Magnus Jansson

High-level production of uniformly 15N-and 13C-enriched fusion proteins in Escherichia coli

SummaryAn approach to produce 13C-and 15N-enriched proteins is described. The concept is based on intracellular production of the recombinant proteins in Escherichia coli as fusions to an IgG-binding domain, Z, derived from staphylococcal protein A. The production method provides yields of 40–200 mg/l of isotope-enriched fusion proteins in defined minimal media. In addition, the Z fusion partner facilitates the first purification step by IgG affinity chromatography. The production system is applied to isotope enrichment of human insulin-like growth factor II (IGF-II), bovine pancreatic trypsin inhibitor (BPTI), and Z itself. High levels of protein production are achieved in shaker flasks using totally defined minimal medium supplemented with 13C6-glucose and (15NH4)2SO4 as the only carbon and nitrogen sources. Growth conditions were optimized to obtain high protein production levels and high levels of isotope incorporation, while minimizing 13C6-glucose usage. Incorporation levels of 13C and/or 15N isotopes in purified IGF-II, BPTI, and Z were confirmed using mass spectrometry and NMR spectroscopy. More than 99% of total isotope enrichment was obtained using a defined isotope-enriched minimal medium. The optimized systems provide reliable, high-level production of isotope-enriched fusion proteins. They can be used to produce 20–40 mg/l of properly folded Z and BPTI proteins. The production system of recombinant BPTI is state-of-the-art and provides the highest known yield of native refolded BPTI.

On Estimation of Covariance Matrices With Kronecker Product Structure

The estimation of signal covariance matrices is a crucial part of many signal processing algorithms. In some applications, the structure of the problem suggests that the underlying, true covariance matrix is the Kronecker product of two valid covariance matrices. Examples of such problems are channel modeling for multiple-input multiple-output (MIMO) communications and signal modeling of EEG data. In applications, it may also be that the Kronecker factors in turn can be assumed to possess additional, linear structure. The maximum-likelihood (ML) method for the associated estimation problem has been proposed previously. It is asymptotically efficient but has the drawback of requiring an iterative search for the maximum of the likelihood function. Two methods that are fast and noniterative are proposed in this paper. Both methods are shown to be asymptotically efficient. The first method is a noniterative variant of a well-known alternating maximization technique for the likelihood function. It performs on par with ML in simulations but has the drawback of not allowing for extra structure in addition to the Kronecker structure. The second method is based on covariance matching principles and does not suffer from this drawback. However, while the large sample performance is the same, it performs somewhat worse than the first estimator in small samples. In addition, the Cramer-Rao lower bound for the problem is derived in a compact form. The problem of estimating the Kronecker factors and the problem of detecting if the Kronecker structure is a good model for the covariance matrix of a set of samples are related. Therefore, the problem of detecting the dimensions of the Kronecker factors based on the minimum values of the criterion functions corresponding to the two proposed estimation methods is also treated in this work.

On Consistency of Subspace Methods for System Identification

Subspace methods for identification of linear time-invariant dynamical systems typically consist of two main steps. First, a so-called subspace estimate is constructed. This first step usually consists of estimating the range space of the extended observability matrix. Secondly, an estimate of system parametersis obtained, based on the subspace estimate. In this paper, the consistency of a large class of methods for estimating the extended observability matrix is analyzed. Persistence of excitation conditions on the input signal are given which guarantee consistent estimates for systems with only measurement noise. For systems with process noise, it is shown that a persistence of excitation condition on the input is not sufficient. More precisely, an example for which the subspace methods fail to give a consistent estimate of the transfer function is given. This failure occurs even if the input is persistently exciting of any order. It is also shown that this problem can be eliminated if stronger conditions on the input signal are imposed.

Analysis of the asymptotic properties of the MOESP type of subspace algorithms

The MOESP type of subspace algorithms are used for the identification of linear, discrete time, finite-dimensional state-space systems. They are based on the geometric structure of covariance matrices and exploit the properties of the state vector extensively. In this paper the asymptotic properties of the algorithms are examined. The main results include consistency and asymptotic normality for the estimates of the system matrices, under suitable assumptions on the noise sequence, the input process and the underlying true system.

A linear regression approach to state-space subspace system identification

Abstract Recently, state-space subspace system identification (4SID) has been suggested as an alternative to the more traditional prediction error system identification. The aim of this paper is to analyze the connections between these two different approaches to system identification. The conclusion is that 4SID can be viewed as a linear regression multistep-ahead prediction error method with certain rank constraints. This allows us to describe 4SID methods within the standard framework of system identification and linear regression estimation. For example, this observation is used to compare different cost-functions which occur rather implicitly in the ordinary framework of 4SID. From the cost-functions, estimates of the extended observability matrix are derived and related to previous work. Based on the estimates of the observability matrix, the asymptotic properties of two pole estimators, namely the shift invariance method and a weighted subspace fitting method, are analyzed. Expressions for the asymptotic variances of the pole estimation error are given. From these expressions, difficulties in choosing userspecified parameters are pointed out. Furthermore, it is found that a row-weighting in the subspace estimation step does not affect the pole estimation error asymptotically.

Subspace Identification and ARX Modeling

Abstract In this paper we present a new identification method that points at the close relationship between high order ARX modeling and subspace identification. A high order ARX model is utilized to obtain initial estimates of certain Markov parameters. These parameters are then used to restructure the data model used for subspace identification to facilitate the estimation of the state sequence. Based on the estimated state sequence, the system parameters are estimated by linear regression. The method is shown to be competitive to existing subspace methods by a simulation example. The method can also be used, without modification, on closed loop data in contrast to most previously published subspace identification methods.

Array interpolation and bias reduction

Interpolation (mapping) of data from a given antenna array onto the output of a virtual array of more suitable configuration is well known in array signal processing. This operation allows arrays of any geometry to be used with fast direction-of-arrival (DOA) estimators designed for linear arrays. Conditions for preserving DOA error variance under such mappings have been derived by several authors. However, in many cases, such as omnidirectional signal surveillance over multiple octaves, systematic mapping errors will dominate over noise effects and cause significant bias in the DOA estimates. To prevent mapping errors from unduly affecting the DOA estimates, this paper uses a geometrical interpretation of a Taylor series expansion of the DOA estimator criterion function to derive an alternative design of the mapping matrix. Verifying simulations show significant bias reduction in the DOA estimates compared with previous designs. The key feature of the proposed design is that it takes into account the orthogonality between the manifold mapping errors and certain gradients of the estimator criterion function. With the new design, mapping of narrowband signals between dissimilar array geometries over wide sectors and large frequency ranges becomes feasible.

Exploiting arrays with multiple invariances using MUSIC and MODE

This paper describes several new techniques for direction of arrival (DOA) estimation using arrays composed of multiple translated and uncalibrated subarrays. The new algorithms can be thought of as generalizations of the MUSIC, Root-MUSIC, and MODE techniques originally developed for fully calibrated arrays. The advantage of these new approaches is that the DOAs can be estimated using either a simple one-dimensional (1-D) search or by rooting a polynomial, as opposed to the multidimensional search required by multiple invariance (MI)-ESPRIT. When it can be applied, the proposed MI-MODE algorithm shares the statistical optimality of MI-ESPRIT. While MI-MUSIC and Root-MI-MUSIC are only optimal for uncorrelated sources, they perform better than a single invariance implementation of ESPRIT and are thus better suited for finding the initial conditions required by the MI-ESPRIT search.

Forward-only and forward-backward sample convariances — a comparative study

In some applications the covariance matrix of the observations enjoys a particular symmetry: it is not only symmetric with respect to its main diagonal but also with respect to the anti-diagonal. The standard forward-only sample covariance estimate does not impose this extra symmetry. In such cases one often uses the so-called forward-backward sample covariance estimate. In this paper, a direct comparative study of the relative accuracy of the two sample covariance estimates is performed. An explicit expression for the difference between the estimation error covariance matrices of the two sample covariance estimates is given. This expression shows quantitatively the gain of using the forward-backward estimate compared to the forward-only estimate. The presented results are also useful in the analysis of estimators based on either of the two sample covariances. As an example, spatial power estimation by means of the Capon method is considered. Using a second-order approximation, it is shown that Capon based on the forward-only sample covariance (F-Capon) underestimates the power spectrum, and also that the bias for Capon based on the forward-backward sample covariance is half that of F-Capon.

The Insulin-like Growth Factor (IGF)Binding Protein 1 Binding Epitope on IGF-I Probed by Heteronuclear NMR Spectroscopy and Mutational Analysis*

NMR spectroscopy studies and biosensor interaction analysis of native and site-directed mutants of insulin-like growth factor I (IGF-I) was applied to identify the involvement of individual residues in IGF-I binding to IGF-binding protein 1 (IGFBP-1). Backbone NMR chemical shifts were found to be affected by IGFBP-1 binding in the following residues: Pro2, Glu3, Cys6, Gly7, Gly19, Pro28–Gly30, Gly32, Arg36, Arg37, Gln40–Gly42, Pro63, Lys65, Pro66, and Lys68–Ala70. Three IGF-I arginine side chains were identified by NMR to participate in IGFBP-1 binding. All IGF-I arginine residues were replaced by alanines, using site-directed mutagenesis, in four single substituted variants, IGF-I(R21A), IGF-I(R50A), IGF-I(R55A), and IGF-I(R56A), and one double replacement mutant, IGF-I(R36A/R37A). Biosensor interaction analysis binding studies demonstrate the involvement of Arg36-Arg37 and Arg50 in IGFBP-1 binding, while experiments with the IGF-I receptor implicate Arg21, Arg36-Arg37, and Arg56 as part of the receptor binding epitope. These overlapping binding surfaces explain why IGF-I receptor and IGFBP-1 binding to IGF-I is competitive. The C terminus of free, but not IGFBP-1-bound, IGF-I is found to exist in two distinct, NMR-detectable conformations at 30 °C. One possible explanation for this structural heterogeneity could be cis-trans isomerization of the Cys6–Cys48 disulfide bond.