A Boolean Gene Regulatory Model of heterosis and speciation

Modelling genetic phenomena affecting biological traits is important for the development of agriculture as it allows breeders to predict the potential of breeding for certain traits. One such phenomenon is heterosis or hybrid vigor: crossing individuals from genetically distinct populations often results in improvements in quantitative traits, such as growth rate, biomass production and stress resistance. Heterosis has become a very useful tool in global agriculture, but its genetic basis remains controversial and its effects hard to predict. We have taken a computational approach to studying heterosis, developing a simulation of evolution, independent reassortment of alleles and hybridization of Gene Regulatory Networks (GRNs) in a Boolean framework. Fitness is measured as the ability of a network to respond to external inputs in a pre-defined way. Our model reproduced common experimental observations on heterosis using only biologically justified parameters. Hybrid vigor was observed and its extent was seen to increase as parental populations diverged, up until a point of sudden collapse of hybrid fitness. We also reproduce, for the first time in a model, the fact that hybrid vigor cannot easily be fixed by within a breeding line, currently an important limitation of the use of hybrid crops. The simulation allowed us to study the effects of three standard models for the genetic basis of heterosis and the level of detail in our model allows us to suggest possible warning signs of the impending collapse of hybrid vigor in breeding. In addition, the simulation provides a framework that can be extended to study other aspects of heterosis and alternative evolutionary scenarios.Comment: See online version for supplementary materia

Purification and analytical characterization of an anti- CD4 monoclonal antibody for human therapy

A purification process for the monclonal anti-CD4 antibody MAX.16H5 was developed on an analytical scale using (NH&SO, precipitation, anion-exchange chromatography on MonoQ or Q-Sepharose, hydrophobic interaction chromatography on phenyl- Sepharose and gel filtration chromatography on Superdex 200. The purification schedule was scaled up and gram amounts of MAX.16H5 were produced on corresponding BioPilot columns. Studies of the identity, purity and possible contamination by a broad range of methods showed that the product was highly purified and free from contaminants such as mouse DNA, viruses, pyrogens and irritants. Overall, the analytical data confirm that the monoclonal antibody MAX.16H5 prepared by this protocol is suitable for human therapy

Symplectic Dirac-K\"ahler Fields

For the description of space-time fermions, Dirac-K\"ahler fields (inhomogeneous differential forms) provide an interesting alternative to the Dirac spinor fields. In this paper we develop a similar concept within the symplectic geometry of phase-spaces. Rather than on space-time, symplectic Dirac-K\"ahler fields can be defined on the classical phase-space of any Hamiltonian system. They are equivalent to an infinite family of metaplectic spinor fields, i.e. spinors of Sp(2N), in the same way an ordinary Dirac-K\"ahler field is equivalent to a (finite) mulitplet of Dirac spinors. The results are interpreted in the framework of the gauge theory formulation of quantum mechanics which was proposed recently. An intriguing analogy is found between the lattice fermion problem (species doubling) and the problem of quantization in general.Comment: 86 pages, late

Nonlinear stochastic evolution equations of second order with damping

Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with an internal approximation. Uniqueness is proved as well.Comment: This is the version of the article accepted for publication. The final publication is available at http://link.springer.co

Gauging and symplectic blowing up in nonlinear sigma-models: I. point singularities

In this paper a two dimensional non-linear sigma model with a general symplectic manifold with isometry as target space is used to study symplectic blowing up of a point singularity on the zero level set of the moment map associated with a quasi-free Hamiltonian action. We discuss in general the relation between symplectic reduction and gauging of the symplectic isometries of the sigma model action. In the case of singular reduction, gauging has the same effect as blowing up the singular point by a small amount. Using the exponential mapping of the underlying metric, we are able to construct symplectic diffeomorphisms needed to glue the blow-up to the global reduced space which is regular, thus providing a transition from one symplectic sigma model to another one free of singularities.Comment: 32 pages, LaTex, THEP 93/24 (corrected and expanded(about 5 pages) version

Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations

The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index and quantify the numerical difficulties in the fully discrete schemes, that are induced by the strangeness of the system. By analyzing the Kronecker index of the difference-algebraic equations, that represent commonly and successfully used time stepping schemes for the Navier--Stokes equations, we show that those time-integration schemes factually remove the strangeness. The theoretical considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909, https://doi.org/10.5281/zenodo.99890

Gauge Orbit Types for Theories with Classical Compact Gauge Group

We determine the orbit types of the action of the group of local gauge transformations on the space of connections in a principal bundle with structure group O(n), SO(n) or $Sp(n)$ over a closed, simply connected manifold of dimension 4. Complemented with earlier results on U(n) and SU(n) this completes the classification of the orbit types for all classical compact gauge groups over such space-time manifolds. On the way we derive the classification of principal bundles with structure group SO(n) over these manifolds and the Howe subgroups of SO(n).Comment: 57 page

Zitterbewegung and semiclassical observables for the Dirac equation

In a semiclassical context we investigate the Zitterbewegung of relativistic particles with spin 1/2 moving in external fields. It is shown that the analogue of Zitterbewegung for general observables can be removed to arbitrary order in \hbar by projecting to dynamically almost invariant subspaces of the quantum mechanical Hilbert space which are associated with particles and anti-particles. This not only allows to identify observables with a semiclassical meaning, but also to recover combined classical dynamics for the translational and spin degrees of freedom. Finally, we discuss properties of eigenspinors of a Dirac-Hamiltonian when these are projected to the almost invariant subspaces, including the phenomenon of quantum ergodicity