The robustness of proofreading to crowding-induced pseudo-processivity in the MAPK pathway

Double phosphorylation of protein kinases is a common feature of signalling cascades. This motif may reduce cross-talk between signalling pathways, as the second phosphorylation site allows for proofreading, especially when phosphorylation is distributive rather than processive. Recent studies suggest that phosphorylation can be `pseudo-processive' in the crowded cellular environment, as rebinding after the first phosphorylation is enhanced by slow diffusion. Here, we use a simple model with unsaturated reactants to show that specificity for one substrate over another drops as rebinding increases and pseudo-processive behavior becomes possible. However, this loss of specificity with increased rebinding is typically also observed if two distinct enzyme species are required for phosphorylation, i.e. when the system is necessarily distributive. Thus the loss of specificity is due to an intrinsic reduction in selectivity with increased rebinding, which benefits inefficient reactions, rather than pseudo-processivity itself. We also show that proofreading can remain effective when the intended signalling pathway exhibits high levels of rebinding-induced pseudo-processivity, unlike other proposed advantages of the dual phosphorylation motif.Comment: To appear in Biohys.

Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting

The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial infinity. Here we start with homogeneous solutions, which have a spatially constant, non-zero mass density and which describe the mass distribution in a Newtonian model of the universe. These homogeneous states can be constructed explicitly, and we consider deviations from such homogeneous states, which then satisfy a modified version of the Vlasov-Poisson system. We prove global existence and uniqueness of classical solutions to the corresponding initial value problem for initial data which represent spatially periodic deviations from homogeneous states.Comment: 23 pages, Latex, report #

Relatives by Blood, Adoption, and Association: Who Should Get What and Why

This Article explores the questions that courts and legislatures must address in order to integrate the social phenomenon of adoption into our succession laws, monitors the progress that has and has not been made in dealing with these questions, and proposes a comprehensive approach to the treatment of adoptees in matters of succession. Specifically, part I introduces the traditional approach to relationship by adoption, while part HI compares the past and present goals of adoption. Part IV discusses the legal status of adoptees in the context of intestate succession. This discussion explores past and present trends and examines the special policy considerations that apply to in-family adoptions. Part V discusses the treatment of adopted-in and adopted-out children under class gifts and also addresses the retroactivity issue which has sharply divided our courts. Part VI deals with adult adoptions and the special problems they pose in succession cases, both testate and intestate. Part VII explores the uncharted terrain of equitable (informal) adoption. It explains the theoretical bases for equitable adoption, discusses the consequences of equitable adoption,and suggests more realistic criteria for judging equitable adoption claims. Part VII concludes by discussing the special policy considerations that should guide the courts in deciding how far to extend the equitable adoption doctrine

The thermodynamics of computational copying in biochemical systems

Living cells use readout molecules to record the state of receptor proteins, similar to measurements or copies in typical computational devices. But is this analogy rigorous? Can cells be optimally efficient, and if not, why? We show that, as in computation, a canonical biochemical readout network generates correlations; extracting no work from these correlations sets a lower bound on dissipation. For general input, the biochemical network cannot reach this bound, even with arbitrarily slow reactions or weak thermodynamic driving. It faces an accuracy-dissipation trade-off that is qualitatively distinct from and worse than implied by the bound, and more complex steady-state copy processes cannot perform better. Nonetheless, the cost remains close to the thermodynamic bound unless accuracy is extremely high. Additionally, we show that biomolecular reactions could be used in thermodynamically optimal devices under exogenous manipulation of chemical fuels, suggesting an experimental system for testing computational thermodynamics.Comment: Accepted versio

Systematic generation of multibody equations of motion suitable for recursive and parallel manipulation

The formulation of a method known as the joint coordinate method for automatic generation of the equations of motion for multibody systems is summarized. For systems containing open or closed kinematic loops, the equations of motion can be reduced systematically to a minimum number of second order differential equations. The application of recursive and nonrecursive algorithms to this formulation, computational considerations and the feasibility of implementing this formulation on multiprocessor computers are discussed

The formation of black holes in spherically symmetric gravitational collapse

We consider the spherically symmetric, asymptotically flat Einstein-Vlasov system. We find explicit conditions on the initial data, with ADM mass M, such that the resulting spacetime has the following properties: there is a family of radially outgoing null geodesics where the area radius r along each geodesic is bounded by 2M, the timelike lines $r=c\in [0,2M]$ are incomplete, and for r>2M the metric converges asymptotically to the Schwarzschild metric with mass M. The initial data that we construct guarantee the formation of a black hole in the evolution. We also give examples of such initial data with the additional property that the solutions exist for all $r\geq 0$ and all Schwarzschild time, i.e., we obtain global existence in Schwarzschild coordinates in situations where the initial data are not small. Some of our results are also established for the Einstein equations coupled to a general matter model characterized by conditions on the matter quantities.Comment: 36 pages. A corollary on global existence in Schwarzschild coordinates for data which are not small is added together with minor modification

The Einstein-Vlasov sytem/Kinetic theory

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic- and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (e.g. fluid models). The first part of this paper gives an introduction to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org

Regularity results for the spherically symmetric Einstein-Vlasov system

The spherically symmetric Einstein-Vlasov system is considered in Schwarzschild coordinates and in maximal-isotropic coordinates. An open problem is the issue of global existence for initial data without size restrictions. The main purpose of the present work is to propose a method of approach for general initial data, which improves the regularity of the terms that need to be estimated compared to previous methods. We prove that global existence holds outside the centre in both these coordinate systems. In the Schwarzschild case we improve the bound on the momentum support obtained in \cite{RRS} for compact initial data. The improvement implies that we can admit non-compact data with both ingoing and outgoing matter. This extends one of the results in \cite{AR1}. In particular our method avoids the difficult task of treating the pointwise matter terms. Furthermore, we show that singularities never form in Schwarzschild time for ingoing matter as long as $3m\leq r.$ This removes an additional assumption made in \cite{A1}. Our result in maximal-isotropic coordinates is analogous to the result in \cite{R1}, but our method is different and it improves the regularity of the terms that need to be estimated for proving global existence in general.Comment: 25 pages. To appear in Ann. Henri Poincar\'

Structural response of a steel-frame building to horizontal and vertical travelling fires in multiple floors

During previous fire events such as the World Trade Centre Towers (WTC) 1, 2 & 7 in New York (2001), the Windsor Tower in Madrid (2005), and the Plasco building in Iran (2017), flames were observed to travel horizontally across the floor plate and vertically to different floors. Such fires are not considered as part of the traditional prescriptive structural design for fire. Recently, the Travelling Fires Methodology (TFM) has been developed to account for such horizontally travelling nature of fires. A dozen of studies have investigated the structural response of steel, concrete, and composite structures to a single-floor travelling fire. 5 out of 6 of the vertically travelling fire studies have been limited to the structures with a long span composite truss system as in the WTC Towers. The aim of this work is to investigate the response of a substantially different structural system, i.e. a generic multi-storey steel frame, subjected to travelling fires in multiple floors, and varying the number of fire floors, including horizontal and vertical fire spread. A two-dimensional 10-storey 5-bay steel frame is modelled in the finite element software LS-DYNA. The number of multiple fire floors is varied between 1 and 10, and for each of these scenarios, 5 different fire types are investigated. They include four travelling fire scenarios and the standard fire. In total, 51 fire simulations are considered. The development of deflections, axial forces, bending moments and frame utilization are analysed. Results show that the largest stresses develop in the fire floors adjacent to cool floors, and their behaviour is independent of the number of fire floors. Results indicate that both the fire type and the number of fire floors have a significant effect on the failure time (i.e. exceeded element load carrying capacity) and the type of collapse mechanism. In the cases with a low number of fire floors (1–3) failure is dominated by the loss of material strength, while in the cases with larger number of fire floors (5–10) failure is dominated by thermal expansion. Collapse is mainly initiated by the pull-in of external columns (1–3-floor fires; 1–9-floor fires for 2.5% TFM) or swaying of the frame to the side of fire origin (5–10-floor fires). This study has assessed a different structural form compared to previous literature under an extensive range of multiple floor travelling fire scenarios. We find that although vertically travelling fires result in larger beam axial forces and initial deflections, simultaneous travelling fires result in shorter failure times and represent a more onerous scenario for the steel frame investigated