On the Mathematics of the Law of Mass Action

In 1864,Waage and Guldberg formulated the "law of mass action." Since that time, chemists, chemical engineers, physicists and mathematicians have amassed a great deal of knowledge on the topic. In our view, sufficient understanding has been acquired to warrant a formal mathematical consolidation. A major goal of this consolidation is to solidify the mathematical foundations of mass action chemistry -- to provide precise definitions, elucidate what can now be proved, and indicate what is only conjectured. In addition, we believe that the law of mass action is of intrinsic mathematical interest and should be made available in a form that might transcend its application to chemistry alone. We present the law of mass action in the context of a dynamical theory of sets of binomials over the complex numbers.Comment: 40 pages, no figure

A Characterization of Scale Invariant Responses in Enzymatic Networks

An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. Recently, it was shown theoretically and experimentally that many adapting systems, both at the organism and single-cell level, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains (approximately) the same even when the background signal level is scaled. In this work, we set out to investigate under what conditions a broadly used model of biochemical enzymatic networks will exhibit scale-invariant behavior. An exhaustive computational study led us to discover a new property of surprising simplicity and generality, uniform linearizations with fast output (ULFO), whose validity we show is both necessary and sufficient for scale invariance of enzymatic networks. Based on this study, we go on to develop a mathematical explanation of how ULFO results in scale invariance. Our work provides a surprisingly consistent, simple, and general framework for understanding this phenomenon, and results in concrete experimental predictions

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation ``futile cycle'' motif which plays a central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove

Performative Social Science

Performative Social Science is positioned within the current era of crosspollination from discipline to discipline. Practitioners from the Arts and Humanities look to the Social Sciences for fresh frameworks, whist Social Science practitioners explore the Arts for potential new tools for enquiry and dissemination. Performative Social Science is defined and the similarities and differences between PSS and Arts-based Research (ABR) are delineated. The history of PSS is then outlined and its development, particularly at the Centre for Qualitative Research at Bournemouth University in the United Kingdom, is reviewed. Relational Aesthetics is then described in depth as the theoretical basis and grounding of Performative Social Science. Relational Aesthetics (Bourriaud, 2002) offers a theoretical ground for the complexities of connections across seemingly disparate disciplines such as the Arts and Social Sciences and for further exploration of the synergies between both disciplines as well as communities beyond the academy. An example of a large, three-year nationally funded project, culminating with the production of an award-winning short biopic, RUFUS STONE, is outlined as a prime example of a multi-method approach to social science research which includes tools from the arts in its progress and outputs. The entry concludes with goals and aspirations for Performative Social Science in the future

Unravelling social constructionism

Social constructionist research is an area of rapidly expanding influence that has brought together theorists from a range of different disciplines. At the same time, however, it has fuelled the development of a new set of divisions. There would appear to be an increasing uneasiness about the implications of a thoroughgoing constructionism, with some regarding it as both theoretically parasitic and politically paralysing. In this paper I review these debates and clarify some of the issues involved. My main argument is that social constructionism is not best understood as a unitary paradigm and that one very important difference is between what Edwards (1997) calls its ontological and epistemic forms. I argue that an appreciation of this distinction not only exhausts many of the disputes that currently divide the constructionist community, but also takes away from the apparent radicalism of much of this work

On local linearization of control systems

We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology

Microtubules in Bacteria: Ancient Tubulins Build a Five-Protofilament Homolog of the Eukaryotic Cytoskeleton

Microtubules play crucial roles in cytokinesis, transport, and motility, and are therefore superb targets for anti-cancer drugs. All tubulins evolved from a common ancestor they share with the distantly related bacterial cell division protein FtsZ, but while eukaryotic tubulins evolved into highly conserved microtubule-forming heterodimers, bacterial FtsZ presumably continued to function as single homopolymeric protofilaments as it does today. Microtubules have not previously been found in bacteria, and we lack insight into their evolution from the tubulin/FtsZ ancestor. Using electron cryomicroscopy, here we show that the tubulin homologs BtubA and BtubB form microtubules in bacteria and suggest these be referred to as “bacterial microtubules” (bMTs). bMTs share important features with their eukaryotic counterparts, such as straight protofilaments and similar protofilament interactions. bMTs are composed of only five protofilaments, however, instead of the 13 typical in eukaryotes. These and other results suggest that rather than being derived from modern eukaryotic tubulin, BtubA and BtubB arose from early tubulin intermediates that formed small microtubules. Since we show that bacterial microtubules can be produced in abundance in vitro without chaperones, they should be useful tools for tubulin research and drug screening

Introduction of Macromolecules into Bovine Adrenal Medullary Chromaffin Cells and Rat Pheochromocytoma Cells (PC12) by Permeabilization with Streptolysin O: Inhibitory Effect of Tetanus Toxin on Catecholamine Secretion

Conditions are described for controlled plasma membrane permeabilization of rat pheochromocytoma cells (PC12) and cultured bovine adrenal chromaffin cells by Streptolysin O (SLO). The transmembrane pores created by SLO invoke rapid efflux of intracellular 86Rb+ and ATP, and also permit passive diffusion of proteins, including immunoglobulins, into the cells. SLO-permeabilized PC12 cells release [3H]dopamine in response to micromolar concentrations of free Ca2+. Permeabilized adrenal chromaffin cells present a similar exocytotic response to Ca2+ in the presence of Mg2+/ ATP. Permeabilized PC12 cells accumulate antibodies against synaptophysin and calmodulin, but neither antibody reduces the Ca2+-dependent secretory response. Reduced tetanus toxin, although ineffective when applied to intact chromaffin cells, inhibits Ca2+-induced exocytosis by both types of permeabilized cells studied. Omission of dithiothreitol, toxin inactivation by boiling, or preincubation with neutralizing antibodies abolishes the inhibitory effect. The data indicate that plasma membrane permeabilization by Streptolysin O is a useful tool to probe and define cellular components that are involved in the final steps of exocytosis

On Quantum State Observability and Measurement

We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence the dynamics by generating all the unitary evolutions in a Lie group. We investigate to what extent, by an appropriate sequence of evolutions and measurements, we can obtain information on the initial state of the system. We present a system theoretic viewpoint of this problem in that we study the {\it observability} of the system. In this context, we characterize the equivalence classes of indistinguishable states and propose algorithms for state identification

"Am iz kwiin" (I'm his queen): Combining interpretative phenomenological analysis with a feminist approach to work with gems in a resource-constrained setting

This article focuses on working with gems using a feminist approach to interpretative phenomenological analysis (IPA) in a resource-constrained setting. The research explores the experiences of maternal disclosure of HIV to children of HIV positive mothers in Kingston, Jamaica. A feminist approach helps recognise power imbalances within research relationships and the women’s lived experiences. We present three “gems” which illuminate women’s lived experiences and explore how popularised representations of women’s sexuality and mothering influence disclosure discourses. We use emotion work as a conceptual resource to structure the women’s narratives and challenge existing policy discourses, which arguably represent disclosure within a binary, rationalist, decision-making framework. This article adds to global literature on maternal HIV disclosure and problematises policy discourses by bringing into relief the emotion work women engage in when deciding if and how to communicate their HIV status to their children. It adds to the body of research using IPA, particularly in resource-constrained settings where IPA has thus far had little application