Strategies for the determination of 3D structures of biological macromolecules using electron crystallography and single-particle electron microscopy utilize powerful tools for the averaging of information obtained from 2D projection images of structurally homogeneous specimens. In contrast, electron tomographic approaches have often been used to study the 3D structures of heterogeneous, one-of-a-kind objects such as whole cells where image-averaging strategies are not applicable. Complex entities such as cells and viruses, nevertheless, contain multiple copies of numerous macromolecules that can individually be subjected to 3D averaging. Here we present a complete framework for alignment, classification, and averaging of volumes derived by electron tomography that is computationally efficient and effectively accounts for the missing wedge that is inherent to limited-angle electron tomography. Modeling the missing data as a multiplying mask in reciprocal space we show that the effect of the missing wedge can be accounted for seamlessly in all alignment and classification operations. We solve the alignment problem using the convolution theorem in harmonic analysis, thus eliminating the need for approaches that require exhaustive angular search, and adopt an iterative approach to alignment and classification that does not require the use of external references. We demonstrate that our method can be successfully applied for 3D classification and averaging of phantom volumes as well as experimentally obtained tomograms of GroEL where the outcomes of the analysis can be quantitatively compared against the expected results.
The DNA triple helix consists of a third strand of nucleic acid lying in the major groove of an intact DNA duplex. The most stable triplexes form on polypurine:polypyrimidine sequences, and pyrimidine interruptions in the purine strand are destabilizing. Sequence stringency is imparted by specific Hoogsteen hydrogen bonds between third strand bases and the purine bases in the duplex. Appropriate base and sugar modifications of triple helix-forming oligonucleotides (TFOs) confer chromosome targeting activity in living cells. However, broad utilization of TFOs as gene targeting reagents in mammalian cells has been limited by the requirement for homopurine target sequences. Although there have been a number of base analogues described that appear to be promising as candidates for triplex target expansion, none has been examined in a biological system. We have employed a postsynthetic strategy to prepare a collection of TFOs with base analogues at a defined position. Following assessment of affinity for a triplex target with a single C:G inversion, TFOs with a second generation of analogues were synthesized. One of these, TFO-5a, with 2′-OMeguanidinylethyl-5-methylcytosine at the position corresponding to the C:G interruption in the target sequence, was further modified to confer bioactivity. The activity of this TFO, linked to psoralen, was measured in a mammalian cell line that was engineered by directed sequence conversion to carry a triplex target with a single C:G interruption. TFO-5a was active against this target and inactive against the corresponding target with an uninterrupted polypurine:polypyrimidine sequence.
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