Dextramabs: A Novel Format of Antibody-Drug Conjugates Featuring a Multivalent Polysaccharide Scaffold

Antibody-drug conjugates (ADCs) are multicomponent biomolecules that have emerged as a powerful tool for targeted tumor therapy. Combining specific binding of an immunoglobulin with toxic properties of a payload, they however often suffer from poor hydrophilicity when loaded with a high amount of toxins. To address these issues simultaneously, we developed dextramabs, a novel class of hybrid antibody-drug conjugates. In these architectures, the therapeutic antibody trastuzumab is equipped with a multivalent dextran polysaccharide that enables efficient loading with a potent toxin in a controllable fashion. Our modular chemoenzymatic approach provides an access to synthetic dextramabs bearing monomethyl auristatin as releasable cytotoxic cargo. They possess high drug-to-antibody ratios, remarkable hydrophilicity, and high toxicity in vitro.     

On the counting function of the lattice profile of periodic sequences

The lattice profile analyzes the intrinsic structure of pseudorandom number sequences with applications in Monte Carlo methods and cryptology. In this paper, using the discrete Fourier transform for periodic sequences and the relation between the lattice profile and the linear complexity, we give general formulas for the expected value, variance, and counting function of the lattice profile of periodic sequences with fixed period. Moreover, we determine in a more explicit form the expected value, variance, and counting function of the lattice profile of periodic sequences for special values of the period.     

Proper actions on cohomology manifolds

Essential results about actions of compact Lie groups on connected manifolds are generalized to proper actions of arbitrary groups on connected cohomology manifolds. Slices are replaced by certain fiber bundle structures on orbit neighborhoods. The group dimension is shown to be effectively finite. The orbits of maximal dimension form a dense open connected subset. If some orbit has codimension at most , then the group is effectively a Lie group.

     

Anomalous dispersion in the Belousov-Zhabotinsky reaction: Experiments and modeling

We report results on dispersion relations and instabilities of traveling waves in excitable systems. Experiments employ solutions of the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction confined to thin capillary tubes which create a pseudo-one-dimensional system. Theoretical analyses focus on a three-variable reaction-diffusion model that is known to reproduce qualitatively many of the experimentally observed dynamics. Using continuation methods, we show that the transition from normal, monotonic to anomalous, single-overshoot dispersion curves is due to an orbit flip bifurcation of the solitary pulse homoclinics. In the case of “wave stacking”, this anomaly induces attractive pulse interaction, slow solitary pulses, and faster wave trains. For “wave merging”, wave trains break up in the wake of the slow solitary pulse due to an instability of wave trains at small wavelength. A third case, “wave tracking” is characterized by the non-existence of solitary waves but existence of periodic wave trains. The corresponding dispersion curve is a closed curve covering a finite band of wavelengths.     

Specht Modules and Simple Modules for Centralizer Algebras of the Symmetric Group

Let Σ_n be the symmetric group on n letters. For l ≤ n identify Σ_l with a subgroup of Σ_n in the natural way. Let k be an algebraically closed field of characteristic p. This article begins to develop a theory for modules over the centralizer algebras kΣ_n^Σ_l that is analogous to James's theory of permutation modules, Specht modules, and simple modules over kΣ_n. We make a conjecture about how to construct all simple kΣ_n^Σ_l-modules, we develop tools to test the conjecture, and we prove that it is correct for all n when l < p.     

On the separation of initial and final state effects in photoelectron spectroscopy using an extension of the auger-parameter concept

First, we show that the quantity Δβ(i) = ΔE_A(kii) + 2ΔE_B(i) — ΔE_B(k) is directly related to the final state relaxation contribution ΔE_R(i) of the binding energy shift ΔE_B(i). ΔE_A(kii) is the kinetic energy shift of the Auger transition which corresponds to the decay of a hole state with a hole in level k into a final state with two holes in level i. The shift parameter Δβ(i), which is based on information on two binding energies, is conceptually similar to Wagner's Auger parameter. To establish the relation between Δβ(i) and ΔR(i) one needs, however, less drastic approximations than in the case of Auger parameter shifts. The only approximation necessary is the assumption that ΔR(i) is determined by coulomb contributions.Secondly, we use Δβ (i) to analyse the experimental data of eighteen gaseous phosphorus-containing compounds obtained by Sodhi and Cavell¹. It is shown that ΔR(P_2p) is strongly related to changes in the polarizability of the ligands. The initial state effects derived from our study deviate from those expected on the basis of simple electronegativity considerations.     

Self-Dual Noncommutative {\phi^4} -Theory in Four Dimensions is a Non-Perturbatively Solvable and Non-Trivial Quantum Field Theory

We study quartic matrix models with partition function \({\mathcal{Z}[E, J] = \int dM}\) exp(trace \({(JM - EM^{2} - \frac{\lambda}{4} M^4)}\) ). The integral is over the space of Hermitean \({\mathcal{N} \times \mathcal{N}}\) -matrices, the external matrix E encodes the dynamics, \({\lambda > 0}\) is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing β-function. As the main application we prove that Euclidean \({\phi^4}\) -quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for \({\mathcal{N} \to \infty}\) the same spectrum as the Laplace operator in four dimensions. Using the theory of singular integral equations of Carleman type we compute (for \({\mathcal{N} \to \infty}\) and after renormalisation of \({E, \lambda}\) ) the free energy density (1/volume) log \({(\mathcal{Z}[E, J]/\mathcal{Z}[E, 0])}\) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which in subsequent work is verified for coupling constants \({\lambda \leq 0}\) .     

On a functional equation by Baak,Boo and Rassias

In Baak et al. (J Math Anal Appl 314(1):150–161, 2006) the authors considered the functional equation

$$\begin{aligned} r f\left( \frac{1}{r}\,\sum _{j=1}^{d}x_j\right)+ & {} \sum _{i(j)\in \{0,1\} \atop \sum _{1\le j\le d} i(j)=\ell }r f\left( \frac{1}{r}\,\sum _{j=1}^d (-1)^{i(j)}x_j\right) \\= & {} \left( {d-1\atopwithdelims ()\ell }-{d-1\atopwithdelims ()\ell -1} +1\right) \sum _{j=1}^{d} f(x_j) \end{aligned}$$

where \(d,\ell \in \mathbb {N}\), \(1<\ell <d/2\) and \(r\in \mathbb {Q}{\setminus }\{0\}\). The authors determined all odd solutions \(f:X\rightarrow Y\) for vector spaces X, Y over \(\mathbb {Q}\). In Oubbi (Can Math Bull 60:173–183, 2017) the author considered the same equation but now for arbitrary real \(r\not =0\) and real vector spaces X, Y. Generalizing similar results from (J Math Anal Appl 314(1):150–161, 2006) he additionally investigates certain stability questions for the equation above, but as for that equation itself for odd approximate solutions only. The present paper deals with the general solution of the equation and the corresponding stability inequality. In particular it is shown that under certain circumstances non-odd solutions of the equation exist.

     

Radiative spectra of thermal electromagnetic noise induced by planar realistic dielectrics

Spectral characteristics of stochastic fields and their spatial derivatives in various planar structures composed by lossy materials described by realistic dielectric functions are numerically calculated based on solutions to the problems of multipolar electromagnetic fields in a plane layered geometry. A displacement of the maximum of the spectral power densities for spatial derivatives of fluctuating fields to the high-frequency domain, a resonant increase in the density of states of the fluctuating fields at the frequencies of interface excitations and interference modes for the radiative part of the spectra, the influence of geometry on the density of states, and other peculiarities are found by numerical calculations and graphically demonstrated. Interpretations of the above effects are provided.