Scaling and Scale Breaking in Polyelectrolyte

We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy with the chain-length divided by the temperature. This scaling is broken at low temperatures by the ultraviolet divergence of the Coulomb potential. By introducing a renormalization of the strength of the nearest- neighbour interaction the scaling is restored, making possible an efficient blocking method for emulating very large polyelectrolytes using small systems. The high temperature behaviour is well reproduced by the analytical high-$T$ expansions even for fairly low temperatures and system sizes. In addition, results from low-$T$ expansions, where the coefficients have been computed numerically, are presented. These results approximate well the corresponding Monte Carlo results at realistic temperatures. A corresponding analysis of screened chains is performed. The situation here is complicated by the appearance of an additional parameter, the screening length. A window is found in parameter space, where scaling holds for the end-to-end distance. This window corresponds to situations where the range of the potential interpolates between the bond length and the size of the chain. This scaling behaviour, which is verified by Monte Carlo results, is consistent with Flory scaling. Also for the screened chain a blocking approach can be devised, that performs well for low temperatures, whereas the low-$T$ expansion is inaccurate at realistic temperatures.Comment: 18 pages, latex, 6 figure

Titrating Polyelectrolytes - Variational Calculations and Monte Carlo Simulations

Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. The Coulomb interactions are emulated by harmonic repulsive forces, the force constants being used as variational parameters to minimize the free energy. For the titrating charges, a mean field approach is used. The accuracy is tested against Monte Carlo data for up to 1000 monomers. For an unscreened chain, excellent agreement is obtained for the end-to-end distance and the apparent dissociation constant. With screening, the thermodynamical properties are invariably well described, although the structural agreement deteriorates. A very simple rigid-rod approximation is also considered, giving surprisingly good results for certain properties.Comment: 22 pages, PostScript, 9 figure

Simultaneous Visualization of Both Signaling Cascade Activity and End-Point Gene Expression in Single Cells

We have developed an approach for simultaneous detection of individual endogenous protein modifications and mRNA molecules in single cells in situ. For this purpose we combined two methods previously developed in our lab: in situ proximity ligation assay for the detection of individual protein interactions and -modifications and in situ detection of single mRNA molecules using padlock probes. As proof-of-principle, we demonstrated the utility of the method for simultaneous detection of phosphorylated PDGFRβ and DUSP6/MKP-3 mRNA molecules in individual human fibroblasts upon PDGF-BB stimulation. Further we applied drugs disrupting the PDGFRβ signaling pathway at various sites to show that this combined method can concurrently monitor the molecular effect of the drugs, i.e. inhibition of downstream signaling from the targeted node in the signaling pathway. Due to its ability to detect different types of molecules in single cells in situ the method presented here can contribute to a deeper understanding of cell-to-cell variations and can be applied to e.g. pinpoint effector sites of drugs in a signaling pathway

A Variational Approach for Minimizing Lennard-Jones Energies

A variational method for computing conformational properties of molecules with Lennard-Jones potentials for the monomer-monomer interactions is presented. The approach is tailored to deal with angular degrees of freedom, {\it rotors}, and consists in the iterative solution of a set of deterministic equations with annealing in temperature. The singular short-distance behaviour of the Lennard-Jones potential is adiabatically switched on in order to obtain stable convergence. As testbeds for the approach two distinct ensembles of molecules are used, characterized by a roughly dense-packed ore a more elongated ground state. For the latter, problems are generated from natural frequencies of occurrence of amino acids and phenomenologically determined potential parameters; they seem to represent less disorder than was previously assumed in synthetic protein studies. For the dense-packed problems in particular, the variational algorithm clearly outperforms a gradient descent method in terms of minimal energies. Although it cannot compete with a careful simulating annealing algorithm, the variational approach requires only a tiny fraction of the computer time. Issues and results when applying the method to polyelectrolytes at a finite temperature are also briefly discussed.Comment: 14 pages, uuencoded compressed postscript fil

VEGF receptor 2/-3 heterodimers detected in situ by proximity ligation on angiogenic sprouts

Peer reviewe

E-cadherin can limit the transforming properties of activating β-catenin mutations

Wnt pathway deregulation is a common characteristic of many cancers. But only Colorectal Cancer predominantly harbours mutations in APC, whereas other cancer types (hepatocellular carcinoma, solid pseudopapillary tumours of pancreas) have activating mutations in β-catenin (CTNNB1). We have compared the dynamics and the potency of β-catenin mutations in vivo. Within the murine small intestine (SI), an activating mutation of β-catenin took much longer to achieve a Wnt deregulation and acquire a crypt-progenitor-cell (CPC) phenotype than Apc or Gsk3 loss. Within the colon, a single activating mutation of β-catenin was unable to drive Wnt deregulation or induce the CPC phenotype. This ability of β-catenin mutation to differentially transform the SI versus the colon correlated with significantly higher expression of the β-catenin binding partner E-cadherin. This increased expression is associated with a higher number of E-cadherin:β-catenin complexes at the membrane. Reduction of E-cadherin synergised with an activating mutation of β-catenin so there was now a rapid CPC phenotype within the colon and SI. Thus there is a threshold of β-catenin that is required to drive transformation and E-cadherin can act as a buffer to prevent β-catenin accumulation

Functional loss of IKBE leads to NF-KB deregulation in aggressive chronic lymphocytic leukemia

NF-?B is constitutively activated in chronic lymphocytic leukemia (CLL); however, the implicated molecular mechanisms remain largely unknown. Thus, we performed targeted deep sequencing of 18 core complex genes within the NF-?B pathway in a discovery and validation CLL cohort totaling 315 cases. The most frequently mutated gene was NFKBIE (21/315 cases; 7%), which encodes I?B?, a negative regulator of NF-?B in normal B cells. Strikingly, 13 of these cases carried an identical 4-bp frameshift deletion, resulting in a truncated protein. Screening of an additional 377 CLL cases revealed that NFKBIE aberrations predominated in poor-prognostic patients and were associated with inferior outcome. Minor subclones and/or clonal evolution were also observed, thus potentially linking this recurrent event to disease progression. Compared with wild-type patients, NFKBIE-deleted cases showed reduced I?B? protein levels and decreased p65 inhibition, along with increased phosphorylation and nuclear translocation of p65. Considering the central role of B cell receptor (BcR) signaling in CLL pathobiology, it is notable that I?B? loss was enriched in aggressive cases with distinctive stereotyped BcR, likely contributing to their poor prognosis, and leading to an altered response to BcR inhibitors. Because NFKBIE deletions were observed in several other B cell lymphomas, our findings suggest a novel common mechanism of NF-?B deregulation during lymphomagenesis. <br/

WRAP53 Is Essential for Cajal Body Formation and for Targeting the Survival of Motor Neuron Complex to Cajal Bodies

The WRAP53 protein regulates the formation and maintenance of Cajal bodies (nuclear sub-organelles), as well as directs the recruitment of nuclear factors to Cajal bodies

Functional loss of IκBε leads to NF-κB deregulation in aggressive chronic lymphocytic leukemia

NF-κB is constitutively activated in chronic lymphocytic leukemia (CLL); however, the implicated molecular mechanisms remain largely unknown. Thus, we performed targeted deep sequencing of 18 core complex genes within the NF-κB pathway in a discovery and validation CLL cohort totaling 315 cases. The most frequently mutated gene was NFKBIE (21/315 cases; 7%), which encodes IκBε, a negative regulator of NF-κB in normal B cells. Strikingly, 13 of these cases carried an identical 4-bp frameshift deletion, resulting in a truncated protein. Screening of an additional 377 CLL cases revealed that NFKBIE aberrations predominated in poor-prognostic patients and were associated with inferior outcome. Minor subclones and/or clonal evolution were also observed, thus potentially linking this recurrent event to disease progression. Compared with wild-type patients, NFKBIE-deleted cases showed reduced IκBε protein levels and decreased p65 inhibition, along with increased phosphorylation and nuclear translocation of p65. Considering the central role of B cell receptor (BcR) signaling in CLL pathobiology, it is notable that IκBε loss was enriched in aggressive cases with distinctive stereotyped BcR, likely contributing to their poor prognosis, and leading to an altered response to BcR inhibitors. Because NFKBIE deletions were observed in several other B cell lymphomas, our findings suggest a novel common mechanism of NF-κB deregulation during lymphomagenesis