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Recently, a pivotal role for cAMP elevation in macrophages in resolving acute peritoneal inflammation has been demonstrated, and this elevation was absent in mice lacking a functional NADPH oxidase 41 , Given these data, we hypothesized that under normal circumstances lyso-PS produced in neutrophils following activation of the NADPH might signal to the macrophage for cAMP production, resulting in enhanced engulfment. In contrast, treatment with higher doses of db-cAMP, known to deactivate macrophages, suppressed engulfment in keeping with a previous report Intracellular cAMP production was also measured over a time course of co-culture of apoptotic cells or carboxylate-modified beads 15 , 39 in the absence or presence of G2A activation by lyso-PS liposomes.
Although the levels measured were variable between experiments, there was a consistent 1. In the presence of the inhibitor, G2A-mediated enhanced efferocytosis was clearly abrogated Fig. This was demonstrated both for the enhanced uptake of lyso-PS neg apoptotic cells delivered with lyso-PS liposomes and for aged apoptotic neutrophils that present their own endogenously produced G2A activator. Adenylyl cyclase inhibition had no effect on the uptake of UV-irradiated lyso-PS neg apoptotic cells. These results support the hypothesis that lyso-PS signals through adenylyl cyclase activation via a cAMP-dependent pathway and that this is distinct from signaling for engulfment by apoptotic cells in the absence of lyso-PS.
A , phagocytic indices were determined as in Fig. Data are displayed as -fold over control. F , Rac1 activity was determined as in Fig. In contrast, pretreatment of macrophages with either inhibitor had no effect on the uptake of UV-irradiated lyso-PS neg apoptotic cells. Similarly, pretreatment of macrophages with KT reduced the uptake of aged neutrophils to levels comparable with the those observed for UV-irradiated cells, again suggesting that endogenously produced lyso-PS in aged neutrophils likely activated this pathway Fig.
To confirm PKA involvement rather than activation of an Epac protein and to rule out a nonspecific effect of the inhibitors, we took advantage of recently available agonists specific for either PKA or Epac Given the dose-dependent effects of the cAMP analog above, concentration effects of each were investigated. Neither dose of the Epac agonist had any effect on uptake of UV-irradiated lyso-PS neg apoptotic cells. Apoptotic cell recognition by macrophages can result in their production of prostanoids, such as PGE 2 9 , 10 , 45 , that might be expected to signal for activation of adenylyl cyclase e.
Culture of aged apoptotic neutrophils alone, in the absence of macrophages, showed no increase in PGE 2 production data not shown. Similar enhancement of PGE 2 production was elicited from wild type macrophages treated with lyso-PS liposomes along with lyso-PS neg apoptotic neutrophils as was seen for aged apoptotic neutrophils Fig. Finally, to rule out any contribution from the apoptotic cells themselves, carboxylate-modified beads serving as apoptotic cell mimics were investigated.
Similar levels of PGE 2 , although somewhat delayed in production, were detected in supernatants of macrophages co-cultured with lyso-PS liposomes plus carboxylate-modified beads Fig.
Increases in the levels of other eicosanoids were not detected in response to apoptotic cells or carboxylate-modified bead mimics in the presence or absence of lyso-PS. Together, these data suggested that macrophages that had ingested apoptotic cells in the presence of the G2A activator, lyso-PS either generated endogenously or provided exogenously , generate more PGE 2 than macrophages that had ingested lyso-PS neg apoptotic cells and that activation of G2A enhanced production of PGE 2 , leading to augmented Rac1 activity via cAMP production and subsequent PKA activation.
These findings were somewhat surprising given that PGE 2 , like db-cAMP, has been associated with macrophage deactivation and inhibition of apoptotic cell uptake 43 , Thus, the effect of exogenously added PGE 2 on apoptotic cell uptake was investigated. As reported in the literature, higher doses of PGE 2 were suppressive Data are representative of three independent experiments. PGE 2 synthesis by prostaglandin-E synthase first requires liberation of arachidonic acid by the action of a phospholipase A 2 followed by COX modification Pos , positive control for COX2 expression; C , control.
Two COX enzymes exist: Pretreatment of macrophages with either inhibitor abrogated G2A-dependent enhanced uptake of UV-irradiated lyso-PS neg apoptotic targets Fig. Enhanced uptake of aged apoptotic neutrophils was similarly abrogated, suggesting activation of a COX enzyme Fig.
Because we had previously shown that other macrophage populations, including inflammatory macrophages thioglycollate-elicited respond to lyso-PS liposomes via G2A signaling for enhanced efferocytosis 15 , we sought to determine whether the key intermediaries of the G2A signaling pathway identified here were utilized in thioglycollate-elicited macrophages as well.
Similarly, low dose PGE 2 also enhanced engulfment of lyso-PS neg apoptotic cells, whereas a higher dose was inhibitory.
The author heeds this warning well. A rectangle can be formed. Today, after going through a mastectomy and chemotherapy, she volunteers at the Seton Highland Lakes Hospital Texas oncology department. Beth Tangeman to Steven Swain, Oct. The sequence is as follows: View all 3 comments. Received Dec 14; Revised Mar
Together, these data support that the G2A signaling pathway defined in resident macrophages is also operative in inflammatory macrophages. Proposed signaling pathway for G2A-mediated enhancement of apoptotic cell engulfment. G2A activation in inflammatory macrophages enhances phagocytosis via the same proposed pathway.
Not all apoptotic cells signal equivalently to macrophages for efferocytosis. The data presented here support the hypothesis that the presence of lyso-PS, either generated endogenously or provided exogenously on liposomes, significantly increased both the number of macrophages ingesting apoptotic cells and the number of cells ingested per macrophage Figs.
Conversely, apoptosis of neutrophils and Jurkat cells; data not shown induced by UV irradiation, an admittedly non-physiologic but widely used stimulus, did not increase lyso-PS production, and uptake by macrophages was consequently reduced.
As such, we hypothesize that generation of lyso-PS and concomitant signaling through macrophage G2A may contribute to high capacity clearance of neutrophils that may promote timely resolution of acute inflammation where neutrophils often vastly outnumber macrophages Given both their numbers and the potential for tissue injury by their toxic intracellular cargo if not recognized and removed, it is critical that these cells are cleared in a facile manner.
Lipid activators of G2A are not thought to be direct ligands but rather likely alter the oligomerization of the receptor 20 , 53 , 54 , and there are significant and as yet unresolved discrepancies between investigations regarding the ability of various lipids to activate this receptor depending on species human versus murine , end point used, and means of delivering lipid 20 , 34 , Although this investigation cannot entirely rule out signaling from other described activators of G2A, their levels were either undetectable in apoptotic neutrophils i.
By contrast, lyso-PS produced in both activated 15 and aged neutrophils was readily detectible and generated in a manner dependent on activation of the NADPH oxidase as would accompany their recruitment to tissue in vivo. As such, the data support that lyso-PS was the most likely endogenously produced activator of G2A signaling for high capacity neutrophil clearance Fig.
Much less efficient on a mole per mole basis was lyso-PS provided in liposomes added simultaneously with lyso-PS neg UV-irradiated neutrophils to macrophage cultures. Furthermore, lyso-PS added on albumin was ineffective altogether Fig. It is important to point out that the data support that lyso-PS signaling via G2A required other ligands presented on the apoptotic cell surface: In contrast, stimulating macrophages with lyso-PS alone did not activate the pathway intermediaries defined in this investigation of enhanced efferocytosis.
We hypothesize that G2A activation and additional apoptotic cell recognition signals must be presented to macrophages in a carefully orchestrated context. Further elucidation of this co-signaling will undoubtedly require development of highly sensitive technologies and simplified manipulable model systems. Enhancement of efferocytosis over base-line uptake in this investigation appeared to be mediated entirely by G2A on macrophages.
PGE 2 production or augmentation of Rac1 activation but were fully functional for enhanced responses when provided these intermediaries downstream of the G2A receptor. We have demonstrated that G2A is present on inflammatory macrophage populations as well as resident populations and that signaling by lyso-PS enhanced efferocytosis by all macrophage populations studied to date Thus, enhancement of efferocytosis by G2A signaling may be fairly ubiquitous among macrophages and serve to differentially augment various recognition pathways that are utilized by distinct macrophage populations G2A is also widely expressed on other hematopoietic cells, including monocytes, dendritic cells, and neutrophils, but also endothelial cells and keratinocytes 56 , These observations suggest that G2A activators, such as lyso-PS presented on activated and apoptosing neutrophils, and other activators may signal in other contexts as well Figs.
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An understanding of signaling downstream of G2A for enhanced efferocytosis was entirely unknown, and elucidation of this pathway was the impetus of this investigation. Several observations deserve further discussion. First, it has long been known that apoptotic cells stimulate the production of prostanoids 9 , 10 , Enhanced production of PGE 2 but not other eicosanoids by macrophages in response to G2A activation by lyso-PS has been demonstrated under several conditions.
Minimal signaling requirements were further defined using G2A-sufficient macrophages; lyso-PS provided along with apoptotic cell mimics carboxylate-modified beads resulted in PGE 2 production similar to that seen for aged neutrophils although in a delayed time course Fig. Furthermore, the uptake of lyso-PS neg UV-irradiated cells was unaffected by inhibition or absence of cPLA 2 in the macrophages, whereas G2A-mediated enhancement by stimulation with lyso-PS under these conditions was completely abrogated Fig.
Dose dependence was also demonstrated for exogenously supplied PGE 2 and db-cAMP; low doses, mimicking those generated in response to G2A activation, likewise enhanced efferocytosis Figs. Stimulation of G2A with lyso-PS, under the conditions investigated thus far, has not inhibited responses in macrophages even with pretreatment of up to several hours The molecular mechanism of efferocytosis involves reorganization of the actin cytoskeleton to produce membrane ruffles, allowing for engulfment of the target in a process that differs from phagocytosis of opsonized particles and more closely resembles macropinocytosis In a variety of settings, RhoA activation negatively regulates efferocytosis 40 , 60 — Furthermore, it has been demonstrated that both Rac1 and RhoA activity can be mutually antagonistic 40 , 60 , The data presented here demonstrate that G2A activation by endogenously produced or exogenously provided activators, such as lyso-PS, along with lyso-PS neg apoptotic cells significantly enhanced Rac1 activation via the G2A-mediated signaling pathway.
If you take one of the numbers and divide it by it's previous number you get closer and closer to phi as you go further in the series. Fibonacci numbers are found everywhere; from the number of petals in a flower, to the number of spirals on a pineapple; to phyllotaxis Greek for "leaf arrangement" ; to the family tree structure of bees, et cetera. I thought it all was pretty cool to tell you the truth. So doesn't that sound pretty cool? Dec 02, Ms. Livio's book examines the convoluted history and applications of phi. It's derivation is deceptively simple. In mathematics, there are many ways to express t Livio's book examines the convoluted history and applications of phi.
In mathematics, there are many ways to express the same relationship. Another way to look at the equation is to multiply both sides of the equation by phi. Written with coefficients of one, the equation reads: Livio addresses the key question about phi immediately. Imagine the point dividing segments a and b is instead a hinge. Bend b up so that a line connecting the beginning of segment a and the end of segment b for an isoceles triangle.
The triangle forms the first leg of a five-pointed star or pentagram. Connecting the points of the star result in a pentagon. Connect the vertices of the pentagon and the result is a smaller pentagram built around a smaller pentagon. Now fold b so that it is perpendicular to a. A rectangle can be formed. Using b as the dimension of a side, cut away a square, and a smaller proportional rectangle remains. The process can be repeated again and again.
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He explains the rule for generating the Fibonacci Sequence in case you haven't read the Dan Brown book! The sequence is as follows: Now create from these numbers the sequence: The decimal equivalents for that series is: In other words, each number in the series approaches closer and closer to the value of phi. Livio's book offers much more than a seemingly endless series of numerical games. He calls attention to Fibonacci's pedagogical genius. In addition, his algebra was often rhetorical, explaining in words the desire solution rather than solving explicit equations as we we would today.
Two of the videos I found most helpful in understanding the math behind this book were: The copious historical detail that Livio introduces can at first seem like a bewildering distraction. However, for me it highlighted the vast gulf between arithmetic as a fingers and toes counting exercise, and the study of abstract relationships which so enamored the ancient Greeks.
I gained a new appreciation for their achievement from reading this book. Livio's book is meant to appeal to a wide audience. I gained much more than I expected. Despite the complexity of some of the concepts, anyone who has made it through high school math will comprehend his explanations.
This is not because you will need that high school knowledge. Rather, when he launches into a theorem or proposition, you will remember that you once knew the references he is citing! Nevertheless, I have to admit that I found the chapter on periodic tilings and the significance of Penrose tiles difficult to understand. A clearer explanation, to me, was the link https: Returning to the question of why phi is important, Livio reveals that the recursive pattern appears in nature: The arrangement of leaves around a branch phytotaxis , and the arrangement of the scales on a pinecone, for example.
The effort it took to understand this book was rewarded by the satisfaction of communicating with so many historical minds on this one abstract concept. Aug 03, Jill rated it really liked it Shelves: The Fibonacci sequence and its consequent relationship to the Golden Ratio is one of my favourite things. So I went into this book already interested and somewhat informed.
Not sure if that would make a difference, though, because Livio's treatment of this topic is really solid. For one thing, it's clearly written -- which always helps for the artsy reader -- and while formulae and proofs litter the pages, concrete examples and pictures show up frequently.
The structure of the book The Fibonacci sequence and its consequent relationship to the Golden Ratio is one of my favourite things. The structure of the book is excellent -- each section moves smoothly and, often, chronologically into the next, while still bring divided by subject. Pretty inspired though the final chapter seems a bit abrupt, especially at the end.
Livio also sees himself as a bit of a detective, using geometry and timeline analysis to check whether work commonly attributed to Golden Ratio influence is actually of that ilk -- and generally, it isn't. Really informative, surprisingly narrative, and a nice, but critical, love letter. Sep 19, R K rated it did not like it. Am I nerd for voluntarily reading this?
I'm not the brainest person on the planet. Actually, I'm not very geeky at all. But I love to learn. I like to spend time analyzing and picking things apart ; dissecting the material and discussing it with someone. However, not everything enchanted me and this book straight up annoyed me. Essentially, I went into this book expecting to be, I don't know, told about Phi. The discovery, the relevance, the applications and help it provided Am I nerd for voluntarily reading this?
The discovery, the relevance, the applications and help it provided to the world? Wouldn't you, based on this title? But what I got instead was pages and pages of conspiracy theories of phi and the "debunking of it". May 20, EJ Natale rated it did not like it. This book is more numerology. The author creates loose and thin parallels to Phi, then refutes them. This happens repeatedly throughout the book. The great pyramids might be built based on a ratio similar to phi. Oh, no, maybe not. Oh, these painting might contain phi built into some of the geometry. The artist didn't even know what phi is.
The content makes no sense. The author goes into lengthy sidebars about art and Terrible book. The author goes into lengthy sidebars about art and astronomy that do not play into the material. The author prattels on about Kepler and some of his work and how it related to phi, and then that all of his work was bunk.
The author writes at length about how some artist might have based their paintings on the golden ratio, but then writes that the dimensions are off. This book is a waste. I find it interesting it is pretty much built upon the mythos of the golden ration that Dan Brown built with the "Da Vinci Code," but the author goes out of his way to state that he will not cover the mona lisa. Save your time and money. Do not read this steam pile of self indulgent crap. Apr 01, Tim rated it really liked it. Mathematical constants make engaging characters in the popular imagination.
At least the rash of books for general audiences in this vein published in the last two decades suggests this.
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Astro-physicist Livio's leading character is a somewhat less well-known constant - those special numbers discovered or created by mathematicians over the centuries. Phi - the so-called Golden Ratio - has been known since Euclid.
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
This equality yields Phi, an irrational number beginning with 1. Livio calls Phi the 'most irrational' of irrational numbers since, written as a continued fraction, it consists entirely of ones and thus converges slower than any other irrational number written as a continued fraction. The character of Phi turns up in many places - for example in construction of the pentagon and pentagram, in Fibonnaci numbers, in mathematical descriptions of the arrangement of buds in a sunflower or leaves on a plant stem, in the shape of galactic spirals.
Particularly important in the history mathematics and in Livio's account is the Fibonnaci sequence where the ratio of successive numbers increasingly approximates Phi. In its many appearances Livio conveys the magic of Phi. But Livio is a debunker too. Phi's magic, he argues, lies not in some natural aesthetic known to ancient peoples, artists, musicians, or others.
Most such claims for the use of Phi - in the construction of the pyramids, in painting, in music, in architecture, or elsewhere - he shows to be 'number juggling', claims founded on ambiguities in measurement and interpretation without strong psychological foundation. Yet the romance of the Golden Ratio does raise for Livio foundational questions about mathematics. As he asks in his closing chapter, "Is God a Mathematician? Or are mathematical constants and the rest of the edifice of mathematics somehow just the creations of brains such as ours?
His own conclusion is that "Our mathematics is the symbolic counterpart of the universe we perceive" where our perceptual apparatus collectively as well as individually is a kind of evolving computer program, a rule-based system which, in interactions with nature - ourselves and the world - generates mathematics, culture, the arts and the uncounted endeavors to which the human presence on this planet gives rise.
May 05, Ob-jonny rated it really liked it. This is a great book about number theory in general and is much more than just the discussion of phi, the golden ratio. It is truly amazing to see how often this number and ratio are found in nature. The widths of the spirals of pinecones and various flowers display the ratio as due patterns in the breeding of rabbits. But some of the numerical properties of the number are equally fascinating.
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There is also a section on prime numbers which is just as inter This is a great book about number theory in general and is much more than just the discussion of phi, the golden ratio. There is also a section on prime numbers which is just as interesting as the discussion about phi and it provides some of the variety to the book I mentioned.
For instance, there are some very large prime numbers which are only composed of the number 1. There is an interesting discussion of the longest prime number found. Another thought-provoking discussion is the tendency for numbers starting with the lower digits appearing in nature and statistics.
For instance, collections of numbers tend to have 1 as a first digit much more often than 9 and the transition is continuous between 1 and 9. It has something to do with how the range of numbers starting with 1 is much wider than for larger numbers when looking at them on a logarithmic scale. This book will really get you thinking and is especially suited for people interested in number theory.
Aug 08, Mikael Lind rated it really liked it Shelves: A fascinating historical expose about how a single number, phi, has or is believed to have influenced human creation within such different fields as music, art, architecture and, of course, mathematics of different kind. The book's strength is that you don't have to be a mathematical minded person to be able to understand it. I could follow the mathematical formulas roughly by the mathematical knowledge I gained more than fifteen years ago, but even though I was persistent enough to try to foll A fascinating historical expose about how a single number, phi, has or is believed to have influenced human creation within such different fields as music, art, architecture and, of course, mathematics of different kind.
I could follow the mathematical formulas roughly by the mathematical knowledge I gained more than fifteen years ago, but even though I was persistent enough to try to follow Livio's formulas, this is not crucial to the story of the book. PA contraction in response to airway hypoxia is an immediate physiological response to redirect blood flow from poorly ventilated regions of the lungs to well oxygenated regions. Although it is now clear that both the O 2 sensor and the effector molecules mediating this response reside in the PASMCs, the O 2 sensor has not yet been identified nor has the mechanism responsible for initiating HPV.
In PA smooth muscle, intracellular glucose is metabolized through glycolysis At the same time, there was a significant reduction in the peak and sustained phases of hypoxia-induced PA contraction. Previously, Leach et al. Moreover, the PPP plays a key role in vascular smooth muscle metabolism 33 , and increases in GlcPD expression and activity in bovine PA smooth muscle promotes production Our present finding Fig.
PASMCs derive energy from metabolism of glucose through aerobic glycolytic and glycogenolytic pathways 34 , 35 , and it is likely that aerobic glycolysis would be the first reaction to stop in PASMCs under hypoxic conditions. Although it has been reported that ATP levels are unaffected by acute short term hypoxia, recent studies have shown that AMP levels are elevated in rat PA under hypoxia 36 , and our present results indicate there is indeed a drop in the ATP-to-ADP ratio.
The following were also shown: On the other hand, even though initiation of HPV is not dependent on oxidative phosphorylation, it has been proposed that mitochondrial ETC could be involved in O 2 sensing 8 , 9 , In that regard, Bell et al. They observed that cells deficient in the complex III subunit cytochrome b , and therefore respiration-incompetent, do not show a hypoxia-induced increase in ROS. Although it is accepted that mitochondrial ROS are involved in mediating HPV, whether their levels increase or decrease is somewhat controversial 3 , 6 , 7. Nonetheless, the observed increase in DHE fluorescence supports the hypothesis that generation is elevated in hypoxic PA 9 , 44 and is strikingly opposite the observations that extramitochondrial levels are decreased in hypoxic coronary artery In these arteries, HPV was not only inhibited but in some cases the KCl-precontracted vessels actually dilated in response to hypoxia.
Taken together, these results further confirm that hypoxia-induced activation of GlcPD is one of the signals through which the O 2 sensor communicates with the effectors that ultimately evoke the HPV response. In conclusion, as shown in the schematic diagram in Fig. National Center for Biotechnology Information , U. Journal List J Biol Chem v. Published online Apr 2. Author information Article notes Copyright and License information Disclaimer. Received Dec 14; Revised Mar This article has been cited by other articles in PMC. Abstract Hypoxic pulmonary vasoconstriction HPV is a physiological response to a decrease in airway O 2 tension, but the underlying mechanism is incompletely understood.
Introduction Pulmonary hypertension PH 2 is a major cause of morbidity and mortality, the incidence of which is increasing around the world. Open in a separate window. PA Contraction Fourth and fifth order PAs were prepared from bovine lungs and studied for changes in isometric force as described previously