An extraordinary number of experiments reported especially in the past 20 years, and detailed herein, indicate that the T cell Antigen Receptor (TCR) behaves similarly, and also that there are several critical numbers of triggered TCRs that determine different fates of the T cells. Moreover, the fates of the cells appear ultimately to be determined by the TCR triggering of the IL2 and IL2 receptor (IL2R) genes, which are also expressed in a very quantal fashion. The "Quantal Theory" states that the fundamental decisions of the T cell immune system are dependent upon the cells receiving a critical number of triggered TCRs and IL2Rs and that the cells respond in an all-or-none fashion. The "Quantal Theory" accounts fully for the development of T cells in the thymus, and such fundamental cellular fates as both "positive" and "negative" selection, as well as the decision to differentiate into a "Regulatory T cell" (T-Reg). In the periphery, the "Quantal Theory" accounts for the decision to proliferate or not in response to the presence of an antigen, either non-self or self, or to differentiate into a T-Reg. Since the immune system discriminates between self and non-self antigens by the accumulated number of triggered TCRs and IL2Rs, therapeutic manipulation of the determinants of these quantal decisions should permit new approaches to either enhance or dampen antigen-specific immune responses.In the past 50 years, immunologists have accumulated an amazing amount of information as to how the immune system functions. However, one of the most fundamental aspects of immunity, how the immune system discriminates between self vs. non-self, still remains an enigma. Any attempt to explain this most intriguing and fundamental characteristic must account for this decision at the level of the whole immune system, but as well, at the level of the individual cells making up the immune system. Moreover, it must provide for a molecular explanation as to how and why the cells behave as they do. The "Quantal Theory", proposed herein, is based upon the "Clonal Selection Theory", first proposed by Sir McFarland Burnet in 1955, in which he explained the remarkable specificity as well as diversity of recognition of everything foreign in the environment. The "Quantal Theory" is built upon Burnet's premise that after antigen selection of cell clones, a proliferative expansion of the selected cells ensues. Furthermore, it is derived from experiments which indicate that the proliferation of antigen-selected cell clones is determined by a quantal, " Perhaps one of the most unique and fundamental aspects of the immune system is the clonal nature of the response to the introduction of antigen. The "Clonal Selection Theory" as originally formulated by Burnet stated that the immune system is made up of cells, each of which are only capable of reacting with a single antigenic molecule. Thus, BAt the time that Burnet formulated the concept of clonal selection in the mid 1950s, the identity of the cells comprising the immune system was unknown. Plasma cells had been found to be the source of antibodies, but lymIn the intervening 50 years since Burnet formulated his theory, much has been discovered and even more has been proposed to explain how the immune system functions, especially how the discrimination between self vs. non-self is made. Since 1959, several modifications of Burnet's original model have been offered, each of which introduced additional cells in an attempt to explain how the entire system could react with absolutely everything in the environment, but not react with any molecules comprising self -15. HoweWe now know that lymphocytes make up the immune system, and we know the molecular structures of the antigen receptors expressed by both T cells and B cells. Consequently we know that Burnet was largely correct. Each cell expresses a unique antigen receptor that has the capacity to bind only a single antigenic epitope. The exception to this rule is the "allelic inclusion" of two T Cell Receptor (TCR) α-chains, resulting in approximately 30% of α/β-chain bearing T cells as having dual antigenic specificity. As well, it is known that T cells recognize epitopes comprised of short peptides of only a few amino acid residues bound to molecules encoded by the Major Histocompatibility gene Complex (MHC), while B cells recognize both the tertiary surface structure of larger molecules, as well as linear determinants of molecules. Despite this information, it still remains unknown how the immune system discriminates between non-self vs. self-molecules, in that the molecular nature of the T cell Antigen Receptors (TCR) and the B cell Antigen Receptors (BCR) that recognize both self- and non-self- epitopes are identical. Moreover, the molecular natures of self-epitopes and non-self -epitopes are identical. Accordingly, it is even more perplexing as to how the immune system manages this discrimination.One key to understanding the way in which the immune system operates is the observation that the capacity to recognize and respond to antigen is dependent on the dose of antigen introduced. Thus, t-6 to 10-4). However, after antigen selection, proliferative clonal expansion increases the frequency of antigen-reactive cells to as high as 1 in 10 cells, an astonishing 1–100,000-fold increase [Another key to understanding the immune response resides in the realization that the absolute frequency of potential antigen-reactive lymphocytes is very low before the introduction of antigen, on the order of 1 in a million cells up to 1 in 10,000 cells  activity that provide molecular signals that markedly stimulate cell cycle progression. Since the principle cytokine with TCGF activity driving T cell proliferation is the interleukin-2 (IL2) molecule,22, the Accordingly, to understand how the immune system discriminates between self vs. non-self antigens, the IL2 molecule is first examined, particularly how IL2 promotes the proliferation of antigen-selected cells. Then, the cellular and molecular determinants of IL2 production and IL2R expression are traced. Ultimately, the maturation of T cells in the thymus must be considered, to understand how cells determine whether to produce IL2 or not, and whether to respond to it or not. Most of the discussion that follows is focused on T cells, but the general principles developed apply to B cells as well.quantal, i.e. it is "all-or-none"[At the level of the individual cell, the proliferative response to IL2 is -or-none",24. Howe50) equals the equilibrium dissociation constant (Kd) of the IL2-IL2R interaction, both of which are ~ 10 pM. Although this is a very high affinity for a ligand-receptor interaction (e.g. most TCR-peptide-MHC affinities are ~ a million-fold lower), it is noteworthy that in molecular terms, the EC50/Kd = 6 billion molecules/mL.Soon after the development of the radiolabeled-IL2 binding assay, which ppopulations, and symmetrically sigmoid log-dose response curves are quite familiar in these circumstances. However, from these experiments it was not possible to discern whether the low thymidine incorporation found at low IL2 concentrations was due to all of the cells in population incorporating only a little thymidine, or whether only a few of the cells could respond at low IL2 concentrations. Therefore, it was not until the IL2 dose-response relationship could be examined at the single cell level did it become apparent that the cell populations are comprised of individual cells that differ markedly as to their responsiveness to the mitogenic ligand. Thus, as shown in Figure Of course, these experiments were performed using cell Once it is realized that the effective IL2 concentrations span 2 orders of magnitude, the question becomes why some cells are capable of responding at only 1 pM, while others require IL2 concentrations that are 100-fold higher. The only logical answer to this question is that there must be intrinsic cellular differences, and that these differences are manifest in molecules that are critical for signaling cell cycle progression. Therefore, in experiments focused on understanding how IL2 promotes T cell proliferation after antigen activation, we found that in addition to the affinity of the IL2/IL2R interaction, and the concentration of IL2, the other variables involved are the IL2 receptor (IL2R) density, and the duration that the IL2 and the IL2R molecules interact.synchronized in early G1, so as to follow the rate at which individual cells progressed through G1 into S-phase. Thus, if G0/1 synchronized IL2R+ cells are exposed to two different IL2 concentrations, one receptor saturating and another only half-saturating; the receptor-saturating concentration promotes cell cycle progression twice as rapidly as the half-saturating IL2 concentration. However, as the ligand concentration dependency of cell cycle progression of cell populations was well known, these results were not surprising.In order to design experiments to approach these variables, it was necessary to use cell populations that were was surprising to find that if one exposes two cell populations, one with a higher IL2R density than another, to the same receptor saturating IL2 concentration, the cell population with the higher IL2R density traverses G1 and enters S-phase more rapidly than the population with the lower IL2R density . Thus, the rate constant, κ = ln2/15 min = 4.67 × 10-2 min-1, governs the rate of new receptor synthesis necessary to maintain the surface expression at steady state. Moreover, 11 hours (660 minutes) of IL2 exposure is necessary to trigger 50% of the cells within the population to undergo cell cycle progression  = κ × R# @ steady state-2 min-1 × 750 R/cell= 4.67 × 10= 35 R/cell/min × 660 min= 23,100 triggered R/cellIt follows that if the mean number of IL2Rs at steady state is lower, e.g. only 375 Rs/cell, 22 hours would be required to reach the quantal number and if the rate of new receptor synthesis is doubled, maintaining twice as many, 1,500 sites/cell, then only 5.5 hours would be required to trigger the cells.7 M-1sec-1), while the β chain contributes a slow dissociation rate (κ' = 10-4 sec-1), which together yield the high affinity (Kd = κ'/κ = 10-11 M) for the ligand observed at steady state[There are 3 chains that make up the trimeric IL2R that has an extremely high affinity for IL2, termed α (CD25), β . Both cyclin D2 and D3 are expressed in response to IL2R triggering, and recll cycle -37. In aBecause of these findings, it has been proposed that the D cyclins serve as intracellular sensors of the extracellular signals  generate1 progression, one involving cyclin D and another that is cyclin D independent.However, recent experiments with mice that have had all 3 of the cyclin D genes deleted have revealed that although hematopoiesis is dependent on the coordinated expression of the cyclin D genes, nonhematopoietic cells can proliferate in the absence of the D-type cyclins and their cyclin-dependent kinases 4 and 6 (cdk4/6),42. Even0 until activated by initial signals received via the TCR, so that it still remains possible that T cells may be capable of proliferating in response to both TCR- and IL2R-derived signals[0 to G1 transition, while the IL2R is responsible for G1 progression to the R-point and S-phase transition. However, another possibility remains that it still may well be that TCR-derived signals can initiate early rounds of cell division, but that for a fully developed clonal expansion, IL2/STAT5-dependent signals are necessary. If so, one would predict that TCR-mediated cell cycle progression is STAT5- and cyclin D-independent, so that the role of IL2 is to markedly accelerate and extend cell cycle progression initiated by the TCR.At this time, it remains unknown as to whether T cells can be stimulated to proliferate by both cyclin D-dependent and independent pathways, or only by cyclin D-dependent (and therefore IL2R/STAT5-dependant) pathways. However, it is clear that T cells are in Gd signals,43,44. AOnce one realizes that the quantal decision of T cells to proliferate is based upon a critical number of IL2-IL2R interactions, it becomes immediately obvious that the availability of IL2, together with the extent of IL2R expression, ultimately determines whether a immune response occurs that will be detectable at the systemic level. Since the discovery -51 and eBefore the elucidation of the structure and function of the receptors involved in antigen recognition, it was difficult to envision how the IL2/IL2R system is regulated. However, the principles from the quantal IL2-IL2R signaling of cell cycle progression can now be extrapolated to this more complex signaling system, and herein resides the ultimate control of "self-non-self" recognition and response. Like the IL2R,27, the Since the cloning and sequencing of the IL2 cDNA and genein vivo without coengagement of each of the distinct factors that bind at neighboring sites[Individual IL2 transcription factors from these three families cannot bind stably to their target DNA response elements ing sites. Also, iing sites. Moreoveing sites. TherefoThe quantal binding of IL2 transcription factors to the IL2 enhancer and promotion of IL2 gene expression has been extended by studies on the allelic expression of the IL2 genes. Under optimal TCR stimulating conditions, where antigen is in excess, and Antigen Presenting Cells (APCs) are not limiting, there is biallelic expression of the IL2 genes. By complck, ZAP-70, PLCγ, and Protein Kinase C-θ (PKC-θ), which simultaneously promote the activation and translocation of AP-1 to the nucleus, and the activation of NF-κB/Rel family members that are already present in the cytoplasm bound to the Inhibitors of κB (IκB)[The activation of NF-AT, AP-1 and NF-κB/Rel family members is controlled by signaling pathways triggered by the TCR, as well as costimulatory molecules and coinhibitory molecules. Thus, TCR triggering promotes the rapid influx of calcium into the cell, which activates the phosphatase calcineurin, thereby dephosphorylating and activating NF-AT, while o κB (IκB). In addi κB (IκB)-70.in vitro. It could not be ascribed to nonspecific toxicity and cell death, in that the cells were still capable of proliferating in response to IL2 added exogenously.Soon after the derivation of the first T cell clones, experimSubsequently, anergy  was shown to be produced by delivery of "Signal-1" (i.e. TCR), without "Signal-2" (i.e. CD28). More reThese findings are reinforced by other experiments, which reveal that inhibitors of calcineurin, such as cyclosporine-A and tacrolimus (FK506), which prevent the activation of NF-AT, also prevent the induction of anergy. As wellBy comparison, NF-κB/Rel appears to be the most critical of the three families of transcription factors involved in the activation of IL2 gene expression. MoreoveAccordingly, for productive CD4+ T cell activation manifest by IL2 gene expression and proliferative clonal expansion, the minimum requirements are optimal activation of the TCR via peptide-MHC complexes, and costimulation via activation of CD28 by the APC B7 ligands. In the case of a low affinity TCR-MHC-peptide interaction, or in the absence of costimulation, NF-AT activation may predominate and anergy can result. The actin vivo activated cells were removed using monoclonal antibodies reactive with the transferrin receptor (CD71), known to be an early TCR/CD28 activation molecule. Both CD4+ and CD8+ resting T cells have undetectable surface or cytoplasmic IL2R α and β chains, as monitored using very sensitive flow cytometry methods. By comparison, IL2R γ chains are detectable in the cytoplasm, but undetectable on the cell surface[Resting T cells that have not been recently activated via TCR/CD28 do not express detectable high affinity IL2Rs. A recenl surface. Upon acThe regulation of α chain (CD25) gene expression is under the control of the TCR/CD28 via activation of NF-κB/Rel, AP-1 and NFAT, which interact with 2 distinct REs . Therefoc chains, which are limiting. The energetics of IL2 chain assembly has now provided an explanation for the excess α chains, in that the law of mass action favors the formation of α,β heterodimers, to which IL2 binds and then recruits the γ chain, thereby forming the stable quaternary signaling complex.In addition to the TCR, IL2 enhances IL2Rα chain gene expression as much as 10–20-fold -87. This0 and to enter early G1, cell cycle progression through G1 to S-phase and mitosis appeared to be mediated by IL2 upon binding to the IL2R[Before the identification of the IL2 molecule in 1983,88, it w the IL2R,91,92. R the IL2R, while p the IL2R.per se could not promote T cell proliferation, and suggested that IL2 drives T cell proliferation after the initial antigen activation. Even so, the monoclonal IL2- or IL2R-reactive antibodies suppressed proliferation by > 90–95%, but never completely abrogated proliferation, leaving open the possibility that either the TCR itself or other mitogenic cytokines might also be operative.Moreover, immunosuppressive pharmacological agents such as glucocorticoids were fouin vitro and in vivo, at least in mice. Initial in vitro experiments testing cells from IL2 (-/-) mice for proliferation in response to activation by the mitogenic lectin Concanavalin-A (Con-A) revealed a 70–75% diminution of tritiated thymidine incorporation, but not a complete abrogation[In 1991, with the advent of IL2 gene deletion through genetic recombination, it became possible to test definitively the functional importance of IL2, both brogation. Therefobrogation or IL7[9brogation, which win vivo experiments with IL2 (-/-) mice infected with Vaccinia Virus (VV) and Lymphocytic Choriomeningitis Virus (LCMV), revealed that the generation of antigen-specific effector cytolytic T cell activity was reduced by only ~ 30% as monitored by Cytolytic T Lymphocyte (CTL) 51Cr-release assays[in vivo experiments with staphylococcal super antigens indicated that CD4+ T cells doubled normally, while CD8+ T cells from IL2 (-/-) mice were only ~ 50% of wild type[in vivo IL2 is redundant for the generation of immune responses, and that the TCR or other cytokines with TCGF activity could substitute for IL2.Even so, it was still a great surprise when initial se assays. Moreovewild type. These fHowever, upon subsequent and more extensive testing of IL2 (-/-) mice, it was found that in the absence of IL2, the marked proliferative expansion of LCMV-induced CD8+ T cells was virtually eliminated, the total cytolytic effector capacity was reduced by > 90%, and IFN-γ production resulting from T cell activation was dramatically inhibited,100. Morin vitro and in vivo. Moreover, IL2 (-/-) mice are immunocompromised without IL2; thereby indicating that the TCR or other yet undiscovered cytokines cannot fully substitute for IL2 in vivo.Therefore, all of these data indicated that IL2 may not be the sole cytokine with TCGF activity, but it is one of the principle TCGFs responsible for the maximal proliferation of antigen selected mature peripheral T cells, as well as their differentiation to effector cells, both c chain [Since IL2 (-/-) mice are immunocompromised, it was entirely unexpected to find that a syndrome of lymphocyte hyperactivity and apparent autoimmunity appears as the mice mature beyond puberty . Thus, ac chain  somehow The accumulation of T cells with an activated phenotype in the setting of an initial lymphopenia and immunodeficiency, has recently been attributed to compensatory over stimulation by the cytokines responsible for homeostatic proliferation, e.g. IL7, IL15 and IL21, all of which signal via the γc chain. Of thesIn vitro assays demonstrated a reduced responsiveness to stimulation by anti-CD3 (11% of control) and phytohemagglutinin (20% of control). Severe immunodeficiency was proven by the patient's inability to reject an allogeneic skin graft. Paradoxically, despite the obvious immunodeficiency, there was a normal sized thymus and lymphocytic infiltration of multiple tissues, including lung, liver, gut, soft tissue and bone. These findings were interpreted as possibly a result of a failure of negative selection of potential autoreactive cells in the thymus, as well as an inability to control autoreactive cells in the periphery, perhaps due to the absence of CD4+CD25+ Regulatory T cells.These observations in mice were reinforced by a report of a human homozygous mutation of CD25. A male nu/nu) mice would also develop a wide spectrum of both organ-specific and systemic autoimmune diseases if they received normal cell populations from which CD4+CD25+ T cells were eliminated[Soon after it was demonstrated that IL2 (-/-) and IL2Rα or β chain (-/-) mice develop an autoimmune syndrome, it was reported that immunocompromised  mice, these ein vitro assay was devised to test their suppressive activity[combination of anti-CD3 + IL2. These data suggest that resting, anergic CD4+CD25+ T cells do not express the IL2R β and γ chains, but they can be induced to express them after activation of the TCR.CD4+CD25+ "suppressor" regulatory T cells (T-Regs) could also be demonstrated in the secondary lymphoid organs of normal adult mice, and an  activity. CD4+CD2When co-cultured with CD4+CD25- cells, these CD4+CD25+ cells were found to markedly suppress the proliferative response of the CD25- cells, provided they are stimulated with low concentrations of soluble, but not solid-phase anti-CD3. This inhibition was dependent on cell-cell contact, not soluble factors, and dependent on the suppression of IL2 production by the CD25- responding cells. The inhibition could be bypassed by the addition of IL2, or costimulation with anti-CD28. These data were interpreted as consistent with the idea that CD4+CD25+ cells in normal unimmunized animals represent a distinct lineage of "professional" suppressor cells that have matured in the thymus. These T-Reg cells have been termed "naturally occurring" (nT-Reg).in vitro by the activation of mature peripheral CD4+CD25- T cells[ex vivo from mature CD4+CD25- T cells, include antigen in the presence of immunosuppressive cytokines such as IL10 and TGFβ, immunosuppressive agents such as vitamin D3 and dexamethasone, CD40-CD40L blockade or immature DC populations[It has also been reported that CD4+ T cells with regulatory function can be generated - T cells. Thus, b- T cells, in thatpulations,120.in vitro and in vivo, low antigen concentrations can promote the differentiation of mature peripheral CD4+ T cells to express CD25, and to become "suppressor" cells rather than effector cells.Furthermore, it was reported recently that subcutaneous infusion of low doses of antigenic peptide by means of osmotic pumps over 14 days transforms mature peripheral T cells into CD4+CD25+ "suppressor cells" that can persist for long periods of time  in the absence of antigen and confer specific immunological tolerance upon challenge with immunogenic doses of antigen. Therefolck promoter, so that mature trimeric IL2Rs capable of signaling are only expressed in the thymus[c chain cytokines, e.g. IL4 and IL7, IL9, and IL21 do not compensate for the lack of T-Regs in IL2Rβ chain (-/-) mice.The dependency on the thymus for maturation of CD4+CD25+ T-Regs, as well as the dependency upon IL2, has been underscored by experiments with IL2β chain (-/-) mice made transgenic for the IL2Rβ chain under the influence of the proximal he thymus,123. TraSuboptimal antigen concentrations and IL2 are both required for the generation and activity of T-Regs, and both in the thymus and in the periphery. However, the forces governing the simple generation of anergic and nonfunctional CD4+CD25+ T cells, as compared with the determinants of the generation of activated proliferating, suppressive CD4+CD25+ "Regulatory T cells", vs. CD4+CD25+ activated proliferating functional effector T cells remain to be defined.Because each of these cell fates is functionally distinct, it is reasonable to hypothesize that these distinct cell fates are determined by different numbers of triggered TCRs and IL2Rs.in vitro via TCR/CD28, there is a characteristic transient expression of the IL2 gene, such that IL2 mRNA first becomes detectable within 6 hours, and then peak levels occur after 12 hours, with a subsequent decline to undetectable levels by 24 hours[Upon productive activation of T cells  24 hours. Detecta 24 hours. By comp 24 hours.The mechanisms accounting for the transient expression of the IL2 gene and the genes encoding the IL2R chains have not been apparent, until recently. It is now realized that surface molecules of the coinhibitory CTLA-4 family appear l1/2) of ~ 2 hours, IL2 is consumed very rapidly, resulting in cessation of IL2-promoted cell cycle progression and eventually apoptosis due to the lack of IL2-promoted anti-apoptosis gene expression, such as Bcl-XL.This coinhibitory ligand-receptor family of molecules belongs to the Ig superfamily and the B7/CD28 costimulatory ligand/receptor family,130. HowThe coinhibitory ligand/receptor pairs identified thus far can be shown to exert their negative effects by attenuating IL2 gene expression, but the administration of IL2 can bypass this block, in that the cells are still IL2-responsive. A similar phenomenon has been found with regard to the effects of T-Regs. T-Regs shut down IL2 gene expression, via a cell-cell contact mechanism that has not yet been delineated. However, IL2 supplementation will bypass the suppressive effects of T-Regs, thereby allowing for T cell proliferation. Also, in both instances, activation of CD28 via monoclonal antibodies serves to counteract the blockades, and permits the suppressed cells to both express the IL2 gene and to proliferate.Accordingly, it would seem a plausible hypothesis that the cell-cell contact mechanisms employed by T-Regs to inhibit IL2 gene expression are mediated by members of the CTLA-4 family of coinhibitory ligands/receptors, either those already identified, or others yet to be identified. This is a particularly attractive hypothesis, in that the ligands that trigger the coinhibitory PD-1 receptor are also expressed by TCR/CD28-activated T cells.in vivo, and to test which proliferative signals are operative. In this regard, T cells from IL2Rβ (-/-) mice that have had the IL2Rβ chain expressed only during thymopoiesis do not express detectable IL2Rβ chains in the periphery, and therefore are incapable of delivering a proliferative signal. However, these cells are capable of undergoing 1–2 divisions upon stimulation with anti-CD3 + anti-CD28[With the advent of the ability to label cells with 5- and 6-carboxyfluorescein diacetate succinimidyl ester (CFSE), combined with the use of gene deleted mice, it has been possible to follow the proliferation of T cells anti-CD28. Similaranti-CD28,134. OneAfter the initial proliferative clonal expansion of antigen-selected cells, the fate of the expanded effector cells has been found to depend greatly upon whether the antigen is cleared or whether it persists. In experimental viral infections where the virus is cleared rapidly within the first week after infection, expanded CD4+ and CD8+ effector cell populations undergo a contraction, with the loss of as much as 90% of the expanded effector cells. We haveWith persistence of antigen, the fate of the expanded effector T cell populations changes dramatically. Instead of differentiating into responsive memory cells, the cells revert to a state of unresponsiveness, which has been termed "exhaustion" by those studying experimental persistent viral infections ,139. Thiin vitro with CFSE, then transferred into recipient mice expressing low levels (~ 100 pM) of antigenic pigeon cytochrome c peptide. The cells become activated, express the IL2R α-chain (CD25) and CD69, and proliferate for the first 4 days, eventually expanding ~ 100-fold. However, over the subsequent 10–14 days, the cells lose expression of CD25 and cell recovery declines by ~ 50%. Thereafter, the cells are said to be in the "adaptive phase", which is characterized by a hyporesponsiveness to antigen in vitro, and is manifest by a decreased capacity to produce IL2 and other cytokines, and to proliferate.A similar phenomenon has been described in experiments employing a paired transgenic model (TCR and Ag). In thisThis adaptive state persists in the host with chronic expression of the antigen, and in contrast to a similar paired transgenic model in a B cell system, is not relative hyporesponsiveness, as compared to either the naïve situation or the host with central memory cells[in vitro, i.e. between 1 nM and 1 μM, a response can be detected, but the antigen dose-response curve is shifted 100–300-fold to the right. In addition, the adaptive phenomenon cannot be ascribed to active suppression by a T-Reg differentiative process, in that the adapted cells do not express CD25, and in vivo experiments have excluded a suppressive mechanism.It is important to emphasize that the adaptive state is only a ory cells,143. If From the discussion thus far, it must be apparent that the strength of the signals delivered to T cells ultimately determines the outcome, i.e. either anergy, or activation of the IL2 gene, and if activation occurs, the duration that it persists. Thus, considerations of the ligand concentrations available, the receptor affinities and numbers expressed, and the duration of the ligand-receptor interactions again become important.The duration of signaling via TCR/CD28 is known to be a major determinant of the magnitude of IL2 production and thus the extent of T cell proliferation. Even in the 1970s the magnitude of the proliferative response after mitogenic lectin administration was found to be directly related to the duration of lectin stimulation. Thus, rWith the discovery that T cell proliferation after mitogen or antigen activation is principally mediated by IL2, it seemA series of experiments reported in the mid 1990s began to provide an explanation for this perplexing problem. By equating "triggered" TCRs with their internalization and disappearance from the cell surface after ligand activation, it was shown that a single peptide-MHC complex is capable of serially triggering up to ~ 200 TCRs,149. FurWith the discovery of Supramolecular Activation Clusters (SMACs), an additional level of complexity was added. Also te10 difference in TCR density among potential responding T cells, and consequently, those cells with the highest density of TCRs, will be capable of responding to lower concentrations of MHC-peptide epitopes, and also capable of responding more rapidly than cells with lower TCR densities to an optimal pMHC concentration. Detailed studies examining the cytokine response of murine T cell clones to graded peptide antigen concentrations have revealed a hierarchical organization of TCR signal-dependent response thresholds for elicitation of different cytokines in individual cells[Regarding the density of the TCR on responding T cells, it is important to restate and emphasize that the TCR density follows the same log-normal distribution as detailed for the log-normal distribution of IL2Rs, even on cloned T cells. Thus, there is at least a 2-logual cells. IL2 proExactly what leads to the heterogeneity of the quantal response of IL2 gene expression on the part of the cells within the cloned cell population has not been determined, but very similar findings have been reported for IFN-γ production by a human T cell clone in response to graded doses of antigenic peptide. The pepExactly the same considerations hold for the distribution of costimulatory and coinhibitory molecules. Thus, there is interplay between all of these receptors, which ultimately impacts the "strength" of the signal and the As already detailed, if CD4+ T cells are activated via the TCR without adequate stimulation via CD28, such as may occur if self peptide is presented on immature dendritic cells as APCs, the conditions would favor the predominant activation of NF-AT yet inadequate AP-1 and NF-κB/Rel activation, which would promote anergy and perhaps even the irreversible differentiation of most of the cells to T-Regs. Thus, the concentration of antigen, the availability of adequate costimulatory molecule function, the affinity and density of the TCR/cell, as well as the duration that the TCR is triggered all influence signal "strength".off rate constants of ~ 0.01–0.1 s-1, yielding t1/2 ~ 7–70 secs[-1 have been found, which yield t1/2 of only ~ 0.15 seconds.With regard to the affinity of the TCRs for the peptide-MHC complex, it is important to note that the TCR does not undergo somatic hypermutation and "affinity maturation" as does the BCR. Accordingly, the Kd of the TCR is fixed after recombination and rearrangement in the thymus, and is relatively low by comparison with the Kd of antibody molecules, which have ~ 1000-fold higher affinity for binding antigen. Measurements of the equilibrium dissociation constants of isolated agonist pMHC binding to TCR molecules by surface plasmon resonance have revealed Kds in the range of 1–100 μM, with k7–70 secs. In contin vivo. Furthermore, new studies have made it possible to "count" the exact number of ligands that a T cell encounters on another cell, and then monitor the consequences of that interaction with respect to the increase of intracellular calcium concentration[Of course, the TCR does not bind MHC-peptide complexes in isolation or in solution. The formation of the immunological synapse greatly alters the way in which TCRs engage antigens and the way in which they are triggered. Thus, Tentration. It has lck to the agonist pMHC/TCR, so that endogenous pMHC/TCR, which are in a large excess, can form a dimeric signaling complex comprised of agonist pMHC and endogenous pMHC[Recent experiments focused on how the TCR can respond to such low concentrations of agonist peptides indicate that the slower off rate of the agonist pMHC/TCR interaction allows the juxtaposition of CD4 with bound nous pMHC. Then, tGiven the long duration necessary to trigger a response, a kinetic model has been proposed to account for how serially triggered TCRs that interact very briefly with peptide-MHC complexes, then are rapidly internalized and degraded can be counted by the T cell, and how transient signaling events can be accumulated over time and integrated into a quantal response. The modAll of these considerations lead one to the conclusion that like the IL2/IL2R-determined quantal decision to undergo cell cycle progression, there appear to be quantal decisions operative at the level of the immunological synapse that lead to distinct cell fates, which in turn are ultimately determined by IL2 and IL2R gene expression. Thus, if the agonist pMHC ligand concentration is low, only T cells with a high density of TCRs will form stable synapses that will result in sustained activation of the IL2 gene and thereby cell cycle progression. It follows that at the same limiting agonist pMHC concentrations, cells with lower TCR densities may have abortive expression of the IL2 gene, which would favor differentiation to T-Regs, while cells with still lower TCR densities would not successfully trigger expression of the IL2 gene, thereby favoring the triggering of differentiation to an anergic state and unresponsiveness. Thus, there are at least 3 distinct cell fates that are determined by the accumulated number of triggered TCRs, which is determined by the agonist pMHC concentration, TCR density and the duration of the pMHC/TCR interaction.The structure and function of the immunological synapse essentially determines the fate of T cells as they mature in the thymus. Again, this cell fate determination is linked to IL2 and IL2R gene expression. From the above discussion, it is now clear that like the quaternary IL2/IL2R complex, the immunological synapse is a dynamic multicomponent molecular complex, the stability of which requires ongoing signaling through the TCR for stable calcium mobilization and kinase activation occurring over several hours. As well, the immunological synapse modulates the overall level of mature T cell activation by integrating positive (costimulatory) signals and negative (coinhibitory) signals from a variety of surface receptors. In this regard, it is noteworthy that the synapse that forms between thymocytes and thymic stromal cells differs qualitatively from that observed between mature peripheral T cells and peripheral APCs. One reaFrom detailed experiments performed primarily with mice made transgenic for the TCR, it is now clear that the interaction of the TCR expressed on developing immature thymocytes with self peptide-MHC molecules expressed on thymic stromal cells is essential for the selection of those cells that ultimately are destined to leave the thymus and populate the periphery -166. ThuWith regard to the generation of quantal cellular responses, it is noteworthy that IL2 has now been implicated to be involved in both positive and negative selection, as well as T-Reg differentiation.Recent experiments focused on the signals generated in thymocytes leading to positive selection have revealed that signaling via calcium and calcineurin is necessary for positive selection but dispensable for negative selection. For exaAs already discussed, experiments performed with IL2, IL2R, JAK3, and STAT5 (-/-) mice have all now demonstrated that the IL2/IL2R interaction is unnecessary for positive selection. In the absence of signals generated via the IL2/IL2R interaction, positive selection proceeds unimpeded, so that during development and after birth, a normal number and composition of cells mature in the thymus and populate the peripheral lymphoid tissues. Thus, if the "weak" signals between the TCR and self peptide-MHC are not strong enough to trigger expression of the IL2 and IL2R genes, the cells are permitted to survive, and leave the thymus to populate the secondary lymphoid tissues. Should agonistic nonself-peptide-MHC complexes be introduced that are capable of binding to the TCR with high affinity, these T cells, which are non-reactive with "nonagonistic" self peptide-MHC complexes, are not anergic. Rather, if stimulated by non-self agonistic peptide, they are fully capable of expressing IL2 and IL2R genes, and of undergoing IL2-dependent proliferative expansion and differentiation to effector cells in the periphery.However, the development of T-Regs (i.e. CD4+CD25+ cells) is dependent on the IL2/IL2R interaction. In the absence of IL2 or functional IL2Rs, T-Regs are low or absent, both in the thymus and in the periphery. Moreover, if the IL2/IL2R interaction is restored, either genetically or pharmacologically, then T-Regs are reconstituted and the autoimmune phenomena are delayed or prevented altogether,168-170.At this juncture, it is logical to propose that the number of triggered TCRs and IL2Rs receptors necessary to generate T-Regs must be higher than the number required to generate simple "positive selection, in that IL2/IL2R gene expression must be triggered,171. In It also appears that differentiative signals triggered by the IL2/IL2R interaction are necessary to promote the differentiation to an anergic and suppressive T-Reg cell. Further"Negative selection" of potential self-reactive T cells has been proposed to occur via a TCR-triggered apoptosis. The exact molecular mechanisms responsible for this effect still remain obscure, but apoptosis appears to occur when there is a strong agonistic TCR-self-peptide-MHC interaction, which should trigger maximal IL2 and IL2R gene expression. However, data have been reported indicating that negative selection of CD8+ T cells proceeds normally without IL2. By compin situ in the thymus, and apoptotic thymocytes up-regulate the expression of IL2Rs. Furthermore, IL2R+ CD4CD8 double-positive and CD4 single-positive thymocytes undergoing apoptosis bind and internalize IL2. As well, IL2-deficient thymocytes are resistant to TCR/CD3-mediated apoptotic death, which is overcome by providing exogenous IL2 to IL2 (-/-) mice. Finally, disruption or blockade of IL2/IL2R interactions in vivo during antigen-mediated negative selection rescues MHC class II restricted thymocytes from apoptosis. Thus, all of these findings provide evidence for the direct involvement of the IL2/IL2R signaling pathway in the deletion of self-reactive double-positive and CD4 single-positive T cells[Quite convincing data have revealed a role for IL2 in CD4+ T cell negative selection  using noe T cells.Accordingly, these data are all entirely consistent with the notion that the CD4+ T cell hyperplasia and autoimmunity observed in IL2 (-/-), IL2R (-/-), and IL2 signaling (-/-) mice are attributable, at least in part, to inefficient deletion of strongly agonistic self-reactive CD4+ T cells, as well as deficient maturation of T-Regs.qualitatively between peptides of self-origin vs. peptides of nonself-origin. Both of these ligands are identical in structure, i.e. they are both peptides. Moreover, the αβ TCRs are also identical structures, whether they recognize self or non-self peptides bound to MHC. It follows that all of the data and logic support a quantitative mechanism of discrimination based upon the accumulated number of triggered TCRs and IL2Rs, as shown in Figure The foregoing considerations lead one to the realization that there are no known molecular mechanisms that can explain how the TCR can discriminate Both in the thymus and in the periphery, there are 3 cellular fates specified by an increasing number of triggered TCRs, which dictates whether IL2 is produced and how much IL2 is produced. Thus, ultimately, the number of IL2-triggered IL2Rs determines the critical quantal fate decisions. A similar conclusion was introduced recently, with the difference that TCR avidity (i.e TCR affinity × density) was postulated to dictate the cell fates, but no role was postulated for IL2. Since uIf T cells that have potential reactivity with self peptide-MHC ligands exit the thymus having escaped negative selection, these T cells will populate the secondary lymphoid tissues in the periphery at very low frequencies, ~ 1 in a million lymphocytes. Thus, these cells make up the TCR repertoire in the periphery, and as long as the distinct self-pMHC complexes remain below the critical number necessary for the formation of a stable synapse, and the TCR-pMHC off-rate is rapid, there is no necessity to introduce any additional mechanism to allow the immune system to ignore self. Instead, in the periphery the immune system only recognizes peptides, whether self or non-self, which are present at a high enough concentration to attain the critical density of 10 peptide-MHC molecules/synapse and as well, that generate a slow enough off-rate from the TCR to form a stable synapse, so that the critical number of triggered TCR/CD28 receptors for activation is reached. The only caveat beyond these considerations is that if an abortive pMHC/TCR synapse forms, the cell receives signals that it interprets as instructions to become anergic, or possibly to differentiate to become suppressive cells (T-Regs), thereby solidifying the non-reactivity on the part of the host to these peptides.The "Quantal Theory" states that the fundamental decisions of the T cell immune system are dependent upon the cells receiving a critical number of triggered TCRs and IL2Rs and that the cells respond in an all-or-none fashion. Any reductionist approach to understand how the immune system discriminates self from non-self must begin with a systemic immunological response that most closely correlates with immunity. Thus, the "Quantal Theory" is based on Burnet's axiom that the proliferative expansion of antigen-selected clones is central to the generation of a protective immune response. SecondlThese considerations lead to the speculation that non-self peptides that are introduced in low enough concentrations may well be perceived by the immune system as "self" and will generate tolerance. Thus, we now have a molecular, cellular and immunological explanation for the phenomenon of "Low Zone Tolerance", first demonstrated by Mitchison 40 years ago. AccordiThe author declares that he has no competing interests.


Drosophila discs-large (DLG) is the sole representative of a large class of mammalian MAGUKs, including human DLG, SAP 97, SAP102, and PSD-95. MAGUKs are thought to be critical for postsynaptic assembly at glutamatergic synapses. However, glutamate receptor cluster formation has never been examined in Drosophila DLG mutants. The fly neuromuscular junction (NMJ) is a genetically-malleable model glutamatergic synapse widely used to address questions regarding the molecular mechanisms of synapse formation and growth. Here, we use immunohistochemistry, confocal microscopy, and electrophysiology to examine whether fly NMJ glutamate receptor clusters form normally in DLG mutants. We also address the question of how DLG itself is localized to the synapse by testing whether presynaptic innervation is required for postsynaptic DLG clustering, and whether DLG localization requires the presence of postsynaptic glutamate receptors.Drosophila NMJ: 1) receptors that contain the subunit GluRIIA, and 2) receptors that contain the subunit GluRIIB. In DLG mutants, antibody staining for the glutamate receptor subunit GluRIIA is normal, but antibody staining for the glutamate receptor subunit GluRIIB is significantly reduced. Electrophysiological analysis shows an overall loss of functional postsynaptic glutamate receptors, along with changes in receptor biophysical properties that are consistent with a selective loss of GluRIIB from the synapse. In uninnervated postsynaptic muscles, neither glutamate receptors nor DLG cluster at synapses. DLG clusters normally in the complete absence of glutamate receptors.There are thought to be two classes of glutamate receptors in the Our results suggest that DLG controls glutamate receptor subunit composition by selectively stabilizing GluRIIB-containing receptors at the synapse. We also show that DLG, like glutamate receptors, is localized only after the presynaptic neuron contacts the postsynaptic cell. We hypothesize that glutamate receptors and DLG cluster in response to parallel signals from the presynaptic neuron, after which DLG regulates subunit composition by stabilizing (probably indirectly) receptors that contain the GluRIIB subunit. The mechanism(s) stabilizing GluRIIA-containing receptors remains unknown. The molecular mechanisms that target postsynaptic glutamate receptors to the postsynaptic membrane, and keep receptors clustered there, remain unknown. Membrane-associated guanylate kinase proteins (MAGUKs) are cell-cell junction proteins with multiple protein-interaction domains  ,4-6. AltDrosophila DLG is a prototypical MAGUK, containing three PDZ domains, an SH3 domain, a hook/4.1-binding domain, and a GUK domain  mutants are nulls that were a gift from Dr Chris Doe, University of Oregon. Df(2L)SP22 mutants remove both GluRIIA and GluRIIB, as previously described [dlg[X1–2] mutants ['Control' genotypes were either Oregon R (OR) or non-homozygous mutant siblings of the appropriate genotype. No statistically significant difference in any measurement was observed between OR and any other control genotype used in this study. Homozygous mutant embryos were identified through the use of an appropriate balancer chromosome expressing GFP. escribed . dlg[X1– mutants  were gifEmbryos and larvae were dissected and stained for immunocytochemistry and electrophysiology as previously described . When anReceptor cluster sizes Fig.  were meaThe number of glutamate receptor clusters per active zone Fig.  was quanDrosophila embryonic saline using standard patch-clamp techniques. Data were acquired and subsequently analyzed using an Axopatch 1D amplifier and PClamp 9 .All electrophysiology Fig.  was perfStatistical significance in figures is represented as follows: *** = p < 0.001; ** = p < 0.01; * = p < 0.05. Unless otherwise specified (e.g. Fig. All immunocytochemistry and microscopy was performed and analyzed by DEF. All electrophysiology was performed and analyzed by KC. The manuscript was written by DEF with input from KC; both authors reviewed and approved the final manuscript.


Endometrial polyps (EMPs) are commonly encountered in routine surgical pathology practice, but opinions differ on whether they are intrinsically a marker for concurrent or subsequent malignancy. The objectives of the present study are 1) to investigate the age-group in which EMP are most commonly encountered 2) to document the age-group in which EMP are most commonly associated with malignancies 3) To investigate whether the age of diagnosis of the various carcinoma subtypes in EMPs is congruent with published data on similar malignancies arising in non-polypoid endometrium and 4) To investigate whether the histologic subtype distribution of malignancies associated with EMPs are similar or different from the distribution of malignancies arising from non-polypoid endometrium based on published data.All cases of EMPs were retrieved from the files of Yale-New Haven Hospital for the period 1986–1995. The patients were divided into 5 age groups: Each group was further subclassified based on an association (or lack thereof) of EMPs with endometrial carcinoma. Chi-square test was used to compare the proportion of malignancy associated EMPs between the age groups.We identified 513 EMPs, of which 209 (41%) were from biopsy specimens and 304 (59%) from hysterectomy specimens. Sixty six (13%) of all EMPs were malignant. The 66 malignant EMPs included 58 endometrioid, 6 serous, 1 carcinosarcoma, and 1 clear cell carcinoma. In age group >35, only 1(2.5%) of 40 EMPs was associated with endometrial malignancy. In contrast, 37(32%) of 115 EMPs were associated with malignancy in the age group > 65. The frequency of malignant EMPs increased with age and reached statistical significance in the age group >65 (p < 0.001). The most common histologic type of malignancy was endometrioid adenocarcinoma.EMPs show statistically significant age dependent association with malignant tumor involvement. Careful search for malignancy, particularly in women with multiple risk factors is advised in daily practice. Additional studies are needed to address the histological features and immunohistochemical profiles in the context of association between endometrioid and high-grade endometrial carcinoma and endometrial polyps. Endometrial polyps (EMPs) are generally considered benign proliferative lesions and are commonly encountered in routine surgical pathology practice. The usual histological pattern of endometrial polyps is characterized by irregular proliferative glands, with a fibrotic stroma containing thick-walled blood vessels . The morMost standard pathology texts list endometrial polyps as being most prevalent in perimenopausal women and suggest possible association between polyps and malignant involvement ,11. HoweAll cases with a diagnosis of EMP were retrieved from the computerized database of the Pathology Department at Yale-New Haven Hospital for the 10-year-period from 1986 to1995. All cases were further investigated for involvement of endometrial cancers including malignancies without myometrial invasion; histologic subtypes of all malignant tumors were catalogued. Histologic types of endometrial malignancies were characterized according to the WHO classification . All casFor comparative purposes, the patients were divided into 5 age groups: 25–35; 36–45; 46–55; 56–65; and >65 years; and each group was further classified based on an association (or lack thereof) with endometrial carcinoma. A starting point of 25 years of age was selected due to the very low incidence of endometrial polyps in patients below this age. Two patients (ages 18 and 19) were excluded from the study as they did not represent a sufficiently large for statistical analysis group. The proportion of both groups  and polyps not associated with malignancies (benign polyps) were statistically compared for each of the aforementioned age-groups. Subsequently, we merged the younger age groups and preserved the >65 year group, which we referred to as "postmenopausal", since significant differences were observed in this specific subset of patients. Larger age groups were arbitrarily designated as reproductive years (25–45), perimenopause  and postmenopause (>65) and statistically analyzed. The postmenopausal status of all women above the age of 65 was verified and the term "postmenopausal" was occasionally used when referring to this particular age group. Our use of this term, although arbitrary, was important in order to put the emphasis on the fact that any pathomorphological findings in this age group are unlikely to be attributed to changes characteristic of the cycling endometrium.Chi-square test was used to compare the proportion of malignancy associated EMPs between the age groups and in regards to particular histological type of malignancies.p < 0.001) in the age group >65 years  endometrial biopsies/curetting samples, and 209 (41%) hysterectomy specimens. In cases in which endometrial biopsies and hysterectomies both showed presence of EMP, only the hysterectomy specimen was considered. The age of patients ranged from 18–91 years with a median of 54 years. Sixty-six (13%) of 513 EMPs were malignant. The histological subtype distribution of those 66 malignancies included 58 endometrioid (87%), 6 serous (9%), 1 carcinosarcoma, and 1 clear cell carcinoma. No mixed histological type of endometrial cancer was found in our series. The incidence of EMP peaked at age group 46–55 years, which was similar to previous reports. In age group 25–35, only 1 (2.5%) of 40 EMPs was associated with endometrial malignancy. In contrast, 37 (32%) of 115 EMPs were associated with malignancy in the age group >65 years  of endometrial carcinomas associated with EMPs were of endometrioid, followed by the serous type (9%). These relative proportions of both major histological subtypes are in accordance with the well-known distribution of similar subtypes of endometrial carcinoma in non-polypoid endometrium  and thuset al.,  reached et al.,  or the eet al., ,19.et al., [This study also confirms previous findings that EMPs are most prevalent in the perimenopausal age group. The reason(s) for this age-segregation, which has remained remarkably consistent across various studies since the mid-fifties, is unclear. Chavez et al.,  speculatDespite the supportive evidence of no difference in the clinico-pathological features and overall distribution of carcinomas arising from EMPs with those arising from non-polypoid endometrium, our data suggest a strong age dependent association between the presence of EMPs and involvement by endometrial carcinoma. The pathogenesis and mechanisms underlying such association are complex and not well established. Recently published data, however, provided some clue of significant differences in receptor expression, response to stimuli, and apoptosis regulation in EMPs compared to benign non-polypoid endometrium which could potentially elucidate some aspects of the possible malignant potential of EMPs. Estrogen and progesterone act as modulators of endometrial proliferation and differentiation through their receptors. Glandular epithelial expression of estrogen and progesterone receptors in polyps is not significantly different from that of the normal cycling endometrium. However, fewer stromal cells express estrogen and progesterone receptors in polyps which suggests that EMPs may result from a decrease in estrogen and progesterone receptors in the stromal cells . In addiet al., who found that 10 (76%) of 13 Tamoxifen-related endometrial carcinomas were associated with EMPs [Another significant histological finding is the glandular epithelia hyperplasia in C-erbB2 -positive polyps as opposed to rather atrophic architecture in C-erbB2 -negative polyps . These fith EMPs .One potential limitation of our study is our lack of consideration of the impact of variables such as hypertension, obesity and family history. However, since data regarding such possible confounders were not available to us, we set the goals of our investigation to be primarily focused on age related distribution of coinciding morphologic findings. Although we are aware of the limitations of our study and the introduced analytical bias, drawbacks that certainly pertain to any similar retrospective pathomorphologic study, we feel that we have adequately addressed the proposed investigative tasks according to the initially set scope of the study. By using the database of Yale-New Haven Hospital, we collected and analyzed a significant number of cases over an extensive period of time and thereby our study population constituted an adequate representation of the general population in respect to the morphological parameters we investigated.In summary, the age distribution, histological subtype distribution, and peak incidence of EMPs was similar to previous reports. In contrast, EMPs in postmenopausal women showed a significantly higher association with malignant tumor involvement. Careful microscopic search for malignancy in patients with multiple risk factors, particularly in postmenopausal women is advised in daily surgical pathology practice.The author(s) declare that they have no competing interests.DH wrote the original version of the manuscript.OF made substantial contributions to the content of the manuscript and participated in manuscript preparation.MM collected clinical and pathological data and revised the final version.WZ analyzed and interpreted the data and supervised the entire project.All authors have read and approved the final manuscript.


In recent years, clustering algorithms have been effectively applied in molecular biology for gene expression data analysis. With the help of clustering algorithms such as K-means, hierarchical clustering, SOM, etc, genes are partitioned into groups based on the similarity between their expression profiles. In this way, functionally related genes are identified. As the amount of laboratory data in molecular biology grows exponentially each year due to advanced technologies such as Microarray, new efficient and effective methods for clustering must be developed to process this growing amount of biological data.Incremental Genetic K-means Algorithm (IGKA). IGKA is an extension to our previously proposed clustering algorithm, the Fast Genetic K-means Algorithm (FGKA). IGKA outperforms FGKA when the mutation probability is small. The main idea of IGKA is to calculate the objective value Total Within-Cluster Variation (TWCV) and to cluster centroids incrementally whenever the mutation probability is small. IGKA inherits the salient feature of FGKA of always converging to the global optimum. C program is freely available at In this paper, we propose a new clustering algorithm, Our experiments indicate that, while the IGKA algorithm has a convergence pattern similar to FGKA, it has a better time performance when the mutation probability decreases to some point. Finally, we used IGKA to cluster a yeast dataset and found that it increased the enrichment of genes of similar function within the cluster. In recent years, clustering algorithms have been effectively applied in molecular biology for gene expression data analysis  [Recently, Krishna and Murty proposed a new clustering method called hm (GKA) , which hIncremental Genetic K-means Algorithm (IGKA) that inherits all the advantages of FGKA including the convergence to the global optimum, and outperforms FGKA when the mutation probability is small. The main idea of IGKA is to calculate the objective value TWCV and to cluster centroids incrementally. We then propose a Hybrid Genetic K-means Algorithm (HGKA) that combines the benefits of FGKA and IGKA. We show that clustering of microarray data by IGKA method has more tendencies to group the genes with the same functional category into a given cluster.In , we propOur experiments were conducted on a Dell PowerEdge 400SC PC machine with 2.24G Hz CPU and 512 M RAM. Three algorithms, FGKA, IGKA and HGKA algorithm were implemented in C language. GKA has convergence pattern similar to FGKA and IGKA, but its time performance is worse than FGKA, see  for morefig2data, introduced in [chodata, introduced in [fig2data data set contains expression data for 517 genes. Each gene has 19 expression data ranges from 15 minutes to 24 hours. In other words, the number of features D is 19. According to [chodata is a yeast dataset, composed of expression data for 2907 genes and the expression data for each gene ranges 0 minutes to 160 minutes, which means that the number of features D is 15. According to the description in [The two data sets used to conduct our experiments are serum data, duced in and yeastrding to , 517 genption in . In thisption in , the popfig2data, and 0.0005 for chodata), IGKA has a better performance. Figure chodata, we should set the mutation probability to 0.0005 to have IGKA outperform FGKA. On the other hand, in order to have IGKA outperform than FGKA, we only need to set the mutation probability to 0.005 in the small data set fig2data. In general, the threshold value depends on the number of patterns and the number of features in the data set. It is easy to understand that the performance gained in IGKA is mainly dependent on how many patterns change their cluster memberships. So, in a large data set, even small number of mutation probability may cause many patterns change their cluster memberships.As indicated in the implementation section, the mutation probability has great impact on IGKA algorithm. We check the performance impact on IGKA in this section, and the convergence in the next section. Figure fig2data and chodata, respectively. These two algorithms have similar convergence results. When the mutation probability changes in these two data sets, it has little impact on these two algorithms during the range that is given in Figure Figures fig2data and chodata, are fed into the algorithms, and the clustering results are exported as a text file. We then use an in-house program to calculate the TWCVs for each result. The experiments on K-means and SOM algorithm are conducted on an open source software [We also make an interesting comparison of IGKA with FGKA, K-means and SOM on TWCV convergence. We treat each algorithm as a black box. Two data sets, the software . As we cFigure chodata using our IGKA algorithm were evaluated according to the scheme of gene classification of MIPS Yeast Genome Database [The clustering results of Database . We founDatabase . The absMost interestingly, we found a remarkable enrichment of ORFs for the functional category of organization of mitochondria. They are mainly located in two clusters: cluster 3 and cluster 18. Cluster 3 has 156 ORFs in total, and 111 ORFs belong to the category, resulting in a very high percentage, 71.2%. Cluster 18, has 184 ORFs in total, in which there are 105 ORFs belonging to the category and the percentage is 57.1%. The percentage of ORFs within the same function category is only 18.8% in the previous paper. It looks that our IGKA method is more likely to increase the degree of enrichment of the genes within functional categories, and to make more biological sense. We also found a new function category: lipid and fatty isoprenoid metabolism distributed in cluster 25, which was not listed in Tavazoie's paper.Incremental Genetic K-means Algorithm (IGKA). IGKA is an extension of FGKA, which in turn was inspired by the Genetic K-means Algorithm (GKA) proposed by Krishna and Murty. The IGKA inherits the advantages of FGKA, and it outperforms FGKA when the mutation probability is small. Since both FGKA and IGKA might outperform each other, a hybrid approach that combines the benefits of them is very desirable. Our experimental results showed that not only the performance of our algorithm is improved but also the clustering result with gene expression data has some interesting biological discovery.In this paper, we propose a new clustering algorithm called N genes and their corresponding N patterns. Each pattern is a vector of D dimensions recording the expression levels of the genes under each of the D monitored conditions or at each of the D time points. The goal of IGKA algorithm is to partition the N patterns into user-defined K groups, such that this partition minimizes the Total Within-Cluster Variation , which is defined as follows.The problem of clustering gene expression data consists of  be the N patterns, and Xnd denotes the dth feature of pattern Xn. Each partition is represented by a string, a sequence of numbers a1....aN,, where an is the number of the cluster that pattern  belongs to in this partition. Let Gk denote the kth cluster and Zk denote the number of patterns in Gk. The centroid ck =  of cluster Gk is defined as ,  where SFkd is the sum of the dth features of all the patterns in Gk. and we use  to denote the vector of sum of all patterns in cluster Gk.Let Z coded solutions, where Z is a parameter specified by the user. Each solution, also called a chromosome, is coded by a string a1...aN of length N, where each an, which is called an allele, corresponds to a gene expression data pattern and takes a value from {1, 2, ..., K} representing the cluster number to which the corresponding pattern belongs. For example, a1a2a3a4a5= "33212" encodes a partition of 5 patterns in which, patterns  and  belong to cluster 3, patterns  and  belong to cluster 2, and pattern  belongs to cluster 1.IGKA maintains a population (set) of Sz = a1 ....aN, let e(Sz) be the number of non-empty clusters in Sz divided by K, e(Sz) is called legality ratio. We say string Sz is legal if e(Sz) = 1, and illegal otherwise.Given a partition K = 3, the string a1a2a3a4a5 = "23232" is illegal because cluster 1 is empty.Hence, an illegal string represents a partition in which some clusters are empty. For example, given P0. The population in the next generation Pi + 1 is obtained by applying genetic operators on the current population Pi. The evolution takes place until a terminating condition is reached. The following genetic operators are used in IGKA: the selection, the mutation and the K-means operator.Figure proportional selection for the selection operator in which, the population of the next generation is determined by Z independent random experiments. Each experiment randomly selects a solution from the current population  according to the probability distribution  defined by , where F(Sz) denotes the fitness value of solution Sz with respect to the current population and will be defined in the next paragraph.We use the so-called TWCV). Therefore, solutions with smaller TWCVs should have higher probabilities for survival and should be assigned with greater fitness values. In addition, illegal strings are less desirable and should have lower probabilities for survival, and thus should be assigned with lower fitness values. We define fitness value of solution Sz, F(Sz) asVarious fitness functions have been defined in the literature  in whichTWCVmax is the maxim TWCV that has been encountered till the present generation, Fmin is the smallest fitness value of the legal strings in the current population if they exist, otherwise Fmin is defined as 1. The definition of fitness function in GKA [where n in GKA  paper inThe intuition behind this fitness function is that, each solution will have a probability to survive by being assigned with a positive fitness value, but a solution with a smaller TWCV has a greater fitness value and hence has a higher probability to survive. Illegal solutions are allowed to survive too but with lower fitness values than all legal solutions in the current population. Illegal strings that have more empty clusters are assigned with smaller fitness values and hence have lower probabilities for survival. The reason we still allow illegal solution survive with low probability is that we believe the illegal solution may mutate to a good solution and the cost of maintain the illegal solution is very low.TWCV for each solution Sz (denoted by Sz.TWCV) and the maximum TWCV (denoted by TWCVmax), have already been calculated before the selection operator is applied.We assume that the a1 ....aN, the mutation operator mutates each allele an to a new value an  with probability MP respectively and independently, where 0 <MP < 1 is a parameter called the mutation probability that is specified by the user. The mutation operator is very important to help reach better solutions. From the perspective of the evolutional theory, offsprings produced by mutations might be superior to their parents. More importantly, the mutation operator performs the function of shaking the algorithm out of a local optimum, and moving it towards the global optimum.Given a solution (chromosome) that is encoded by a1 ....aN, each allele an corresponds to a pattern  and its value indicates the number of the cluster to which  belongs. During mutation, we replace allele an by an' for n = 1,...,N simultaneously, where an is a number randomly selected from  with the probability distribution  defined by:Recall that in solution  is the Euclidean distance between pattern  and the centroid ck of the kth cluster, and . If the kth cluster is empty, then  is defined as 0. The bias 0.5 is introduced to avoid divide-by-zero error in the case that all patterns are equal and are assigned to the same cluster in the given solution. Our definition of the mutation operator is similar to the one defined in the GKA paper [where KA paper . However might be reassigned randomly to each cluster with a positive probability; (2) the probability of changing allele value an to a cluster number k is greater if  is closer to the centroid of the kth cluster Gk; and (3) empty clusters are viewed as the closest clusters to . The first property ensures that an arbitrary solution, including the global optimum, might be generated by the mutation from the current solution with a positive probability; the second property encourages that each  is moving towards a closer cluster with a higher probability; the third property promotes the probability of converting an illegal solution to a legal one. These properties are essential to guarantee that IGKA will eventually converge to the global optimum fast.The above mutation operator is defined such that (1) K-means operator (KMO) is introduced. Given a solution that is encoded by a1 ....aN, we replace an by an' for n = 1,...,N simultaneously, where an' is the number of the cluster whose centroid is closest to  in Euclidean distance. More formally, In order to speed up the convergence process, one step of the classical K-means algorithm, which we call  = +∞ if the kth cluster is empty. This definition is different from mutation operator, in which we defined  = 0 if the kth cluster is empty. The motivation for this new definition here is that we want to avoid reassigning all patterns to empty clusters. Therefore, illegal string will remain illegal after the application of KMO.To accommodate illegal strings, we define In the following, we first present FGKA algorithm that is proposed in . We thenP0 with Z solutions. For each generation Pi, we apply the three operators, selection, mutation and K-means operator sequentially which generate population , , and Pi + 1 respectively. This process is repeated for G iterations, each of which corresponds to one generation of solutions. The best solution so far is observed and recorded in So before the selection operator. So is returned as the output solution when FGKA terminates.FGKA shares the same flowchart of IGKA given in Figure  is reassigned from cluster k to cluster k', then only the centroids and WCVs of these two clusters need to be recalculated. Furthermore, the centroids of these two clusters can be calculated incrementally since the memberships of other patterns have not changed; The TWCV can be calculated incrementally as well since the WCVs of other clusters have not changed. In the following, we describe how we can calculate TWCV and cluster centroids  incrementally.Although FGKA outperforms GKA significantly, it suffers from a potential disadvantage. If the mutation probability is small, then the number of allele changes will be small, and the cost of calculating centroids and TWCV from scratch can be much more expensive than calculating them in an incremental fashion. As a simple example, if a pattern , we maintain the difference values of ZkΔ,  for old solution and new solution when allele changes. With these two values, incremental update of Zk and  can be achieved as Zk = Zk + ZkΔ, and . Then the new centroids for new solution  can be achieved by .In order to obtain the new centroid TWCV, we can maintain a difference value TWCVΔ that denotes the difference between old TWCV and new TWCV for one solution. It is obvious that TWCVΔ is attributed from the difference of new WCVk and old WCVk for cluster k. However, WCVk has to be calculated from scratch since  is changed. In this way, TWCV can be updated incrementally as well. Since the calculation of TWCV dominates all iterations, our incremental update of TWCV will have a better performance when mutation probability is small . However, if the mutation probability is large, too many alleles change their cluster membership, the maintenance of Zk Δ and  becomes expensive and IGKA becomes inferior to FGKA in performance, as confirmed in the experimental study.Similarly, in order to obtain the new The above discussion presents a dilemma – both FGKA and IGKA are likely to outperform each other: when the mutation probability is smaller than some threshold, IGKA outperforms FGKA; otherwise, FGKA outperforms IGKA.The key idea of HGKA is to combine the benefits of FGKA and IGKA. However, it is very difficult to derive the threshold value, which is dataset dependant. In addition, the running times of all iterations will vary as solutions converge to the optimum. We propose the following solution: we periodically run one iteration of FGKA followed by one iteration of IGKA while monitoring their running times, and then run the winning algorithm for the following iterations until we reach another competition point.It has been proved in  that FGK. The source code and database scheme are freely distributed to academic users upon request to the authors.IGKA algorithm is available at WCV: Within-Cluster Variation; TWCV: Total Within-Cluster Variation; IGKA: Incremental Genetic K-means Algorithm; FGKA: Fast Genetic K-means Algorithm; HGKA: Hybrid Genetic K-means Algorithm; ORF: Open Reading Frame.YL carried out the study and drafted the manuscript. SL and FF designed the algorithms. YD designed the whole project, participated in analyzing gene functional data and wrote part of manuscript. SJB corrected English and helped to interpret the data analysis results.


Individuals with chronic fatigue syndrome (CFS) have been shown to have reduced activity levels associated with heightened feelings of fatigue. Previous research has demonstrated that exercise training has beneficial effects on fatigue-related symptoms in individuals with CFS.The aim of this study was to sustain an increase in daily physical activity in CFS patients for 4 weeks and assess the effects on fatigue, muscle pain and overall mood.Six CFS and seven sedentary controls were studied. Daily activity was assessed by a CSA accelerometer. Following a two week baseline period, CFS subjects were asked to increase their daily physical activity by 30% over baseline by walking a prescribed amount each day for a period of four weeks. Fatigue, muscle pain and overall mood were reported daily using a 0 to 100 visual analog scale and weekly using the Profile of Mood States (Bipolar) questionnaire.3 counts/day vs. 267.2 ± 79.5 × 103 counts/day) during a 2-week baseline period. At baseline, the CFS patients reported significantly (P < 0.01) higher fatigue and muscle pain intensity compared to controls but the groups did not differ in overall mood. CFS subjects increased their daily activity by 28 ± 19.7% over a 4 week period. Overall mood and muscle pain worsened in the CFS patients with increased activity.CFS patients had significantly lower daily activity counts than controls (162.5 ± 51.7 × 10CFS patients were able to increase their daily physical activity for a period of four weeks. In contrast to previous studies fatigue, muscle pain, and overall mood did not improve with increased activity. Increased activity was not presented as a treatment which may account for the differential findings between this and previous studies. The results suggest that a daily "activity limit" may exist in this population. Future studies on the impact of physical activity on the symptoms of CFS patients are needed. Chronic fatigue syndrome (CFS) is characterized by persistent debilitating fatigue often accompanied by a complex of other symptoms  lasting at least six months that is unresolved with rest or medication ,2. A priIt is widely accepted that a sedentary lifestyle may greatly increase the risk of development of cardiovascular disease and Type II diabetes, as well as contributing to bone loss, and an age-related loss of function in a person's ability to perform daily activities -9. RecenFew randomized controlled trials designed to assess the efficacy of exercise training have been conducted in the CFS population. Two studies used graded exercise performed several days-a-week over a period of 12–26 weeks and both reported an improvement in fatigue-related symptoms and aerobic capacity ,12. AddiThe purpose of this study was to assess normal daily physical activity levels in CFS patients using accelerometers over a two-week period and compare these values to a group of healthy sedentary individuals. Additionally, the CFS patients were asked to increase their daily physical activity approximately 30% over a four week period by walking a prescribed amount each day while maintaining their non-exercise daily physical activity. Daily ratings of mood, fatigue, and muscle pain intensity were assessed and compared between the groups as well as in response to increased daily activity in the CFS patients.All experimental procedures were approved by the Institutional Review Board at the University of Georgia, and informed consent was obtained from each participant. All participants were recruited from the general community and either responded to a newspaper ad, responded to a flyer placed around campus, or were referred to the study by their physician. Seventeen CFS and twenty-one controls responded and were screened as possible study participants. A physician's diagnosis of CFS was required for inclusion. Additionally, CFS patients were required to confirm a self-report of decreased physical activity compared to pre-CFS levels, and self-reported inability to sustain high levels of physical activity without a subsequent exacerbation of CFS symptoms for study inclusion. CFS participants with a self-reported history of depression or other psychiatric illness were excluded. Control participants were chosen to be similar in age, height, and weight to the CFS patients and were defined as sedentary by self-report of one bout of regular exercise per week or less. The most sedentary participants  were given first priority for study inclusion. Control participants were also apparently healthy and reported no illnesses or disease conditions. Medications were monitored in all participants. The CFS participants were found to be taking many medications, both prescription and over-the-counter. Analgesics such as Vioxx, Celebrex, Advil, and Aleve were common.Initially, participants received instructions for wearing the activity monitors and for completing a daily activity log. A "pre" score from the 30-item Profile of Mood States short form questionnaire (POMS) was obtained . Participants proceeded to wear the monitors for two weeks during which time they were instructed to maintain normal daily activity. After the two weeks, data were collected from the activity monitors, and the monitors were reset. The participants then wore the monitors for an additional four weeks. The CFS patients were asked to increase their daily physical activity (30% above baseline) during this four week period by walking a prescribed amount each day in order to approximate the daily physical activity of a healthy sedentary person. This was based upon averaging the findings of others that suggested CFS patients had activity levels that were 15% to 40% reduced from healthy but sedentary individuals . CFS patDaily physical activity was assessed by a CSA accelerometer . To ensure accurate measurements, the procedure recommended by CSA was followed – the monitors were positioned over the subject's anterior superior iliac spine with the belt fitting snuggly so as to limit extraneous monitor movement. Participants were asked to wear the monitors at all times of the day, including sleep. Two minute epochs were used. Data were retrieved from the monitors using a specially designed docking module that input data into a computer.Recommended percent increases in daily activity were calculated based on each subject's average daily counts during their two-week baseline activity period. Counts are arbitrary units assigned to movements detected by the accelerometer. Counts are assigned based upon the magnitude of a change in velocity during a given time period. The number of counts needed to raise daily activity approximately 30% was calculated. Participants were then asked to walk on a treadmill at what they considered to be a comfortable walking pace. Walking speed was recorded, and used to calculate the recommended daily walking time. The approximate number of counts per minute for various walking speeds was assessed prior to the onset of the study (unpublished observations). Additionally, a pedometer was also used to aid participants in achieving the desired daily activity increase. Participants were given an approximate number of steps to take each day during their walk based upon their prescribed walking pace and time. Steps per minute for various walking speeds were assessed in a similar manner as counts per minute prior to the study (unpublished observations).Data concerning daily activity, mood, fatigue, and muscle pain were obtained from each subject via daily self-report. Participants were asked to report all daily activities and time spent engaged in each. Time periods when the activity monitor was not worn were also reported. A series of five questions concerning daily mood, fatigue intensity, and muscle pain intensity were also answered. Participants ranked, using a 10 cm (0 to 100 mm) visual analog scale their general overall daily mood for that day , the intensity of their fatigue that day (with 0 being no fatigue and 100 being the highest intensity fatigue imaginable), and the intensity of their muscle pain that day (with 0 being no pain and 100 being the worst imaginable pain). A similar visual analog scale has been used previously in CFS patients to rate daily fatigue . AdditioIndependent samples t-tests were conducted to compare for differences in subject characteristics between the groups. A repeated measures ANOVA was conducted to determine differences between activity level and mood in CFS and control participants. When a significant interaction was observed a one-way repeated measure ANOVA was performed to analyze simple effects with planned comparisons performed to analyze differences in treatment means. All values are reported means ± SD. Analyses were conducted and significance was assumed at an α level of 0.05.No participants (CFS or controls) reported adverse events associated with the increased activity program. Data were obtained from six CFS patients as well as seven sedentary control participants. Additionally, two other CFS patients began the testing protocol but were removed from the study at their own request. One was removed on doctor's recommendation due to an injury (unrelated to the study) and the second was removed due to a change in residence. The physical characteristics of all participants are presented in Table P = 0.017). All six of the CFS participants were successful in increasing their daily physical activity. Their daily activity counts increased 28%, on average, during the four-week training period (P < 0.001). However, it should be noted that 4 of the 6 CFS participants did not reach the prescribed 30% increase in daily activity. Interestingly, following their activity increase the CFS participants had activity levels that were still 24% reduced from those of the control group (P = 0.08).Individual as well as mean group daily activity counts are presented in Table Figures P = 0.016, Eta2 = 0.311) in overall mood. CFS participants reported a worsening of overall mood over time compared to controls. Neither an interaction nor a time main effect was observed in ratings of fatigue intensity. A significant group difference was observed between the CFS and control participants . Although not statistically significant, ratings of fatigue intensity in the CFS group did increase from 58.2 ± 8.5 to 67.0 ± 17.5 (indicating a worsening of symptoms). A significant group-by-time interaction  was seen between the CFS and control participants in their ratings of muscle pain intensity . Additionally, the CFS participants also reported experiencing a significantly greater amount of time spent with muscle pain each day . A significant time main effect was found for time spent with fatigue each day . A significant difference was found between baseline activity, 451 ± 528 min/day, compared to the final two weeks of increased activity 521 ± 566 min/day . The CFS participants also demonstrated a non-significant increase in time spent with muscle pain each day during baseline activity, the first two weeks of increased activity and the final two weeks of increased activity (554 ± 507 min/day vs. 642 ± 546 min/day vs. 713 ± 557 min/day). Control participants demonstrated no change over time in time spent each day with fatigue or muscle pain.The amount of time spent with fatigue each day as well as the amount of time spent with muscle pain each day was also reported by both groups. During baseline activity, the CFS participants reported experiencing a significantly greater amount of time spent with fatigue per day compared to the control participants . No change was observed in the fatigue scores of the CFS participants as their daily physical activity was increased. The control participants also demonstrated no change over time. Similarly, a significant difference was also observed between the CFS and control groups when vigor scores were compared . No change was observed in the vigor scores over time or in response to increased activity in either group.Figures 4A primary finding of this study was that individuals with CFS can increase their daily physical activity 28% on average over a four week period. Average daily activity counts, measured by accelerometer, increased in all six of the CFS participants who participated in the study. The magnitude of the observed increases in daily activity ranged from approximately 13% to 60%. These results are consistent with previous studies that have shown that CFS patients can sustain training programs lasting 12 to 26 weeks ,12. The Another interesting aspect of this study was the fact that even after increasing their daily activity 28%, our CFS participants were still approximately 25% less active than our sedentary control participants. We attempted a 30% increase in daily physical activity with the hope of bringing the daily activity levels of our CFS participants up to those of sedentary individuals. This was based upon the findings of others that suggested CFS patients had activity levels that were 15% to 40% reduced from healthy but sedentary individuals . Our resTo our knowledge, this study was one of the first to obtain daily ratings of fatigue intensity from a group of CFS participants under normal daily physical activity conditions as well as during periods of increased daily physical activity. Consistent with their diagnosis, CFS patients reported much greater daily ratings of fatigue intensity, time spent each day with fatigue, as well as fatigue recalled during the prior week compared to healthy sedentary participants. This large difference was expected based on the diagnosis and demonstrated the usefulness of ratings of this type to confirm fatigue symptoms.We found that overall mood, muscle pain intensity, and time spent each day with fatigue worsened following increased activity in our CFS participants compared to controls. Additionally, daily ratings of fatigue intensity (VAS) increased moderately over time while weekly fatigue (POMS) remained stable but elevated in the CFS patients. These observations are contrary to previous studies of increased exercise in this population where exercise training has been shown to reduce fatigue-related symptoms ,12. ThesIt is not clear why our study did not find increased daily physical activity to reduce symptom severity, as reported in previous studies -13. One Presentation of exercise as a possible treatment for CFS symptoms could have played a role in the improvements in symptom severity observed with exercise training -13. CognA third explanation of our findings is that there may have been something inherent in our exercise protocol that prevented fatigue symptoms from improving. Our method of activity increase, self-paced walking, was no more strenuous than the exercise used in other studies -13. HoweOur prescribed exercise was less intense and occurred over a shorter time period than that of previous studies -13. It iFive of our six CFS participants also reported having fibromyalgia. Fibromyalgia is a related syndrome with a primary symptom of muscle pain and tenderness . Interes2 values from 0.101 to 0.377), suggesting that more participants would be needed to detect differences between the subject groups. Consequently, additional studies will be needed to confirm our results.It is important to note that our small sample size is a key limitation in our study. The study is under powered to detect differences between our groups. Most of the measured variables had small to moderate effect sizes (EtaIn conclusion, this study found that individuals with CFS were able to increase their daily physical activity by approximately 28% for four weeks without serious health complications. At baseline activity our CFS participants exhibited significantly lower daily activity than sedentary controls. This reduced level of daily activity was larger than previously reported values,4,6. Lar