Anatomical and developmental patterns of interleukin-2 gene expression in the mouse: analysis of IL-2 expressing cells and partial characterization of interactions involved in mediating IL-2 gene expression in vivo

Interleukin-2 (IL-2) is an important mediator in the vertebrate immune system. IL-2 is a potent growth factor that mature T lymphocytes use as a proliferation signal and the production of IL-2 is crucial for the clonal expansion of antigen-specific T cells in the primary immune response. IL-2 driven proliferation is dependent on the interaction of the lymphokine with its cognate multichain receptor. IL-2 expression is induced only upon stimulation and transcriptional activation of the IL-2 gene relies extensively on the coordinate interaction of numerous inducible and constitutive trans-acting factors. Over the past several years, thousands of papers have been published regarding molecular and cellular aspects of IL-2 gene expression and IL-2 function. The vast majority of these reports describe work that has been carried out in vitro. However, considerably less is known about control of IL-2 gene expression and IL-2 function in vivo.

To gain new insight into the regulation of IL-2 gene expression in vivo, anatomical and developmental patterns of IL-2 gene expression in the mouse were established by employing in situ hybridization and immunohistochemical staining methodologies to tissue sections generated from normal mice and mutant animals in which T -cell development was perturbed. Results from these studies revealed several interesting aspects of IL-2 gene expression, such as (1) induction of IL-2 gene expression and protein synthesis in the thymus, the primary site of T-cell development in the body, (2) cell-type specificity of IL-2 gene expression in vivo, (3) participation of IL-2 in the extrathymic expansion of mature T cells in particular tissues, independent of an acute immune response to foreign antigen, (4) involvement of IL-2 in maintaining immunologic balance in the mucosal immune system, and (5) potential function of IL-2 in early events associated with hematopoiesis.

Extensive analysis of IL-2 mRNA accumulation and protein production in the murine thymus at various stages of development established the existence of two classes of intrathymic IL-2 producing cells. One class of intrathymic IL-2 producers was found exclusively in the fetal thymus. Cells belonging to this subset were restricted to the outermost region of the thymus. IL-2 expression in the fetal thymus was highly transient; a dramatic peak ofiL-2 mRNA accumulation was identified at day 14.5 of gestation and maximal IL-2 protein production was observed 12 hours later, after which both IL-2 mRNA and protein levels rapidly decreased. Significantly, the presence of IL-2 expressing cells in the day 14-15 fetal thymus was not contingent on the generation of T-cell receptor (TcR) positive cells. The second class of IL-2 producing cells was also detectable in the fetal thymus (cells found in this class represented a minority subset of IL-2 producers in the fetal thymus) but persist in the thymus during later stages of development and after birth. Intrathymic IL-2 producers in postnatal animals were located in the subcapsular region and cortex, indicating that these cells reside in the same areas where immature T cells are consigned. The frequency of IL-2 expressing cells in the postnatal thymus was extremely low, indicating that induction of IL-2 expression and protein synthesis are indicative of a rare activation event. Unlike the fetal class of intrathymic IL-2 producers, the presence of IL-2 producing cells in the postnatal thymus was dependent on to the generation of TcR+ cells. Subsequent examination of intrathymic IL-2 production in mutant postnatal mice unable to produce either αβ or γδ T cells showed that postnatal IL-2 producers in the thymus belong to both αβ and γδ lineages. Additionally, further studies indicated that IL-2 synthesis by immature αβ -T cells depends on the expression of bonafide TcR αβ-heterodimers. Taken altogether, IL-2 production in the postnatal thymus relies on the generation of αβ or γδ-TcR^+ cells and induction of IL-2 protein synthesis can be linked to an activation event mediated via the TcR.

With regard to tissue specificity of IL-2 gene expression in vivo, analysis of whole body sections obtained from normal neonatal mouse pups by in situ hybridization demonstrated that IL-2 mRNA^+ cells were found in both lymphoid and nonlymphoid tissues with which T cells are associated, such as the thymus (as described above), dermis and gut. Tissues devoid of IL-2 mRNA^+ cells included brain, heart, lung, liver, stomach, spine, spinal cord, kidney, and bladder. Additional analysis of isolated tissues taken from older animals revealed that IL-2 expression was undetectable in bone marrow and in nonactivated spleen and lymph nodes. Thus, it appears that extrathymic IL-2 expressing cells in nonimmunologically challenged animals are relegated to particular epidermal and epithelial tissues in which characterized subsets of T cells reside and thatinduction of IL-2 gene expression associated with these tissues may be a result of T-cell activation therein.

Based on the neonatal in situ hybridization results, a detailed investigation into possible induction of IL-2 expression resulting in IL-2 protein synthesis in the skin and gut revealed that IL-2 expression is induced in the epidermis and intestine and IL-2 protein is available to drive cell proliferation of resident cells and/or participate in immune function in these tissues. Pertaining to IL-2 expression in the skin, maximal IL-2 mRNA accumulation and protein production were observed when resident Vγ_3^+ T-cell populations were expanding. At this age, both IL-2 mRNA^+ cells and IL-2 protein production were intimately associated with hair follicles. Likewise, at this age a significant number of CD3ε^+ cells were also found in association with follicles. The colocalization of IL-2 expression and CD3ε^+ cells suggests that IL-2 expression is induced when T cells are in contact with hair follicles. In contrast, neither IL-2 mRNA nor IL-2 protein were readily detected once T-cell density in the skin reached steady-state proportions. At this point, T cells were no longer found associated with hair follicles but were evenly distributed throughout the epidermis. In addition, IL-2 expression in the skin was contingent upon the presence of mature T cells therein and induction of IL-2 protein synthesis in the skin did not depend on the expression of a specific TcR on resident T cells. These newly disclosed properties of IL-2 expression in the skin indicate that IL-2 may play an additional role in controlling mature T-cell proliferation by participating in the extrathymic expansion of T cells, particularly those associated with the epidermis.

Finally, regarding IL-2 expression and protein synthesis in the gut, IL-2 producing cells were found associated with the lamina propria of neonatal animals and gut-associated IL-2 production persisted throughout life. In older animals, the frequency of IL-2 producing cells in the small intestine was not identical to that in the large intestine and this difference may reflect regional specialization of the mucosal immune system in response to enteric antigen. Similar to other instances of IL-2 gene expression in vivo, a failure to generate mature T cells also led to an abrogation of IL-2 protein production in the gut. The presence of IL-2 producing cells in the neonatal gut suggested that these cells may be generated during fetal development. Examination of the fetal gut to determine the distribution of IL-2 producing cells therein indicated that there was a tenfold increase in the number of gut-associated IL-2 producers at day 20 of gestation compared to that observed four days earlier and there was little difference between the frequency of IL-2 producing cells in prenatal versus neonatal gut. The origin of these fetally-derived IL-2 producing cells is unclear. Prior to the immigration of IL-2 inducible cells to the fetal gut and/or induction of IL-2 expression therein, IL-2 protein was observed in the fetal liver and fetal omentum, as well as the fetal thymus. Considering that induction of IL-2 protein synthesis may be an indication of future functional capability, detection of IL-2 producing cells in the fetal liver and fetal omentum raises the possibility that IL-2 producing cells in the fetal gut may be extrathymic in origin and IL-2 producing cells in these fetal tissues may not belong solely to the T lineage. Overall, these results provide increased understanding of the nature of IL-2 producing cells in the gut and how the absence of IL-2 production therein and in fetal hematopoietic tissues can result in the acute pathology observed in IL-2 deficient animals.

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.