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Anti-microRNA (miRNA) oligonucleotides (AMOs) with 2'-O-Methyl (2'OMe) residues are commonly used to study miRNA function and can achieve high potency, with low cytotoxicity. Not withstanding this, we demonstrate the sequence-dependent capacity of 2'OMe AMOs to inhibit Toll-like receptor (TLR) 7 and 8 sensing of immunostimulatory RNA, independent of their miRNA-targeting function. Through a screen of 29 AMOs targeting common miRNAs, we found a subset of sequences highly inhibitory to TLR7 sensing in mouse macrophages. Interspecies conservation of this inhibitory activity was confirmed on TLR7/8 activity in human peripheral blood mononuclear cells. Significantly, we identified a core motif governing the inhibitory activity of these AMOs, which is present in more than 50 AMOs targeted to human miRNAs in miRBaseV20. DNA/locked nucleic acids (LNA) AMOs synthesized with a phosphorothioate backbone also inhibited TLR7 sensing in a sequence-dependent manner, demonstrating that the off-target effects of AMOs are not restricted to 2'OMe modification. Taken together, our work establishes the potential for off-target effects of AMOs on TLR7/8 function, which should be taken into account in their therapeutic development and in vivo application.

In this paper we introduce new methods based upon integrating Lie symmetries for the construction of explicit fundamental solutions of multi-dimensional second order parabolic PDEs. We present applications to the problem of finding transition probability densities for multi-dimensional diffusions and to representation theory. Many explicit examples are given to illustrate the techniques. © 2011 Elsevier Inc.

In this paper we introduce new methods based upon integrating Lie symmetries for the construction of explicit fundamental solutions of multi-dimensional second order parabolic PDEs. We present applications to the problem of finding transition probability densities for multi-dimensional diffusions and to representation theory. Many explicit examples are given to illustrate the techniques. © 2011 Elsevier Inc.

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Lie group symmetry methods provide a powerful tool for the analysis of PDEs. Over the last thirty years, considerable progress has been made in the development of this field. In this article, we provide a brief introduction to the method developed by Lie for the systematic computation of symmetries, then move on to a survey of some of the more recent developments. Our focus is on the use of Lie symmetry methods to construct fundamental solutions of partial differential equations of parabolic type. We will show how recent work has uncovered an intriguing connection between Lie symmetry analysis and the theory of integral transforms. Fundamental solutions of families of PDEs which arise in various applications, can be obtained by exploiting this connection. The major applications we give will be in financial mathematics. We will illustrate our results with the problem of pricing a so called zero coupon bond, as well as giving some applications to option pricing. We also discuss some results on group invariant solutions and show how an important PDE in nilpotent harmonic analysis can be studied via its group invariant solutions.

Lie group symmetry methods provide a powerful tool for the analysis of PDEs. Over the last thirty years, considerable progress has been made in the development of this field. In this article, we provide a brief introduction to the method developed by Lie for the systematic computation of symmetries, then move on to a survey of some of the more recent developments. Our focus is on the use of Lie symmetry methods to construct fundamental solutions of partial differential equations of parabolic type. We will show how recent work has uncovered an intriguing connection between Lie symmetry analysis and the theory of integral transforms. Fundamental solutions of families of PDEs which arise in various applications, can be obtained by exploiting this connection. The major applications we give will be in financial mathematics. We will illustrate our results with the problem of pricing a so called zero coupon bond, as well as giving some applications to option pricing. We also discuss some results on group invariant solutions and show how an important PDE in nilpotent harmonic analysis can be studied via its group invariant solutions.