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  • 1. Cheng, Kimberley
    et al.
    Koeck, Philip J. B.
    Södertörn University, School of Life Sciences. Karolinska Institutet.
    Elmlund, Hans
    Idakieva, Krassimira
    Parvanova, Katja
    Schwarz, Heinz
    Ternström, Tomas
    Hebert, Hans
    Rapana thomasiana hemocyanin (RtH): Comparison of the two isoforms, RtH1 and RtH2, at 19 angstrom 16 angstrom resolution2006In: Micron, ISSN 0968-4328, E-ISSN 1878-4291, Vol. 37, no 6, p. 566-576Article in journal (Refereed)
    Abstract [en]

    Three-dimensional (3D) reconstructions of the two 8.4 MDa Rapana thomasiana hemocyanin isoforms, RtH1 and RtH2, have been obtained by cryoelectron microscopy of molecules embedded in vitreous ice and single particle image processing. The final 3D structures of the RtH1 and RtH2 didecamers at 19 angstrom and 16 angstrom resolution, respectively, are very similar to earlier reconstructions of gastropodan hemocyanins, revealing structural features such as the obliquely oriented subunits, the five- and two-fold symmetrical axes. Three new interactions are defined; two of them connecting the arch and the wall while the third is formed between the collar and the wall. The collar-wall connection and one of the arch-wall connections are positioned between two individual subunit dimers, while the second arch-wall connection is located between two subunits within the subunit dimer. All three interactions establish connections to the first tier of the wall. Furthermore, for each interaction we have allocated two first tier functional units most likely involved in forming the connections.

  • 2.
    Koeck, Philip J. B.
    Södertörn University, School of Chemistry, Biology, Geography and Environmental Science. Karolinska Institute.
    Missing data in image and signal processing: The case of binary objects2004In: Optik (Stuttgart), ISSN 0030-4026, E-ISSN 1618-1336, Vol. 115, no 10, p. 459-472Article in journal (Refereed)
    Abstract [en]

    I investigated which portions of the Fourier transform of binary signals, images and three-dimensional objects are necessary to correctly identify an object in the presence of noise. This is practically possible for very small binary data sets since the total number of possible objects is then very limited. There are for example 512 different binary images with 9 pixels. It is easy to see that this number soon becomes impractically large for bigger images or if one allows more than two possible pixel values. It turns out that even in the presence of large amounts of noise a relatively small portion of the Fourier transform is essential for deciding which of all possible binary objects the Fourier transform belongs to. These 'decision experiments' can be used as a standard for how well algorithms for retrieval of missing Fourier components perform. In another set of computer experiments I investigate the possibility of retrieving various missing Fourier components algorithmically. The main finding of this second set of computer experiments is that the simple retrieval algorithm (a limited form of 'projection onto convex sets') used falls very much short of what one might expect from the 'decision experiments'. I conclude with a discussion what this discrepancy might be due to and some suggestions how to improve the performance of retrieval algorithms for binary objects.

  • 3.
    Koeck, Philip J B
    Södertörn University, Avdelning Naturvetenskap. Karolinska Institutet.
    Quantization errors in averaged digitized data2001In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 81, no 2, p. 345-356Article in journal (Refereed)
    Abstract [en]

    Analytic expressions which describe average quantization errors in digitized data with additive noise are derived. The magnitude of this error depends on the noise present in the analog signal, the bin-size (the difference between neighboring quantization levels) and also the signal itself. An iterative process, which corrects for these residual quantization errors after averaging, is proposed and tested in simulations. Alternatively a method for avoiding quantization errors during digitization of signals which will later be averaged is suggested.

  • 4.
    Koeck, Philip J. B.
    et al.
    Södertörn University, School of Life Sciences. KTH / Karoliska institutet.
    Purhonen, P.
    Alvang, R.
    Grundberg, B.
    Hebert, H.
    Single particle refinement in electron crystallography: A pilot study2007In: Journal of Structural Biology, ISSN 1047-8477, E-ISSN 1095-8657, Vol. 160, no 3, p. 344-352Article in journal (Refereed)
    Abstract [en]

    Electron crystallography can be used to determine the structures of membrane proteins at near-atomic resolution in some cases. However, most electron crystallography projects remain at a resolution around 10 Å. This might be partly due to lack of flatness of many two-dimensional crystals. We have investigated this problem and suggest single particle processing of locally averaged unit cells to improve the quality and possibly the resolution of three-dimensional maps. Applying this method to the secondary transporter melibiose permease we have calculated a three-dimensional map that is clearer and easier to interpret than the map derived using purely electron-crystallographic methods.

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