Mutants only Partially Represent Characteristics of Calcium-ReleaseActivated Calcium Channel Gating

Calcium-release-activated calcium(CARC)channels are one of the major pathways of calcium entry in non-excitable cells.Despite a decade or two of research,its regulatory mechanism is not yet thoroughly understood.The slow progress is due to the complexity of its pores(i.e.,Orai)on one hand and the difficulty in capturing its regulatory complex on the other hand.As a result,possible gating mechanisms have often been speculated by exploring the structure and properties of constitutive open mutants.However,there is much debate about how they can truly reflect the gating of CRAC channels under physiological conditions.In the present study,we combined molecular dynamics simulations with free energy calculations to study three dOrai mutants(G170P,H206A,and P288A),and further calculated their current-voltage curves.Results show that these constructs adopt different approaches to maintain their conductive state.Meanwhile they have unique pore structures and distinctive rectification properties and ion selectivity for cations compared to wild-type pores.We conclude that although the mutants may partially capture the gating motion characteristics of wild-type pores,the information obtained from these mutants is likely not a true reflection of CRAC channel gating under physiological conditions.

On Self-dual 4-dimensional Pseudo-Riemannian Manifolds

For a 4-dimensional Riemannian manifold(M,g),Atiyah et al.in[Proc.Roy.Soc.London Ser.A,1978,362(1711):425-461]used the kernel of twistor operator D to construct a distribution V(D)on the dual bundle of the anti-self-dual spinor bundle on M.Now V(D)forms an almost complex structure on dual bundle.Moreover,they showed that this almost complex structure is integrable if and only if M is self-dual.In this paper,we extend the construction of V(D)to 4-dimensional pseudo-Riemannian manifolds of signature(2,2).And we give a new method to prove the curvature condition in the integrability condition of V(D).Using this new method,we study the integrability conditions and structure of V(D)when the signature of g is(2,2).

Conditional Kernel Covariance and Correlation

The conditional kernel correlation is proposed to measure the relationship between two random variables under covariates for multivariate data.Relying on the framework of reproducing kernel Hilbert spaces,we give the definitions of the conditional kernel covariance and conditional kernel correlation.We also provide their respective sample estimators and give the asymptotic properties,which help us construct a conditional independence test.According to the numerical results,the proposed test is more effective compared to the existing one under the considered scenarios.A real data is further analyzed to illustrate the efficacy of the proposed method.

Area-minimizing Cones over Stiefel Manifolds

We study the area-minimization property of the cones over Stiefel manifolds V_(m)(F^(n))(F=R,C or H)and their products,where the Stiefel manifolds are embedded into the unit sphere of Euclidean space in a standard way.We will show that these cones are areaminimizing if the dimension is at least 7,using the Curvature Criterion of[Mem.Amer.Math.Soc.,1991,91(446):vi+111 pp.].This extends the results of corresponding references,where the cones over products of Grassmann manifolds were considered.

Continuity of truncated Hardy-Littlewood maximal function

This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of the truncated Hardy-Littlewood maximal function when the truncated parameterγchanges,we obtain an equivalent condition of the continuity of the truncated Hardy-Littlewood maximal function.