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ii iii Abstract. Let S be the sphere spectrum. We construct an associative, commutative, and unital smash product in a complete and cocomplete category M S of "S-modules" whose derived category D S is equivalent to the classical stable homotopy category. This allows a simple and algebraically manageable definition of "S-algebras" and "commutative S-algebras" in terms of associative, or associative and commutative, products R ∧ S R −→ R. These notions are essentially equivalent to the earlier notions of A ∞ and E ∞ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of R-modules in terms of maps R ∧ S M −→ M .When R is commutative, the category M R of R-modules also has an associative, commutative, and unital smash product, and its derived category D R has properties just like the stable homotopy category.Working in the derived category D R , we construct spectral sequences that specialize to give generalized universal coefficient and Künneth spectral sequences. Classical torsion products and Ext groups are obtained by specializing our constructions to Eilenberg-Mac Lane spectra and passing to homotopy groups, and the derived category of a discrete ring R is equivalent to the derived category of its associated Eilenberg-Mac Lane S-algebra.We also develop a homotopical theory of R-ring spectra in D R , analogous to the classical theory of ring spectra in the stable homotopy category, and we use it to give new constructions as MU-ring spectra of a host of fundamentally important spectra whose earlier constructions were both more difficult and less precise.Working in the module category M R , we show that the category of finite cell modules over an S-algebra R gives rise to an associated algebraic K-theory spectrum KR. Specialized to the Eilenberg-Mac Lane spectra of discrete rings, this recovers Quillen's algebraic K-theory of rings. Specialized to suspension spectra Σ ∞ (ΩX) + of loop spaces, it recovers Waldhausen's algebraic K-theory of spaces.Replacing our ground ring S by a commutative S-algebra R, we define Ralgebras and commutative R-algebras in terms of maps A ∧ R A −→ A, and we show that the categories of R-modules, R-algebras, and commutative R-algebras are all topological model categories. We use the model structures to study Bousfield localizations of R-modules and R-algebras. In particular, we prove that KO and KU are commutative ko and ku-algebras and therefore commutative S-algebras.We define the topological Hochschild homology R-module T HH R (A; M ) of A with coefficients in an (A, A)-bimodule M and give spectral sequences for the calculation of its homotopy and homology groups. Again, classical Hochschild homology and cohomology groups are obtained by specializing the constructions to Eilenberg-Mac Lane spectra and passing to homotopy groups. iv

Working in the category T of based spaces, we give the basic theory of diagram spaces and diagram spectra. These are functorsD→T for a suitable small topological categoryD. WhenD is symmetric monoidal, there is a smash product that gives the category of D‐spaces a symmetric monoidal structure. Examples include prespectra, as defined classically, symmetric spectra, as defined by Jeff Smith, orthogonal spectra, a coordinate‐free analogue of symmetric spectra with symmetric groups replaced by orthogonal groups in the domain category, Γ‐spaces, as defined by Graeme Segal, W‐spaces, an analogue of Γ‐spaces with finite sets replaced by finite CW complexes in the domain category. We construct and compare model structures on these categories. With the caveat that Γ‐spaces are always connective, these categories, and their simplicial analogues, are Quillen equivalent and their associated homotopy categories are equivalent to the classical stable homotopy category. Monoids in these categories are (strict) ring spectra. Often the subcategories of ring spectra, module spectra over a ring spectrum, and commutative ring spectra are also model categories. When this holds, the respective categories of ring and module spectra are Quillen equivalent and thus have equivalent homotopy categories. This allows interchangeable use of these categories in applications. 2000Mathematics Subject Classification: primary 55P42; secondary 18A25, 18E30, 55U35.

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Summary Autophagy is a fundamental biological process of the eukaryotic cell contributing to diverse cellular and physiological functions including cell-autonomous defense against intracellular pathogens. Here we screened the Rab family of membrane trafficking regulators for effects on autophagic elimination of Mycobacterium tuberculosis var. bovis BCG and found that Rab8b and its downstream interacting partner, innate immunity regulator TBK-1, are required for autophagic elimination of mycobacteria in macrophages. TBK-1 was necessary for autophagic maturation. TBK-1 coordinated assembly and function of the autophagic machinery and phosphorylated the autophagic adaptor p62 (sequestosome 1) on Ser-403, a residue essential for its role in autophagic clearance. A key pro-inflammatory cytokine, IL-1β, induced autophagy leading to autophagic killing of mycobacteria in macrophages and this IL-1β activity was dependent on TBK-1. Thus, TBK-1 is a key regulator of immunological autophagy and is responsible for the maturation of autophagosomes into lytic bactericidal organelles.

Autophagy is a cell biological pathway affecting immune responses. In vitro, autophagy acts as a cell-autonomous defense against Mycobacterium tuberculosis, but its role in vivo is unknown. Here we show that autophagy plays a dual role against tuberculosis: antibacterial and anti-inflammatory. M. tuberculosis infection of Atg5 fl/fl LysM-Cre + mice relative to autophagy-proficient littermates resulted in increased bacillary burden and excessive pulmonary inflammation characterized by neutrophil infiltration and IL-17 response with increased IL-1α levels. Macrophages from uninfected Atg5 fl/fl LysM-Cre + mice displayed a cell-autonomous IL-1α hypersecretion phenotype, whereas T cells showed propensity toward IL-17 polarization during nonspecific activation or upon restimulation with mycobacterial antigens. Thus, autophagy acts in vivo by suppressing both M. tuberculosis growth and damaging inflammation.utophagy is a fundamental cell biological process (1) with impact on aging, development, cancer, neurodegeneration, myodegeneration, metabolic disorders (2), idiopathic inflammatory diseases, and infection and immunity (3). Much of the physiological effects of autophagy are the result of degradative activities of autophagy (1), although biogenesis and secretory roles (4-6) of autophagy are beginning to be recognized (7). The execution of autophagy depends on factors collectively termed "Atg proteins," such as Atg5 (1) and Beclin 1 (Atg6) (8), whereas regulation of autophagy responds to various inputs via mammalian target of rapamycin (mTOR), including the presence of microbes (9), the TAB2/3-TAK1-IKK signaling axis (10), and processes downstream of pattern-recognition receptors and immune cytokine activation (3,(11)(12)(13).In the context of its immunological functions, autophagy acts in four principal ways (14). (i) Autophagy cooperates with conventional pattern-recognition receptors (PRRs), such as Toll-like receptors, RIG-I-like receptors (RLRs), and NOD-like receptors, and acts as both a regulator (11,12,15,16) and an effector of PRR signaling (17-19). (ii) Autophagy affects the presentation of cytosolic antigens in the context of MHC II molecules (20) in T-cell development, differentiation, polarization, and homeostasis (21,22). (iii) Most recently, autophagy has been shown to contribute to both the negative (6,7,(23)(24)(25) and positive (6, 7) regulation of unconventional secretion of the leaderless cytosolic proteins known as "alarmins," such as IL-1β and HMGB1. (iv) Autophagy can capture and eliminate intracellular microbes, including Mycobacterium tuberculosis (17, 26-29), which was one of the first two bacterial species (26, 30) to be recognized as targets for autophagic removal. This activity recently has been shown to depend on the recognition and capture of microbes by adaptors that represent a specialized subset of PRRs termed "sequestosome-like receptors" (SLRs) (31).M. tuberculosis is one of the first microbes recognized as being subject to elimination by immunological autophagy by murine and human...

SUMMARY Selective autophagy performs an array of tasks to maintain intracellular homeostasis, sterility, and organellar and cellular functionality. The fidelity of these processes depends on precise target recognition and limited activation of the autophagy apparatus in a localized fashion. Here we describe cooperation in such processes between the TRIM family and Galectin family of proteins. TRIMs, which are E3 ubiquitin ligases, displayed propensity to associate with Galectins. One specific TRIM, TRIM16, interacted with Galectin-3 in an ULK1-dependent manner. TRIM16, through integration of Galectin- and ubiquitin-based processes, coordinated recognition of membrane damage with mobilization of the core autophagy regulators ATG16L1, ULK1, and Beclin 1 in response to damaged endomembranes. TRIM16 affected mTOR, interacted with TFEB and influenced TFEB’s nuclear translocation. The cooperation between TRIM16 and Galectin-3 in targeting and activation of selective autophagy protects cells from lysosomal damage and Mycobacterium tuberculosis invasion.