Takeshi Tsukada

The Tryptophan Residue at the Active Site Tunnel Entrance of Trichoderma reesei Cellobiohydrolase Cel7A Is Important for Initiation of Degradation of Crystalline Cellulose

Background: Mutation of Trp-40 in the Cel7A cellobiohydrolase from Trichoderma reesei (TrCel7A) causes a loss of crystalline cellulose-degrading ability. Results: Mutant W40A showed reduced specific activity for crystalline cellulose and diffused the cellulose chain from the entrance of the active site tunnel. Conclusion: Trp-40 is essential for chain end loading to initiate processive hydrolysis of TrCel7A. Significance: The mechanisms of crystalline polysaccharide degradation are clarified. The glycoside hydrolase family 7 cellobiohydrolase Cel7A from Trichoderma reesei is one of the best studied cellulases with the ability to degrade highly crystalline cellulose. The catalytic domain and the cellulose-binding domain (CBD) are both necessary for full activity on crystalline substrates. Our previous high-speed atomic force microscopy studies showed that mutation of Trp-40 at the entrance of the catalytic tunnel drastically decreases the ability to degrade crystalline cellulose. Here, we examined the activities of the WT enzyme and mutant W40A (with and without the CBD) for various substrates. Evaluation and comparison of the specific activities of the enzymes (WT, W40A, and the corresponding catalytic subunits (WTcat and W40Acat)) adsorbed on crystalline cellulose indicated that Trp-40 is involved in recruiting individual substrate chains into the active site tunnel to initiate processive hydrolysis. This was supported by molecular dynamics simulation study, i.e. the reducing end glucose unit was effectively loaded into the active site of WTcat, but not into that of W40Acat, when the simulation was started from subsite −7. However, when similar simulations were carried out starting from subsite −5, both enzymes held the substrate for 50 ns, indicating that the major difference between WTcat and W40Acat is the length of the free chain end of the substrate required to allow initiation of processive movements; this also reflects the difference between crystalline and amorphous celluloses. The CBD is important for enhancing the enzyme population on crystalline substrate, but it also decreases the specific activity of the adsorbed enzyme, possibly by attaching the enzyme to non-optimal places on the cellulose surface and/or hindering processive hydrolysis.

Crystal structure of intracellular family 1 β-glucosidase BGL1A from the basidiomycete Phanerochaete chrysosporium

The white‐rot fungus Phanerochaete chrysosporium has two intracellular β‐glucosidases (BGL1A and BGL1B) belonging to glycoside hydrolase (GH) family 1. BGL1B effectively hydrolyzes cellobiose and cellobionolactone, but BGL1A does not. We have determined the crystal structure of BGL1A in substrate‐free and gluconolactone complexed forms. The overall structure and the characteristic of subsite −1 (glycone site) were similar to those of other known GH1 enzymes. The loop regions covering on the (β/α)8 barrel was significantly deviated, and they form a unique subsite +1 (aglycone site) of BGL1A.

Untyped recursion schemes and infinite intersection types

A new framework for higher-order program verification has been recently proposed, in which higher-order functional programs are modelled as higher-order recursion schemes and then model-checked. As recursion schemes are essentially terms of the simply-typed lambda-calculus with recursion and tree constructors, however, it was not clear how the new framework applies to programs written in languages with more advanced type systems. To circumvent the limitation, this paper introduces an untyped version of recursion schemes and develops an infinite intersection type system that is equivalent to the model checking of untyped recursion schemes, so that the model checking can be reduced to type checking as in recent work by Kobayashi and Ong for typed recursion schemes. The type system is undecidable but we can obtain decidable subsets of the type system by restricting the shapes of intersection types, yielding a sound (but incomplete in general) model checking algorithm.

Two-level game semantics, intersection types, and recursion schemes

We introduce a new cartesian closed category of two-level arenas and innocent strategies to model intersection types that are refinements of simple types. Intuitively a property (respectively computation) on the upper level refines that on the lower level. We prove Subject Expansion--any lower-level computation is closely and canonically tracked by the upper-level computation that lies over it--which is a measure of the robustness of the two-level semantics. The game semantics of the type system is fully complete: every winning strategy is the denotation of some derivation. To demonstrate the relevance of the game model, we use it to construct new semantic proofs of non-trivial algorithmic results in higher-order model checking.

Nondeterminism in Game Semantics via Sheaves

Harmer and McCusker have developed a fully abstract game model for nondeterministic Idealised Algol and, at the same time, revealed difficulties in constructing game models for stateless nondeterministic languages and infinite nondeterminism. We propose a novel approach in which a strategy is not a set, but a tree, of plays, and develop a fully abstract game model for a nondeterministic stateless language. Mathematically such a strategy is formalised as a sheaf over an appropriate site of plays. We conclude with a study on the difficulties pointed out by Harmer and McCusker in terms of the structure of the coverage of the sites.

Exact flow analysis by higher-order model checking

We propose a novel control flow analysis for higher-order functional programs, based on a reduction to higher-order model checking. The distinguished features of our control flow analysis are that, unlike most of the control flow analyses like k -CFA, it is exact for simply-typed (λ )-calculus with recursion and finite base types, and that, unlike Mossins exact flow analysis, it is indeed runnable in practice, at least for small programs. Furthermore, under certain (arguably strong) assumptions, our control flow analysis runs in time cubic in the size of a program. We formalize the reduction of control flow analysis to higher-order model checking, prove the correctness, and report preliminary experiments.

Unsafe Order-2 Tree Languages Are Context-Sensitive

Higher-order grammars have been extensively studied in 1980’s and interests in them have revived recently in the context of higher-order model checking and program verification, where higherorder grammars are used as models of higher-order functional programs. A lot of theoretical questions remain open, however, for unsafe higherorder grammars (grammars without the so-called safety condition). In this paper, we show that any tree languages generated by order-2 unsafe grammars are context-sensitive. This also implies that any unsafe order-3 word languages are context-sensitive. The proof involves novel technique based on typed lambda-calculus, such as type-based grammar transformation.

Generalised species of rigid resource terms

This paper introduces a variant of the resource calculus, the rigid resource calculus, in which a permutation of elements in a bag is distinct from but isomorphic to the original bag. It is designed so that the Taylor expansion within it coincides with the interpretation by generalised species of Fiore et al., which generalises both Joyals combinatorial species and Girards normal functors, and which can be seen as a proof-relevant extension of the relational model. As an application, we prove the commutation between computing Böhm trees and (standard) Taylor expansions for a particular nondeterministic calculus.

Higher-Order Program Verification via HFL Model Checking

There are two kinds of higher-order extensions of model checking: HORS model checking and HFL model checking. Whilst the former has been applied to automated verification of higher-order functional programs, applications of the latter have not been well studied. In the present paper, we show that various verification problems for functional programs, including may/must-reachability, trace properties, and linear-time temporal properties (and their negations), can be naturally reduced to (extended) HFL model checking. The reductions yield a sound and complete logical characterization of those program properties. Compared with the previous approaches based on HORS model checking, our approach provides a more uniform, streamlined method for higher-order program verification.

Plays as Resource Terms via Non-idempotent Intersection Types

A program is interpreted as a collection of resource terms by the Taylor expansion, as a collection of plays by game semantics, and as a collection of types by a non-idempotent intersection type assignment system. This paper investigates the connection between these models and aims to show that they are essentially the same in a certain sense. Technically we study the relational interpretations of resource terms and of plays, which can be seen as non-idempotent intersection type assignment systems for resource terms and plays, respectively. We show that both relational interpretations are injective, have the same image, and respect composition. This result allows us to study a property of the game model by using the syntax of a resource calculus and vice versa.