistic fashion at all levels of T cell development by the induction of high-affinity IL2 receptors and the resultant IL2-dependent proliferative responses. To determine whether exogenous administration of interleukins would induce T lymphocyte development in aged mice, we chemically thymectomized aged mice with a steroid hormone and treated them with mixed interleukins or thymic hormones such as thymosin. We found that mixed interleukins, but not thymosin, restored thymic weight and cellularity and enhanced thymocyte responses to interleukins and mitogen. Thymosin potentiated the effect.

A decline in the capacity of bone marrow cells to differentiate to T lymphocytes was found when cells from young and old donors were seeded onto an alymphoid fetal thymus. A step-by-step analysis of cell-cell interactions of the lymphohemopoietic cells and the thymic stroma indicated an effect of age on a variety of cell differentiation parameters. These included a decrease in the affinity of bone marrow cells to the stroma, and in their capacity to compete with the thymic lymphoid resident cells on colonization of the thymus. There was a significant decrease in the ability of cells of old donors to replicate sequentially within the thymic microenvironment. There was a reduced capacity of bone marrow cells from aging mice to express a developmental preference after seeding onto a syngeneic fetal thymus in a mixture with cells from allogeneic donors. We addressed the question whether the aging thymus contains increased levels of immature cells that fail to differentiate in the involuted thymic microenvironment by seeding thymocytes from young and old donors onto the fetal thymic stroma. The values of T cells that developed from the old donor inoculum were lower under these conditions. Our studies suggest that at least some of the manifestations of aging in the T cell compartment are related to developmentally programmed events in the lymphohemopoietic cell compartment.

A common and generally accepted assumption is that with advancing age, the thymus undergoes progressive and irreversible involution. This is considered the main cause for the age-related deterioration of various immune functions and, ultimately, for the increased incidence of infectious, neoplastic, and automimmune diseases in old age. This assumption is no longer tenable because of several clear-cut demonstrations that age-related thymic involution is not an intrinsic and irreversible phenomenon. Various neuroendocrine or nutritional manipulations can to induce a regrowth of the thymus, even when applied in old age. This thymic reconstitution is followed by a consistent recovery of peripheral immune functions. These data strongly support the idea that thymic involution is a phenomenon secondary to age-related alterations in neuroendocrine-thymus interactions and that it is the disruption of such interactions in old age that is responsible for most of the age-associated dysfunctions. On the basis of this experimental and clinical evidence and as an alternative to purely immune or neuroendocrine theories of aging, a neuroendocrine-immune hypothesis is proposed. Further work is required to determine if the age-related disruption of neuroendocrine-immune interactions occurs because of progressive accumulation of stressor-dependent consequences at the level of one or the other system or if it may depend on a single common cause.

Previous experimental results have demonstrated progressive impairments in beta-adrenergic responsiveness with advancing age. Beta-adrenoceptors are involved in the alterations as their density progressively decreases during aging. Alterations in both in vivo responsiveness and receptor density are corrected by neonatal thymic grafts. In the present paper adenylyl-cyclase (AC) activity has been studied in the same animal models used before. Results show that no statistically significant changes can be observed when AC is assayed in absence of beta-adrenergic stimulation. On the contrary, when assayed after Isoproterenol stimulation, AC activity shows a shift of the peak and a decrease of its height in aged animals. A neonatal thymus grafted into old recipients one month before the experiment was performed, is capable of correcting the altered height of the peak but not the peak concentration.

Skin allograft rejection was noticeably delayed in rats following hypophysectomy. Daily injections of hypophyseal growth hormone restored the normal reaction. Additional thymectomy had no influence on the rejection of hypophysectomized rats. In these animals growth hormone by itself had no significant influence on the graft rejection. It only restored a normal reaction when given together with thymic hormone. Corticotropin injections accelerated the allograft rejection. On this action of corticotropin thymic hormone has shown a significant inhibitory influence. The thymus was thus proved to be a synergist to growth hormone and an antagonist to corticotropin. Previous observations made with usual endocrinological test- are thus confirmed with an immunological test.

Our data permitted us to postulate an immunoregulatory circuit linking the neuroendocrine structure and the immune system via hormones secreted by the thymus which permit differentiation of T cells. In our first approach we have considered the thymus as a key organ; it exerts its function upon the two systems. We can also consider the thymus a key organ because a major part of the lymphoid cells responsible for the secretion of immunotransmitters or described as target cells for immunohormones or opioids are mature T cells; these T cells have had contact--either cellular (nurse cells) or humoral (thymic hormones)--with thymus during ontogeny. We hypothesize that during this differentiation the properties of secreting hormones or opioids and of receiving an endocrine message appear. Concerning the effect of TF V, the different thymosin properties led us to postulate that among the TF V polypeptides some could exert their effects on the immune system and some on the endocrine system directly or indirectly, either in synergism or in antagonism with classical hormones. There is no doubt that neurotransmitters and hormones can modulate in vivo ontogenesis, differentiation, and expression of the immune response. We believe that the thymus via its hormonal function is one factor in this modulation and one of the main channels of this bidirectional action between the immune and the endocrine systems. We have summarized our hypothesis in Figure 2.

Thymic involution is a normal consequence of aging. It has often been speculated that if this age-associated atrophy of the thymus gland could be prevented, the natural decline that occurs in a number of T-cell-mediated immune responses could be reversed. It has recently become clear that thymic involution can indeed be reversed by altering the hormonal environment of aged animals. These data support the concept of an active and functional pituitary-thymus axis. Since thymic reconstitution can result in restoration of some T-cell responses, it would appear that intrinsic defects which exist in T cells of aged animals can be at least partially reversed. This suggests that the aged environment plays a greater role in the decline of T-cell functions than has been previously recognized. Furthermore, phorbol esters and calcium ionophores can restore suppressed proliferative responses of T cells from aged rodents, so we speculate that intrinsic defects in T cells of aged subjects lie between the recognition system for antigen/lectin and intracellular transmission of this signal.

Thymosin fraction 5 contains several distinct hormonal-like factors which are effective in partially or fully inducing and maintaining immune function. Several of the peptide components of fraction 5 have been purified, sequenced and studied in assay systems designed to measure T-cell differentiation and function. These studied indicate that a number of the purified peptides act on different subpopulations of T-cells (see Figure 1). Thymosin beta 3 and beta 4 peptides act on terminal deoxynucleotidyl transferase (TdT) negative precursor T-cells to induce TdT positive cells. Thymosin alpha 1 induces the formation of functional helper cells and conversion of Lyt- cells to Lyt 1+, 2+, 3+ cells. Thymosin alpha 7 induces the formation of functional suppressor T-cells and also converts Lyt- cells to Lyt 1+, 2+, 3+ cells. These studies have provided further evidence that the thymus secretes a family of distinct peptides which act at various sites of the maturation sequence of T-cells to induce and maintain immune function. Phase I and Phase II clinical studied with thymosin in the treatment of primary immunodeficiency diseases, autoimmune diseases, and cancer point to a major role of the endocrine thymus in the maintenance of immune balance and in the treatment of diseases characterized by thymic malfunction. It is becoming increasingly clear that immunological maturation is a process involving a complex number of steps and that a single factor initiating a single cellular event might not be reflected in any meaningful immune reconstitution unless it is the only peptide lacking. Given the complexity of the maturation sequence of T-cells and the increasing numbers of T-cell subpopulations that are being identified, it would be surprising if a single thymic factor could control all of the steps and populations involved. Rather, it would appear that the control of T-cell maturation and function involves a complex number of thymic-specific factors and other molecules that rigidly control the intermediary steps in the differentiation process.