Systematic derivation of partition functions for ligand binding to two-dimensional lattices

The Ising problem consists in finding the analytical solution of the partition function of a lattice once the interaction geometry among its elements is specified. No general analytical solution is available for this problem, except for the one-dimensional case. Using site-specific thermodynamics, it is shown that the partition function for ligand binding to a two-dimensional lattice can be obtained from those of one-dimensional lattices with known solution. The complexity of the lattice is reduced recursively by application of a contact transformation that involves a relatively small number of steps. The transformation implemented in a computer code solves the partition function of the lattice by operating on the connectivity matrix of the graph associated with it. This provides a powerful new approach to the Ising problem, and enables a systematic analysis of two-dimensional lattices that model many biologically relevant phenomena. Application of this approach to finite two-dimensional lattices with positive cooperativity indicates that the binding capacity per site diverges as Na (N = number of sites in the lattice) and experiences a phase-transition-like discontinuity in the thermodynamic limit N → ∞. The zeroes of the partition function tend to distribute on a slightly distorted unit circle in complex plane and approach the positive real axis already for a 5×5 square lattice. When the lattice has negative cooperativity, its properties mimic those of a system composed of two classes of independent sites with the apparent population of low-affinity binding sites increasing with the size of the lattice, thereby accounting for a phenomenon encountered in many ligand-receptor interactions.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

The dual functions of Fas ligand in the regulation of peripheral CD8+ and CD4+ T cells

Although Fas ligand (FasL) is well characterized for its capacity to deliver a death signal through its receptor Fas, recent work demonstrates that FasL also can receive signals facilitating antigen (Ag)-specific proliferation of CD8+ T cells. The fact that the gld mutation differentially influences the proliferative capacity of CD8+ and CD4+ T cells presented the intriguing possibility that a single molecule may play opposing roles in these two subpopulations. The present study focuses on how these positive and negative regulatory roles are balanced. We show that naive CD4+ T cells are responsive to FasL-mediated costimulation on encounter with Ag when Fas-mediated death is prevented. Thus, the machinery responsible for transducing the FasL positive reverse signal operates in both CD4+ and CD8+ T cells. Instead, differential control of FasL expression distinguishes the role of FasL in these two T cell subpopulations. FasL costimulation occurs immediately on T cell receptor ligation and correlates with the up-regulation of FasL expression on CD8+ and naive CD4+ T cells, both of which are sensitive to the FasL costimulatory signal. Conversely, FasL-initiated death occurs late in an immune response when high levels of FasL expression are maintained on CD4+ T cells that are sensitive to Fas-mediated death, but not on CD8+ T cells that are relatively insensitive to this signal. This careful orchestration of FasL expression during times of susceptibility to costimulation and conversely, to death, endows FasL with the capacity to both positively and negatively regulate the peripheral T cell compartment.

Thyroid hormone receptor-associated proteins and general positive cofactors mediate thyroid hormone receptor function in the absence of the TATA box-binding protein-associated factors of TFIID

Coactivators previously implicated in ligand-dependent activation functions by thyroid hormone receptor (TR) include p300 and CREB-binding protein (CBP), the steroid receptor coactivator-1 (SRC-1)-related family of proteins, and the multicomponent TR-associated protein (TRAP) complex. Here we show that two positive cofactors (PC2 and PC4) derived from the upstream stimulatory activity (USA) cofactor fraction act synergistically to mediate thyroid hormone (T3)-dependent activation either by TR or by a TR-TRAP complex in an in vitro system reconstituted with purified factors and DNA templates. Significantly, the TRAP-mediated enhancement of activation by TR does not require the TATA box-binding protein-associated factors of TFIID. Furthermore, neither the pleiotropic coactivators CBP and p300 nor members of the SRC-1 family were detected in either the TR-TRAP complex or the other components of the in vitro assay system. These results show that activation by TR at the level of naked DNA templates is enhanced by cooperative functions of the TRAP coactivators and the general coactivators PC2 and PC4, and they further indicate a potential functional redundancy between TRAPs and TATA box-binding protein-associated factors in TFIID. In conjunction with earlier studies on other nuclear receptor-interacting cofactors, the present study also suggests a multistep pathway, involving distinct sets of cofactors, for activation of hormone responsive genes.

Calcineurin and vacuolar-type H+-ATPase modulate macrophage effector functions

While effector molecules produced by activated macrophages (including nitric oxide, tumor necrosis factor α, interleukin 1, etc.) help to eliminate pathogens, high levels of these molecules can be deleterious to the host itself. Despite their importance, the mechanisms modulating macrophage effector functions are poorly understood. This work introduces two key negative regulators that control the levels and duration of macrophage cytokine production. Vacuolar-type H+-ATPase (V-ATPase) and calcineurin (Cn) constitutively act in normal macrophages to suppress expression of inflammatory cytokines in the absence of specific activation and to inhibit macrophage cytokine responses induced by bacterial lipopolysaccharide (V-ATPase), interferon γ (V-ATPase and Cn), and calcium (Ca2+) flux (Cn). Cn and V-ATPase modulate effector gene expression at the mRNA level by inhibiting transcription factor NF-κB. This negative regulation by Cn is opposite to its crucial positive role in T cells, where it activates NFAT transcription factor(s) leading to expression of interleukin 2, tumor necrosis factor α, and other cytokine genes. The negative effects of V-ATPase and Cn on NF-κB-dependent gene expression are not limited to the macrophage lineage, as similar effects have been seen with a murine fibroblast cell line and with primary astrocytes.

Lagging strand replication of rolling-circle plasmids: Specific recognition of the ssoA-type origins in different gram-positive bacteria

Many bacterial plasmids replicate by a rolling-circle mechanism that involves the generation of single-stranded DNA (ssDNA) intermediates. Replication of the lagging strand of such plasmids initiates from their single strand origin (sso). Many different types of ssos have been identified. One group of ssos, termed ssoA, which have conserved sequence and structural features, function efficiently only in their natural hosts in vivo. To study the host specificity of sso sequences, we have analyzed the functions of two closely related ssoAs belonging to the staphylococcal plasmid pE194 and the streptococcal plasmid pLS1 in Staphylococcus aureus. The pLS1 ssoA functioned poorly in vivo in S. aureus as evidenced by accumulation of high levels of ssDNA but supported efficient replication in vitro in staphylococcal extracts. These results suggest that one or more host factors that are present in sufficient quantities in S. aureus cell-free extracts may be limiting in vivo. Mapping of the initiation points of lagging strand synthesis in vivo and in vitro showed that DNA synthesis initiates from specific sites within the pLS1 ssoA. These results demonstrate that specific initiation of replication can occur from the pLS1 ssoA in S. aureus although it plays a minimal role in lagging strand synthesis in vivo. Therefore, the poor functionality of the pLS1 in vivo in a nonnative host is caused by the low efficiency rather than a lack of specificity of the initiation process. We also have identified ssDNA promoters and mapped the primer RNAs synthesized by the S. aureus and Bacillus subtilis RNA polymerases from the pE194 and pLS1 ssoAs. The S. aureus RNA polymerase bound more efficiently to the native pE194 ssoA as compared with the pLS1 ssoA, suggesting that the strength of RNA polymerase–ssoA interaction may play a major role in the functionality of the ssoA sequences in Gram-positive bacteria.

The PTEN/MMAC1 tumor suppressor phosphatase functions as a negative regulator of the phosphoinositide 3-kinase/Akt pathway

The PTEN/MMAC1 phosphatase is a tumor suppressor gene implicated in a wide range of human cancers. Here we provide biochemical and functional evidence that PTEN/MMAC1 acts a negative regulator of the phosphoinositide 3-kinase (PI3-kinase)/Akt pathway. PTEN/MMAC1 impairs activation of endogenous Akt in cells and inhibits phosphorylation of 4E-BP1, a downstream target of the PI3-kinase/Akt pathway involved in protein translation, whereas a catalytically inactive, dominant negative PTEN/MMAC1 mutant enhances 4E-BP1 phosphorylation. In addition, PTEN/MMAC1 represses gene expression in a manner that is rescued by Akt but not PI3-kinase. Finally, higher levels of Akt activation are observed in human prostate cancer cell lines and xenografts lacking PTEN/MMAC1 expression when compared with PTEN/MMAC1-positive prostate tumors or normal prostate tissue. Because constitutive activation of either PI3-kinase or Akt is known to induce cellular transformation, an increase in the activation of this pathway caused by mutations in PTEN/MMAC1 provides a potential mechanism for its tumor suppressor function.

Two forms of replication initiator protein: Positive and negative controls

The pir gene of plasmid R6K encodes the protein, π, a replication and transcription factor. Two translational options for the pir gene give rise to two forms of π protein: a 35.0-kDa form (π35.0) and a shortened 30.5-kDa form (π30.5). Although both proteins bind to a series of 22-bp direct repeats essential for plasmid R6K replication, only π35.0 can bind to a site in the (A⋅T)-rich segment of its γ ori and activate the γ ori in vivo and in vitro. However, unlike π35.0, π30.5can inhibit in vivo and in vitro replication (activated by π35.0). We propose that the two forms of π might have distinct functions in replication. We show that although both forms of π produce dimers, the nature of these dimers is not identical. The N-terminal 37 amino acid residues appear to control the formation of the more stable π35.0 dimers, whereas another, apparently weaker interface holds together dimers of π30.5. We speculate that the leucine zipper-like motif, absent in π30.5, controls very specific functions of π protein.

Zeta functions and Eisenstein series on classical groups

We construct an Euler product from the Hecke eigenvalues of an automorphic form on a classical group and prove its analytic continuation to the whole complex plane when the group is a unitary group over a CM field and the eigenform is holomorphic. We also prove analytic continuation of an Eisenstein series on another unitary group, containing the group just mentioned defined with such an eigenform. As an application of our methods, we prove an explicit class number formula for a totally definite hermitian form over a CM field.

Positive regulation of general transcription factor SIII by a tailed ubiquitin homolog.

General transcription factor SIII, a heterotrimer composed of 110-kDa (p110), 18-kDa (p18), and 15-kDa (p15) subunits, increases the catalytic rate of transcribing RNA polymerase II by suppressing transient pausing by polymerase at multiple sites on DNA templates. Here we report molecular cloning and biochemical characterization of the SIII p18 subunit, which is found to be a member of the ubiquitin homology (UbH) gene family and functions as a positive regulatory subunit of SIII. p18 is a 118-amino acid protein composed of an 84-residue N-terminal UbH domain fused to a 34-residue C-terminal tail. Mechanistic studies indicate that p18 activates SIII transcriptional activity above a basal level inherent in the SIII p110 and p15 subunits. Taken together, these findings establish a role for p18 in regulating the activity of the RNA polymerase II elongation complex, and they bring to light a function for a UbH domain protein in transcriptional regulation.