Intersection of two straight lines Statistics Exam Questions: Normal Distribution In Indian philosophy, Maharishi Kanada was the first to systematically develop a theory of atomism around 200 BCE though some authors have allotted him an earlier era in the 6th century BCE. (B) Sleep duration and correlation diagram of daily PWS and PSW of mice expressing double-phopshomimetic mutants with sleep maintenance activity. ln(x) & ex equations I Biology. https://doi.org/10.1371/journal.pbio.3001813.s003. This is consistent with previous studies suggesting that the stable binding of Ca2+/CaM renders T306 and T307 inaccessible to the kinase domain of CaMKII, and their phosphorylation requires the temporal removal of Ca2+/CaM from the kinase [4043] or gradual phosphorylation of T306 and T307 occurs in the absence of apparent Ca2+ in the reaction buffer [44,45]. Pure Maths Paper 1 June 2018 Partial Fractions Tutorial II After microinjection, the embryos were cultured for 1 h in KSOM medium (Merck, Germany, or ARK Resource, Japan) in a 5% CO2 incubator at 37 C. On the other hand, our study demonstrated that the kinase-active form (T287D) of CaMKII has a sleep induction activity and the kinase activation marked by the phosphorylation of T287 residue is promoted by extended awake duration, providing a reasonable working hypothesis connecting the awake-associated neuronal activity and the induction of sleep. Multiple comparison tests were performed between all individual groups in each phase. Mar 2021 Pure Maths 1 9709/12, Oct 2020 Pure Maths 1 9709/11 As with T287D single mutant, the prolonged sleep duration for the T287D:T306A:T307A can be explained by an increase in PWS (i.e., sleep induction). Trigger point therapy is not a miracle cure for chronic pain. As for the mutants with 25% or lower expression levels compared to WT CaMKII, we could not adjust the relative expression level compared to WT, and mutant cell lysates without dilution were used for the kinase assay. Differentiation Exam Questions IV Supervision, Statistics & Mechanics Paper 3 October 2020, 9MA0/03 The underlying data can be found in S1 Data. The procedure to use the summation calculator is as follows: Function Exam Questions III The SRM-based mass spectrometry analysis was carried out the similar process described in the Mass spectrometry and western blotting of mice brain samples section. S12D Fig indicates that T287 phosphorylation occurs in the presence of 0.5 mM Ca2+ (conditions #3 and #4) but not in the absence of explicitly added Ca2+ in the reaction buffer (conditions #1 and #2). Other sleep parameters were shown in Fig 1G1I. This may be because the sleep-promoting effect of environmental light antagonizes the sleep inhibition effect of AIP2 expression. Vector Exam Questions I Error bars: SEM, *p < 0.05, **p < 0.01, ***p < 0.001, n.s. The enhanced sleep promoting activity found in S26A:T287D:T306D:T307D versus T287D (Fig 6B) might reflect that part of the sleep canceling effect carried out by S26 phosphorylation is disrupted by S26A mutation. If the central dogma is true, and if it is also true that nucleic acids are the only means whereby information is transmitted between awarded the new qualification. Essex's intellect caught the attention of Apocalypse, a powerful mutant, the very embodiment of Essex's predictions. The qPCR results indicate that triple gRNA sequences used for this KO effectively induced deletion mutations in the chromosomal target-1 and target-2 regions covered by the alternative primer pair #2. Integration: Area under a Graph Questions I The Quan Browser of the Quan Browser data system, version 3.0.63 (Thermo Fisher Scientific, USA) was used for data processing and quantification. The Spine Journal, the official journal of the North American Spine Society, is an international and multidisciplinary journal that publishes original, peer-reviewed articles on research and treatment related to the spine and spine care, including basic science and clinical investigations.. Time course of phosphorylation at each residue indicates that these autophosphorylation events proceed slower than T287 autophosphorylation (S12D Fig). The copy numbers of both the AAV vector genomes and mouse genomic DNA were quantified with a standard curve generated from known amounts of DNA. Male ESCs were cultured as described previously [74,75]. Dulbeccos Modified Eagle Medium; DTE, We analyzed the time course changes in the phosphorylation levels of each sleep-controlling residues in CaMKII (S26, S182, T287, T306, T307, and T311). Error bars: SEM, *p < 0.05, **p < 0.01, ***p < 0.001, n.s. Find Equation of a Circle given Three Points at the Circumference and Scientific Research (C) JP20K06576 (JSPS KAKENHI) (to K.L.O. NCERT Solutions For Class 12 Biology; NCERT Solutions For Class 12 Maths; NIOS A Level Syllabus. Sewage treatment (or domestic wastewater treatment, municipal wastewater treatment) is a type of wastewater treatment which aims to remove contaminants from sewage to produce an effluent that is suitable for discharge to the surrounding environment or an intended reuse application, thereby preventing water pollution from raw sewage discharges. Questions January 2008 (B, C) EEG power spectra (B) and NREM power density in delta and theta domains (C) of mice expressing AIP2 or the RARA mutant. Questions June 2013 The dried peptides were solubilized in 200 L of 2% acetonitrile and 0.1% TFA. Each joint has its own level of flexibility, expressed in degrees. The SRM transitions of the target peptides were determined based on the preanalysis of several samples including mice brains, 293T cells expressing CaMKII, and synthesized peptides, and optimized using Pinpoint software, version 1.3 (Thermo Fisher Scientific, USA) (S2 and S3 Tables). The dodecameric CaMKII structure may have many intermediate states [23]. Stationary Points I How to Use the Summation Calculator? Glutamate is a very major constituent of a wide variety of proteins; consequently it is one of the most abundant amino acids in the human body. Photosynthesis. Approximately 1 to 2 pL of RNase free water (Nacalai Tesque) containing 100 ng/l gRNA, 100 ng/l Cas9 mRNA, and 100 ng/l ssODN was injected into the cytoplasm of fertilized eggs in M2 medium (Merck, Germany or ARK Resource, Japan) at room temperature. The aggregate current is always the summation of all the individual currents. The mass spectrometer was equipped with an UltiMate 3000 RSLC nano nano-high-performance liquid chromatography (HPLC) system (Thermo Fisher Scientific, USA), and a PepMap HPLC trap column (C18, 5 m, 100 A; Thermo Fisher Scientific, USA) for loading samples. The kinase reaction was initiated by adding 0.5 M CaM to each sample. Step 1: Enter the function in the first input field and apply the summation limits from and to in the respective fields. Level up on all the skills in this unit and collect up to 3200 Mastery points! Following primer sequences were used to produce gRNA targeting the Camk2b locus. Error bars: SEM. The sleep deprivation was conducted by gentle handling and cage changing [28] at every 2 h. The other mice were housed under ad lib sleep conditions. A well-known mechanism of CaMKII activation is the intracellular Ca2+ influx that occurs upon excitatory synaptic input and subsequent neuronal firing [10,11]. C1 and C2 have been combined to create one unit. CaM, calmodulin; CaMKII, calmodulin-dependent protein kinase II; SRM, selected reaction monitoring; WT, wild-type. Donate or volunteer today! Proving Trig Identities I papers that are suitable for A Level Maths. We focused on the sleep maintenance function of T306 and T307 because these residues are a well-known autonomous negative feedback control for CaMKII kinase activation. The relative kinase activity measured by the level of phosphorylated substrate suggests that S26D, S182D, and T311D mutation leads to the loss of kinase activity similar to the kinase-dead K43R mutant (S12C Fig). Partial Fractions Exam Questions I Mass spectrometrybased quantification was carried out by SRM analysis using a TSQ Quantiva triple-stage quadrupole mass spectrometer (Thermo Fisher Scientific, USA) as described above. Note that some of the mutated residues would not be the target of phosphorylation in vivo, the outcome of this screening does not directly confer the evidence of phosphorylation-dependent control. ln(x) & ex equations II Trigonometry C3 Exam Questions II The Factor Theorem The idea is summarized as follows: If a gene copy confers a benefit B on another vehicle at cost C to its own vehicle, its costly action is strategically beneficial if pB > C, where p is the probability that a copy of the gene is present in the vehicle that benefits. (A) The 29 serine and 40 threonine residues throughout CaMKII. The Hanseatic League was a commercial and defensive alliance of the merchant guilds of towns and cities in northern and central Europe. A one-tenth of the mixture underwent LC-MS analysis to quantify the amount of expressed CaMKII. Simultaneous Equations - Logarithms Cre-mediated recombination of AAV genomes results in Camk2b gene expression in the target cells. (C) Daily sleep duration of mice expressing CaMKII phosphomimetic mutants (n = 610) in the presence of endogenous WT CaMKII. Data curation, Mark Scheme June 2013 Integration by Substitution Tutorial II EEG power was normalized relative to the total power in each frequency band. The company provided support in the form of salary for Y.N., and technical advice on the setup of mass spectrometers. Johann Carl Friedrich Gauss (/ a s /; German: Gau [kal fid as] (); Latin: Carolus Fridericus Gauss; 30 April 1777 23 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Need some A Level Maths help? At least, the present study excludes the core circadian transcription repressors as downstream factors of CaMKII sleep induction (Fig 4) and future research should be required for identifying downstream targets of CaMKII in sleep control. The Price equation is a covariance equation that is a mathematical description of evolution and natural selection. Differentiate Parametric Equations II This process produces adaptations for the benefit of alleles that promote the reproductive success of the organism, or of other organisms containing the same allele (kin altruism and green-beard effects), or even its own propagation relative to the other genes within the same organism (selfish genes and intragenomic conflict). Completing the Square & Graph Transformation Mar 2020 Pure Maths 3 9709/32, May 2022 Mechanics 4 9709/43 Binomial Expansion Formula The calculation was conducted same as S3 Fig. [11], Since Gould's death in 2002, Niles Eldredge has continued with counter-arguments to gene-centered natural selection. Moments 3 Taking moments at an angle Differentiation Combining Chain, Product & Quotient Rules III [20] A selfish gene could be favored by selection by producing altruism among organisms containing it. Proof of A cos x + B sin x = R cos (x - alpha) The EEG/EMG recordings revealed that T287D mice had significantly higher daily nonrapid eye movement (NREM) and REM sleep duration (Fig 1G and 1H) and PWS (Fig 1I) than WT-expressing mice. We cannot quantify the S182 phosphorylation in the 293T condition because of our technical limitations in the detection of this peptide in crude samples. There was no correlation between the ensemble of sleep duration and AAV transduction efficiency among the analyzed mutants (S3B Fig), indicating that the observed sleep phenotypes can be attributed to the nature of the introduced mutations rather than to a possible difference in AAV transduction efficacy. ), MEXT Quantum Leap Flagship Program (MEXT QLEAP) JPMXS012033064 (Japan Science and Technology Agency: https://www.jst.go.jp/stpp/q-leap/en/index.html) (to H.R.U.). However, the underlying mechanism by which CaMKII supports sleep regulation is largely unknown. Error bars: SEM, *p < 0.05, **p < 0.01, ***p < 0.001, n.s. Differentiation Lessons III Quadratic Log Equations https://doi.org/10.1371/journal.pbio.3001813, Academic Editor: Achim Kramer, Charit - Universittsmedizin Berlin, GERMANY, Received: April 17, 2022; Accepted: September 1, 2022; Published: October 4, 2022. Shaded areas represent SEM. Is the Subject Area "Sleep" applicable to this article? In this case, it would be interesting to ask whether the changes in learning phenotype are simply due to sleep abnormalities. The summation notation is a way to quickly write the sum of a series of functions. For wired recordings, mice were implanted with EEG and EMG electrodes for polysomnographic recordings. Sketch Quadratic Graphs by Completing the Square His orders also lowered the number of days an adult inmate could be subject to solitary confinement from 365 days to 60 days. Scale bar in the center image, 3 mm; other scale bars, 100 m. Simplifying Indices Binomial Expansion Approximations & Estimations The procedure to use the summation calculator is as follows: Sleep measurements were started at 8 weeks old following the AAV administration at 6 weeks old. problem solver below to practice various math topics. Even so, it becomes necessary to model the genes in combination with their vehicle as well as in combination with the vehicle's environment. From the supernatant, AAVs were concentrated by adding polyethylene glycol at a final concentration of 8% followed by centrifugation. Straight Line Graphs, Parallel & Perpendicular Lines Mark Scheme June 2013 Brain DNA was purified using an Agencourt DNAdvance (Beckman Coulter, USA). After the SSS measurements, we purified the AAV vector genomes from the mice brains and then quantified them with a WPRE-specific primer set and normalized to mouse genomes. Under light/dark (LD) conditions, the daily sleep duration of T287D-expressing Cry1/2 DKO and Per1/2 DKO mice was significantly higher than that of WT CaMKII-expressing mice (Fig 4A, 4B, 4E and 4F), and the relative magnitude of sleep increase is higher in the dark phase. Binomial Expansion Beginners Tutorial II It was further elaborated by the Buddhist atomists Dharmakirti and Dignga during the 1st millennium CE. Anyone can earn credit-by-exam regardless of age or education level. (D) Sleep parameters of mice expressing AIP2 or RARA mutant shown in Fig 2E and 2F during light or dark period. Poisson Distribution: Hypothesis Testing In parallel with these sleep-controlling phosphorylation residues in CaMKII, PP1 and PP2 have been shown to be involved in the dephosphorylation of CaMKII T286 phosphorylation in the postsynapse [59,60]. Integration by Substitution Tutorial I Trigonometric Equations - Identity Types Geometric Sequences & Series Tutorial I (C) In vitro kinase activity of CaMKII phosphomimetic mutants. Phosphorylation (%) indicates the percentage of the phosphorylated substrate relative to the total peptide in the presence or absence of CaM. Subsequently, the viral genome was obtained by phenol-chloroform-isoamyl alcohol extraction followed by isopropanol precipitation. Mark Scheme June 2011 After incubating at 37 C for 10 min, the reaction was stopped by incubating at 98 C for 10 min. Further Maths Paper 1 May 2020, 9FM0/02, Edexcel Jan 2022 IAL Pure Maths WMA11/01 Thus, the mechanism of sleep maintenance by T287D:T306D:T307D may not be attributed to the loss of CaMKIICaM interaction itself. Conceptualization, We used cell lysates of 293T cells expressing the CaMKII mutants, which can be used to measure the kinase activity of expressed CaMKII protein [39]. (A) Sleep/wake parameters of mice expressing the quadruple-phosphomimetic CaMKII mutants related to T311. Edexcel has redeveloped their AS/A level in Mathematics for international centres, called Edexcel The shaded areas represent SEM. Multiplying Polynomials Inverse & Self-Inverse Functions Exam Questions, Rules of Indices (Review) Pythagoras Theorem, Sine Rule, Cosine Rule, Area of non-right Triangle, Linear Inequalities (Review) To survey the role of multisite phosphorylation in the sleep control, we created a series of double-phosphomimetic mutants of CaMKII, in which besides T287, we mutated one of the remaining 68 S or T residues to D. Most of the analyzed these double-phosphomimetic mutants showed extended sleep duration similar to the T287D single mutant (Fig 5A and S10A Fig). May 2021 Pure Maths 3 9709/33 Questions June 2008 Worked solutions for some A-level maths past year examinations. Complex Numbers 8 Comparing imaginary numbers Square roots of a complex number The gene-centric view has been opposed by Ernst Mayr, Stephen Jay Gould, David Sloan Wilson, and philosopher Elliott Sober. For the comparisons of sleep duration, multiple testing was performed against WT CaMKII-expressing mice. CaMKII, calmodulin-dependent protein kinase II; EEG, electroencephalogram; EMG, electromyogram; NREM, nonrapid eye movement; REM, rapid eye movement; WT, wild-type; ZT, zeitgeber time. Differential Equations I Second Derivatives Otherwise, a 2-sample Wilcoxon test was applied. Visualization, For instance, an individual has a p = 1/2 in relation to his brother, and p = 1/8 to his cousin, so we would expect, ceteris paribus, greater altruism among brothers than among cousins. (G) Differences in transition probabilities (between wakefulness (W), NREM sleep (N), and REM sleep (R)) between mice expressing WT CaMKII or the T287D:T306D:T307D mutant. These residues did not exhibit significant sleep phenotypes in our single/double-phosphomimetic screening but may have a role in sleepwake control in other combinations of multisite phosphorylation of CaMKII. One necessary condition is that the selected entity must have a high degree of permanence and a low rate of endogenous change, relative to the degree of bias (differences in selection coefficients). Complex Numbers 2 Powers of i Multiplying Complex Numbers Binomial Expansion Examples II, Trigonometry Tutorial 1 Integration of Trigonometric Functions I In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. Social constructionism is a theory of knowledge which describes the relationship between the objectivity of reality and the capacity of human senses and cognition. A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. fast Fourier transformation; HPLC, The medium in each well was replaced with fresh culture medium 24 h after the transfection. Transition probabilities were calculated from all 2 consecutive epochs in the measurement period. The reduced sleep duration in SSS by AIP2-expression or Camk2b knockout can be attributed to the reduced NREM sleep because NREM sleep constitutes the most portion of total sleep time, although CaMKII/CaMKII may also have a role in the control of REM sleep as observed in reduced REM sleep duration in these EEG/EMG recordings. Binomial Distribution Tutorial Methodology, Questions on Triangles II, Midpoint & Distance Formula Indeed, T306 and T307 are well-established autophosphorylation target [1921]. See also S6S8 Figs. Although we could not completely exclude the possibility that any contaminated kinase phosphorylated each residue especially for the unconventional autophosphorylation residues, it is unlikely that a misregulated or contaminated Ca2+/CaM-independent kinase activity phosphorylated S26, S182, and T311 residues because these phosphorylation are suppressed in the absence of Ca2+ (condition #4). Logs & Exponential Equations II Another common interpretation is that the integral of a rate function describes the accumulation of the quantity whose rate is given. https://doi.org/10.1371/journal.pbio.3001813.s005. (D-F) Sleep phenotypes of mice expressing WT CaMKII or the T287D:T306D:T307D mutant measured by EEG/EMG recordings. Kinematics Vertical Motion II Since S182 phosphorylation has not been detected in culture cells/in vivo partly because of the unsuitable sequence around the S182 for conventional trypsin-based proteomics technique, its physiological role is currently unclear. First, they show ion selectivity, permitting some inorganic ions to pass, but not others.This suggests that their pores must be narrow enough in places to force permeating ions into intimate contact with the walls of the The T311 phosphorylation was also detected in the other set of phosphoproteomic analyses of in vivo mice brains [4], although sequence identity around the T311 residue makes it difficult to distinguish CaMKII and CaMKII. More Reciprocal Trig Identities May 2021 Prob & Stats 1 9709/53 The underlying data can be found in S1 Data. In addition, there are several mutants, of which kinase activities in cell lysates are not matched with the sleep phenotypes in vivo (e.g., T242D), suggesting the existence of an additional layer of regulation such as substrate specificity or protein localization. Methodology, Affiliations "[23] In other words, we expect selfish genes ("selfish" meaning that it promotes its own survival without necessarily promoting the survival of the organism, group or even species). Using the dot blot data, the cell lysate expressing each mutant CaMKII was diluted so that the relative expression levels between WT and mutant CaMKII are to be the same. Most mathematical activity involves the discovery of What are the changes to the International Advanced Level in Mathematics specification? Department of Systems Pharmacology, Graduate School of Medicine, The University of Tokyo, Bunkyo-ku, Tokyo, Japan, Roles Orange and magenta lines represent serine and threonine residues, respectively. Solutions January 2013 Conditional Probability & Probability Tree Diagrams Although the level of phosphorylation at S25 was indicated for approximately 5% of total CaMKII at 4-min incubation time [22], it is possible that the level of this phosphorylation continuously increases given the slow dynamics of autophosphorylation at S26 of CaMKII found in this study. Summing Finite Series I with limits, with geometric series, proof by induction Level up on all the skills in this unit and collect up to 3200 Mastery points! The simulation and estimation of time constants for the daily increase and decrease of NREM-EEG delta power were carried out as described in the previous study [27]. Binomial Expansion C4 Exam Questions I May 2021 Prob & Stats 2 9709/61 (J) Differences in transition probabilities (between wakefulness (W), NREM sleep (N), and REM sleep (R)) between WT CaMKII or T287D-expressing mice under the hSyn1 promoter. The definite integral of a function gives us the area under the curve of that function. The underlying data can be found in S1 Data. Details are provided in the Methods section. Mathematics (from Ancient Greek ; mthma: 'knowledge, study, learning') is an area of knowledge that includes such topics as numbers (arithmetic and number theory), formulas and related structures (), shapes and the spaces in which they are contained (), and quantities and their changes (calculus and analysis).. : no significance. In normal sexual reproduction, an entire genome is the unique combination of father's and mother's chromosomes produced at the moment of fertilization. Sum of moments about a point The Price equation was derived by George R. Price, working in London to rederive W. D. Hamilton's work on kin selection. : no significance. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. Matrices Finding Linear Transformations The synthesized gRNAs for Camk2b (150 ng/L in total) and Cas9 mRNA (100 ng/L) were coinjected into the cytoplasm of fertilized eggs in M2 medium (Merck, Germany or ARK Resource, Japan) at room temperature. PBS: PBS-injected mice (n = 6). Because CaMKII is known to switch its biochemical property through the autophosphorylation, it may be possible that some of the multisite phosphorylation status proposed above (i.e., multisite phosphorylations at S26, S182, T287, T306, T307, or T311) can be achieved through autophosphorylation. The cell lysates showed kinase activity towards conventional peptide substrate for CaMKII depending on both ectopic CaMKII expression and addition of Ca2+/CaM, suggesting that the effects of endogenous CaMKII and other kinases are negligible. More Graph Transformations Trigonometry C2 Exam Questions I The low Ca2+ concentration condition also promotes T311 phosphorylation, which is spatially close to T306 and T307. Inclined Planes Finding Coefficient of Friction & Missing Angles Actions with substantial costs therefore require significant values of p. Two kinds of factors ensure high values of p: relatedness (kinship) and recognition (green beards).

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