This paper proposes a novel application of cohomology to protein structure analysis. Since proteins interact each other by forming transient protein complexes, their shape (e.g., shape complementarity) plays an import...This paper proposes a novel application of cohomology to protein structure analysis. Since proteins interact each other by forming transient protein complexes, their shape (e.g., shape complementarity) plays an important role in their functions. In our mathematical toy models, proteins are represented as a loop of triangles (2D model) or tetrahedra (3D model), where their interactions are defined as fusion of loops. The purpose of this paper is to describe the conditions for loop fusion using the language of cohomology. In particular, this paper uses cohomology to describe the conditions for “allosteric regulation”, which has been attracted attention in safer drug discovery. I hope that this paper will provide a new perspective on the mechanism of allosteric regulation. Advantages of the model include its topological nature. That is, we can deform the shape of loops by deforming the shape of triangles (or tetrahedra) as long as their folded structures are preserved. Another advantage is the simplicity of the “allosteric regulation” mechanism of the model. Furthermore, the effect of the “post-translational modification” can be understood as a resolution of singularities of a flow of triangles (or tetrahedra). No prior knowledge of either protein science, exterior calculus, or cohomology theory is required. The author hopes that this paper will facilitate the interaction between mathematics and protein science.展开更多
We propose a conjecture on the relative twist formula of l-adic sheaves,which can be viewed as a generalization of Kato-Saito’s conjecture.We verify this conjecture under some transversal assumptions.We also define a...We propose a conjecture on the relative twist formula of l-adic sheaves,which can be viewed as a generalization of Kato-Saito’s conjecture.We verify this conjecture under some transversal assumptions.We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward.A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.展开更多
文摘This paper proposes a novel application of cohomology to protein structure analysis. Since proteins interact each other by forming transient protein complexes, their shape (e.g., shape complementarity) plays an important role in their functions. In our mathematical toy models, proteins are represented as a loop of triangles (2D model) or tetrahedra (3D model), where their interactions are defined as fusion of loops. The purpose of this paper is to describe the conditions for loop fusion using the language of cohomology. In particular, this paper uses cohomology to describe the conditions for “allosteric regulation”, which has been attracted attention in safer drug discovery. I hope that this paper will provide a new perspective on the mechanism of allosteric regulation. Advantages of the model include its topological nature. That is, we can deform the shape of loops by deforming the shape of triangles (or tetrahedra) as long as their folded structures are preserved. Another advantage is the simplicity of the “allosteric regulation” mechanism of the model. Furthermore, the effect of the “post-translational modification” can be understood as a resolution of singularities of a flow of triangles (or tetrahedra). No prior knowledge of either protein science, exterior calculus, or cohomology theory is required. The author hopes that this paper will facilitate the interaction between mathematics and protein science.
文摘We propose a conjecture on the relative twist formula of l-adic sheaves,which can be viewed as a generalization of Kato-Saito’s conjecture.We verify this conjecture under some transversal assumptions.We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward.A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.
