Resource transition systems and full abstraction for linear higher-order effectful programs

We investigate program equivalence for linear higher-order (sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear \u3b3-calculus with explicit copying and algebraic effects \ue0 la Plotkin and Power. Such a calculus makes explicit the interaction between copying and linearity, which are intensional aspects of computation, with effects, which are, instead, extensional. We review some of the notions of equivalences for linear calculi proposed in the literature and show their limitations when applied to effectful calculi where copying is a first-class citizen. We then introduce resource transition systems, namely transition systems whose states are built over tuples of programs representing the available resources, as an operational semantics accounting for both intensional and extensional interactive behaviours of programs. Our main result is a sound and complete characterization of contextual equivalence as trace equivalence defined on top of resource transition systems

Inactivation of TRPM2 channels by extracellular divalent copper

Cu2+ is an essential metal ion that plays a critical role in the regulation of a number of ion channels and receptors in addition to acting as a cofactor in a variety of enzymes. Here, we showed that human melastatin transient receptor potential 2 (hTRPM2) channel is sensitive to inhibition by extracellular Cu2+. Cu2 + at concentrations as low as 3 μM inhibited the hTRPM2 channel completely and irreversibly upon washing or using Cu2+ chelators, suggesting channel inactivation. The Cu2+-induced inactivation was similar when the channels conducted inward or outward currents, indicating the permeating ions had little effect on Cu2+-induced inactivation. Furthermore, Cu2+ had no effect on singe channel conductance. Alanine substitution by site-directed mutagenesis of His995 in the pore-forming region strongly attenuated Cu2+-induced channel inactivation, and mutation of several other pore residues to alanine altered the kinetics of channel inactivation by Cu2+. In addition, while introduction of the P1018L mutation is known to result in channel inactivation, exposure to Cu2+ accelerated the inactivation of this mutant channel. In contrast with the hTRPM2, the mouse TRPM2 (mTRPM2) channel, which contains glutamine at the position equivalent to His995, was insensitive to Cu2+. Replacement of His995 with glutamine in the hTRPM2 conferred loss of Cu2+-induced channel inactivation. Taken together, these results suggest that Cu2+ inactivates the hTRPM2 channel by interacting with the outer pore region. Our results also indicate that the amino acid residue difference in this region gives rise to species-dependent effect by Cu2+ on the human and mouse TRPM2 channels

Effectful applicative similarity for call-by-name lambda calculi

We introduce a notion of applicative similarity in which not terms but monadic values arising from the evaluation of effectful terms, can be compared. We prove this notion to be fully abstract whenever terms are evaluated in call-by-name order. This is the first full-abstraction result for such a generic, coinductive methodology for program equivalence

A biophysical approach to quantify skeletal stem cells trans-differentiation as a model for the study of osteoporosis

The stroma of human bone marrow contains a population of skeletal stem cells (hBM-MSC) which are common ancestors, among the others, of osteoblasts and adipocytes. It has been proposed that the imbalance between hBM-MSC osteogenesis and adipogenesis, which naturally accompanies bone marrow senescence, may contribute to the development of bone-associated diseases, like osteoporosis. The possibility to reproduce this mechanism in vitro has been demonstrated, providing a good model to disclose the details of the complex bone-fat generation homeostasis. Nevertheless, the lack of a simple approach to quantitatively assess the actual stage of a cellular population hindered the adoption of this in vitro model. In this work, the direct differentiation of hBM-MSCs towards a single (osteo or adipo) lineage was characterized using quantitative biophysical and biological approaches, together with the parallel process of trans-differentiation from one lineage to the other. The results confirm that the original plasticity of hBM-MSCs is maintained along the initial stages of the differentiation, showing that in vitro conversion of pre-osteoblasts into adipocytes and, vice versa, of pre-adipocytes into osteoblasts is extremely efficient, comparable with the direct differentiation. Moreover, a method based on digital holography is proposed, providing a quantitative indication of the phenotype stage along differentiation

On the Versatility of Open Logical Relations: Continuity, Automatic Differentiation, and a Containment Theorem

Logical relations are one among the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be immediately proved by means of logical relations, for instance program continuity and differentiability in higher-order languages extended with real-valued functions. Informally, the problem stems from the fact that these properties are naturally expressed on terms of non-ground type (or, equivalently, on open terms of base type), and there is no apparent good definition for a base case (i.e. for closed terms of ground types). To overcome this issue, we study a generalization of the concept of a logical relation, called open logical relation, and prove that it can be fruitfully applied in several contexts in which the property of interest is about expressions of first-order type. Our setting is a simply-typed-calculus enriched with real numbers and real-valued first-order functions from a given set, such as the one of continuous or differentiable functions. We first prove a containment theorem stating that for any collection of real-valued first-order functions including projection functions and closed under function composition, any well-typed term of first-order type denotes a function belonging to that collection. Then, we show by way of open logical relations the correctness of the core of a recently published algorithm for forward automatic differentiation. Finally, we define a refinement-based type system for local continuity in an extension of our calculus with conditionals, and prove the soundness of the type system using open logical relations

Molecular determinants of multiple effects of Ni2+ on NMDA receptor channels

The N-methyl-D-aspartate receptor (NR) is a ligand-gated channel with unique properties, such as requirements for two different agonists, glutamate and glycine, Mg-mediated voltage-dependence and high calcium permeability, as well as several recognition sites for endogenous and exogenous modulators. NRs form tetrameric channels containing two copies each of NR1 and NR2 (A, B, C or D) subunits, of which the commonest are NR2A and NR2B. The transition metal nickel (Ni) affects the NR channel activity in a voltage-dependent (Mg-like) manner, but also causes enhancement of activity of NR2B-containing channels and voltage-independent inhibition of those containing NR2A. This work was aimed to identify the critical residues for Ni interaction on the NR2A and NR2B subunit by expressing wild-type and mutated NR1a-NR2A and NR1a-NR2B receptors in either HEK293 cells or Xenopus laevis oocytes and measuring the response to saturating doses of agonists. The voltage-dependent block was similar in the two channel types, had an apparent IC50 between 40 and 60 \ub5M at -60 mV, and was completely abolished by the single mutation N616G in NR2B subunit, a residue located in the narrow constriction of the channel (N+1 site). This mutation also enhanced the facilitation and unmasked a voltage-independent inhibition with IC50 > 300 \ub5M. The voltage-independent inhibition was more prominent in NR1a-NR2A channels with IC50 close to 80 \ub5M. When NR2 subunits deleted for their entire amino terminal domain (ATD) were expressed with wild-type NR1a subunit, voltage-independent inhibition was not modified, but, in NR1a-NR2B channels, the potentiation effect was abolished. In the latter channels, potentiation of the current was drastically reduced also by H127A, D101A, D104A point mutations and by the double mutation H127AD101A, all located in lobe I of NR2B ATD, and to a lesser extent by the point mutation T233A located in lobe II of NR2B ATD, suggesting that the interaction site that causes potentiation shares common determinants with the Zn and ifenprodil binding sites. In contrast, as the binding site responsible for voltage-independent block of NR2A-containing channels is not located in the ATD, we postulate the existence of an additional divalent cation binding site in the M3-M4 extracellular loop. Indeed, the point mutation H801A in the NR2A subunit caused an important reduction of the block, with a 8-time increase in IC50. The block was also partially decreased by H705A and H709A mutations in the same region of NR1a. This additional binding site can be responsible for specific heavy metal interaction with NR channels

Histidines are responsible for Zinc potentiation of the current in KDC1 carrot channels

Unlike all plant inward-rectifying potassium channels, the carrot channel KDC1 has two histidine pairs (H161,H162) in the S3-S4 and (H224,H225) in the S5-S6 linkers. When coinjected with KAT1 in Xenopus oocytes, KDC1 participates in the formation of heteromultimeric KDC1:KAT1 channels and the ionic current is potentiated by extracellular Zn2+. To investigate the potential interactions between KDC1 and zinc, a KDC1-KAT1 dimer was constructed. The dimeric and heteromeric channels displayed similar characteristics and the same sensitivity to zinc and other metals; this result suggests that zinc binding is mediated by residues in a single channel subunit. The KDC1:KAT1 currents were also potentiated by external Pb2+ and Cd2+ and inhibited by Ni2+. To investigate further the role of KDC1-histidines, these amino acids were mutated into alanines. The single mutations H225A, H161A, and H162A did not affect the response of the heteromeric channels to zinc. Conversely, the single mutant H224A and the double mutants (H224A,H225A) and (H161A,H162A) abolished zinc potentiation, but not that induced by Pb2+ or Cd2+. These results suggest that Zn2+ potentiation cannot be ascribed to simple electrostatic interactions between zinc and channel residues and that histidine 224 is crucial for zinc but not for lead potentiation of the current