Solving Logarithmic Equations The underlying numerical data can be found in S1 Data, and uncropped or raw image files for S3A Fig are provided in S2 and S3 Data files. Trig. Simplifying Indices (J) Differences in transition probabilities (between wakefulness (W), NREM sleep (N), and REM sleep (R)) between mice expressing AIP2 or the RARA mutant. Area within a Parametric Graph The expanded ESCs were collected by adding 0.25% trypsin-EDTA solution and prepared as a cell suspension. It was further elaborated by the Buddhist atomists Dharmakirti and Dignga during the 1st millennium CE. Tangents & Normal I 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. In brief, 200 L of Solution B containing phosphatase inhibitors was added to the 293T cells cultured in a 35-mm dish. 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. (D) Schematic diagram of CaMKII inhibition by AIP2 expression. The dirty segments were excluded from the subsequent processes [72]. Scale bar in the center image, 3 mm; other scale bars, 100 m. Integration Help IV These datasets include known CaMKIIs substrate/binding proteins that show different phosphorylation levels in response to the sleepwake cycle or sleep deprivation, such as NMDA receptors and Synapsin-1 protein. Department of Systems Pharmacology, Graduate School of Medicine, The University of Tokyo, Bunkyo-ku, Tokyo, Japan, Each joint has its own level of flexibility, expressed in degrees. Oct 2020 Pure Maths 3 9709/33 Thus, the expected sleep regulation sequence is physiologically reasonable: the increased transition rate from awake to sleep phase promoted by T287 phosphorylation, and then the induced sleep is stabilized by subsequent multisite T287/T306/T307 phosphorylation (Fig 6D). Mar 2022 Mechanics 4 9709/42, Oct 2021 Mechanics 4 9709/41 (C) Total CaMKII and T286-phosphorylated peptides from brains of sleep-deprived and control mice, analyzed by SRM quantitative mass spectrometry. Parametric Equations II He saw the theory as leading to a simplistic "algorithmic" theory of evolution, or even to the re-introduction of a teleological principle. Mechanics Exam Questions Friction There was no significant change in normalized delta power during NREM sleep (S7B and S7C Fig). nonrapid eye movement; PTS, Summation notation is a speedy method for writing the sum of a series of functions. 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). The Summation Calculator is a free online tool that displays the sum of the given series. Questions January 2013 AAV, adeno-associated virus; CaMKII, calmodulin-dependent protein kinase II; hSyn1, human synapsin-1. In summary, the sleep induction and maintenance effect of CaMKII elicited by T287 phosphorylation followed by T306 and T307 phosphorylation appears to be terminated by S26 and S182 phosphorylation, and phosphorylation of T311 may only cancel the sleep induction activity elicited by T287 phosphorylation. (D) Time series changes of sleep-controlling residues phosphorylation under different Ca2+ conditions in vitro. We should note that although our AAV-based screening covers every possible phosphorylation mimicking mutation for single mutants, the possible combinations of multisite phosphorylation in CaMKII are far more numerous than those tested in this study. Mechanics Exam Questions Impulse, Momentum As in the case of T287D, a tendency for increased sleep duration and PWS in the del mutant was observed in both light and dark phases, and the relative amount of increased sleep duration compared with WT is higher in the dark phase (Fig 2C, S6A and S6B Fig). The mice used in each experiment were randomly chosen from colonies. The brains of the sleep-deprived and control mice were collected for MS-based peptide quantification. Oct 2020 Physics 2 9702/23, May 2015 C2 Exam Questions Binomial Expansion Tutorial May 2021 Pure Maths 1 9709/11 (D-F) Sleep phenotypes of mice expressing WT CaMKII or the T287D:T306D:T307D mutant measured by EEG/EMG recordings. Defining integrals with Riemann sums. May 2020 Pure Maths 3 9709/31 Unexpectedly, we also noticed that the increased PSW by AIP expression is mostly observed in the dark phase (S6C and S6D Fig). However, the underlying mechanism by which CaMKII supports sleep regulation is largely unknown. Questions June 2012 Equilibrium - taking moments Oct 2021 Pure Maths 3 9709/32 (E, F) Sleep profiles (E) and total sleep duration from ZT0 to ZT2 (F) of mice expressing WT CaMKII (WT, n = 6) and the CaMKII T287D mutants (T287D, n = 4) after cage change at ZT0. Formal analysis, Another common interpretation is that the integral of a rate function describes the accumulation of the quantity whose rate is given. Solving Equations using Identities Edexcel Jan 2021 IAL Pure Maths WMA11/01 If the central dogma is true, and if it is also true that nucleic acids are the only means whereby information is transmitted between It dominated marine trade in the Baltic Sea, the North Sea and along the connected navigable rivers during the Late Middle Ages (12th to 15th centuries). For data analysis, we excluded the first day and used 4 days of measurement data under each light condition. The company provided support in the form of salary for Y.N., and technical advice on the setup of mass spectrometers. Edexcel Jan 2020 IAL Pure Maths WMA13/01 (B) Sleep parameters of mice expressing the CaMKII del mutants shown in Fig 2B and 2C during light or dark period. In this vein, geneticist J. Writing review & editing, Affiliations Biology. Step 2: Now click the button Submit to get the output. CaMKII, calmodulin-dependent protein kinase II; EEG, electroencephalogram; EMG, electromyogram; hSyn1, human synapsin-1; NREM, nonrapid eye movement; REM, rapid eye movement; WT, wild-type; ZT, zeitgeber time. The membrane was washed by TTBS (0.9% NaCl, 0.1% Tween-20, and 100 mM Tris-HCl at pH 7.5) and nonspecific protein binding was blocked by incubating with Blocking One solution (Nacalai Tesque, Japan) for 1 h at room temperature. CaMKII, calmodulin-dependent protein kinase II; MS, mass spectrometry; SRM, selected reaction monitoring. Vector genomes per cell were calculated by dividing the copy number of AAV vector genomes by diploid copies of the Tbp gene in the sample. Reports suggest that T311 autophosphorylation occurs in CaMKII [22] and that the phosphorylation level of the corresponding residue in CaMKII was reduced during the dark phase (mostly awake phase in mice) [3]. MS data were analyzed by Proteome Discoverer version 2.2 (Thermo Fisher Scientific, USA) with the Swiss-Prot section of UniProtKB mouse database (as of August 9, 2018). 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. Arithmetic Sequences & Series II Transformation of Trig. Solutions June 2013 Because it is well understood that the sleepwake cycle affects the learning process, CaMKII-expressing mice with changes in sleep phenotype may also have changes in learning phenotype. Division of Molecular and Medical Genetics, Center for Gene and Cell Therapy, The Institute of Medical Science, the University of Tokyo, Minato-city, Tokyo, Japan, Current address: Laboratory of Animal Genetics and Breeding, Graduate School of Bioagricultural Sciences, Nagoya University, Chikusa, Nagoya, Japan, Affiliation Step 2: Now click the button Submit to get the output. We prepared an internal control by mixing 500 L of each peptide solution. Infinite Series Definition Donate or volunteer today! Simplifying Algebraic Fractions III Biology Papers; Biology Revision; Chemistry. C57BL/6N mice (CLEA Japan, Japan) were housed in a lightdark controlling rack (Nippon Medical & Chemical instruments, Japan) and habituated to a 12-h LD cycle for at least 1 week. The phosphorylation hypothesis of sleep [2,6] assumes that the neural activity associated with wakefulness acts as an input to activate sleep-promoting kinases such as CaMKII/CaMKII [2], SIK1/SIK2/SIK3 [7,8], and ERK1/ERK2 [9]. The trapped peptides were subjected to dimethyl-labeling with formaldehyde (light label) as described above. A-level. Phosphorylation of S26 (CaMKII) or S25 (CaMKII) residue in mice brain. Williams argued that "[t]he natural selection of phenotypes cannot in itself produce cumulative change, because phenotypes are extremely temporary manifestations." The target site abundance was calculated using a standard curve obtained from WT genomic DNA. Solving Logarithmic Inequalities The design of gRNAs for Camk2b was previously shown as set 1 in a previous study [2]. 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). The T287D:T306D:T307D mice had higher NREM to NREM and REM to REM transition probabilities than WT-expressing mice (Fig 5G). Infinite Series Definition 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. We can approximate integrals using Riemann sums, and we define definite integrals using limits of Riemann sums. Besides Richard Dawkins and George C. Williams, other biologists and philosophers have expanded and refined the selfish-gene theory, such as John Maynard Smith, George R. Price, Robert Trivers, David Haig, Helena Cronin, David Hull, Philip Kitcher, and Daniel C. Dennett. Binomial Expansions with Surds Phosphorylation (%) indicates the percentage of the phosphorylated substrate relative to the total peptide in the presence or absence of CaM. Questions June 2010 Genetic screening studies have revealed that protein kinases play an important role in sleep duration regulation. Integration: Mixed Examples II Discrete Random Variables Solutions June 2011 Proving Trig Identities IV These genes can persist in a population even when their transmission results in reduced fertility. Multiple comparison tests were performed between all individual groups. NCERT Solutions For Class 12 Biology; NCERT Solutions For Class 12 Maths; NIOS A Level Syllabus. An equal amount of medium-labeled internal control mixture was added to each light-labeled individual sample. https://doi.org/10.1371/journal.pbio.3001813.s007. The DTE of Map2 were amplified and cloned from C57BL/6N mouse genomic DNA [65]. The phenotypic effect of a particular gene is contingent on its environment, including the fellow genes constituting with it the total genome. Proof of A sin x + B cos x = R sin (x + alpha) Approximately 15 to 30 embryos were then transferred to the oviducts of pseudopregnant female ICR mice. Mark Schemes January 2011 Similar to the case of T287D mutant, reduced sleep duration by AIP2 expression was observed both in light and dark phases, but the magnitude of effect in the amount of sleep is higher in the dark phase (Fig 2F, S6C and S6D Fig). The third personal leadership is an "inner" level and concerns a person's growth toward greater leadership presence, knowhow and skill. (Japan Agency for Medical Research and Development: https://www.amed.go.jp/en/index.html), Grant-in-Aid for Scientific Research (S) JP18H05270 (JSPS KAKENHI) (to H.R.U.) Mark Scheme January 2007, A-level Exam Q1 - Q5 Trigger point therapy isnt too good to be true its probably just ordinary good. (C) Sleep transition profiles of mice expressing AIP2 or RARA mutant under hSyn1 promoter shown in Fig 2E and 2F. C3 and C4 have been combined to create one unit. Summation value of the given function is displayed in a fraction of seconds. Remainder & Factor Theorem I Additional Maths 2008 Q5 - Q8 For DIO constructs, the inverted FLAG-Camk2b sequence flanked by lox2272 and loxP was inserted between the hSyn1 promoter and the Camk2b 3 UTR of the pAAV vector as illustrated in Fig 3G. The underlying data can be found in S1 Data. Donate or volunteer today! Most mathematical activity involves the discovery of Based on the purpose of the comparison, normality and equality of variance were checked, and appropriate statistical method was selected. In summary, we propose that multisite phosphorylation status of CaMKII controls different aspects of sleep-promoting effect of CaMKII including sleep induction, maintenance, and potential cancellation effect of the sleep-promoting effect. For nuclear staining, the brain was rinsed with PBS and incubated in 1:250 diluted RedDot2 (Biotium, 40061) in staining buffer (10% (w/w) Triton X-100, 10% (w/w) Urea, 5% (w/w) N,N,N,N-Tetrakis(2-hydroxypropyl)ethylenediamine, 500 mM NaCl) for 3 days at 37 C. Multiple comparison tests were performed between all individual groups in each phase. Modulus Graphs II Camk2b-FLAG ssODN (capital letter: FLAG tag sequence). Statistics & Mechanics Sample Paper 3 June 2017, Further Maths Paper 1 May 2020, 9FM0/01 Mark Schemes January 2007 Although the sleepwake cycle affects the level of such multisite autophosphorylation of CaMKII and CaMKII [35,24,25], little is known about the actual function of the multisite autophosphorylation in the regulation of the sleepwake cycle. Application units available include: Pure Maths Paper 1 June 2018 Alternatively, it is equally possible that the possible effect of CaMKII mutants on neuronal plasticity is not just the functional output of sleep abnormalities, but changes in the sleep phenotypes are the behavioral phenotype associated with such changes in the neuronal functions. A gene never has a fixed effect, so how is it possible to speak of a gene for long legs? Dulbeccos Modified Eagle Medium; DTE, Methodology, Oct 2020 Pure Maths 1 9709/12 After 37 C overnight incubation, 5 g of trypsin (Roche, Switzerland) was added and the mixture was further incubated at 37 C overnight. Graphs I It is also called sigma notation because the symbol used is the letter sigma of the Greek alphabet. The regulation process of CaMKII by autophosphorylation serves as a neuronal timer in a minutes timescale in fruits fly [15]. Biology is the scientific study of life. The dimethyl-labeled spike peptides were eluted with an 80% acetonitrile and 0.1% TFA solution and dried with a SpeedVac (Thermo Fisher Scientific, USA). After further incubation at 98 C for 30 min, the samples were reduced with 10 mM dithiothreitol (FUJIFILM Wako Pure Chemical, Japan) at room temperature for 30 min, and then alkylated with 100 mM iodoacetamide (Sigma-Aldrich, USA) at room temperature for 30 min. Comparative biology and evolution. To investigate possible neuronal cell types responsible for the CaMKII-mediated sleep induction, we expressed the CaMKII mutants under the Camk2a promoter, which is a well-characterized promoter inducing gene expression preferentially to the excitatory neurons [34]. As Fig 3A and 3B show, the daily sleep duration of T287D mice was higher than that of WT-expressing mice, which is consistent with the results obtained with the hSyn1 promoter. Edexcel Oct 2020 IAL Pure Maths WMA13/01 Sleep measurements were started at 8 weeks old following the AAV administration at 6 weeks old. Differentiation: Maximum Volume Oct 2020 Physics 1 9702/13, Mar 2021 Physics 2 9702/22 After 10 days of recovery, the mice were placed in experimental cages with a connection of spring supported recording leads. The gene-centered view of evolution is a model for the evolution of social characteristics such as selfishness and altruism.. Acquired characteristics. Other than sleep control, phosphorylation-mimicking or nonphosphorylatable-mimicking mutants of CaMKII have been shown to exhibit defects in neuronal plasticity and some type of learning [49,50]. Continuous Random Variable: Mode, Mean & Variance Your Mobile number and Email id will not be published. Methodology, T287-phosphorylated CaMKII induces sleep from wakefulness (sleep induction). We do not currently have a straightforward explanation for this observation, but some states of CaMKII/CaMKII related to the interaction with AIP2 might be modulated by external light conditions. Because knockout mice of Camk2b showed the most pronounced decrease in sleep duration per day compared with Camk2a knockout mice [2], this study will focus on CaMKII. Addition of Ca2+ also promoted the S26 and S182 phosphorylations following to T287 phosphorylation. The fundamental theorem of calculus ties The Hanseatic League was a commercial and defensive alliance of the merchant guilds of towns and cities in northern and central Europe. Investigation, (A) Calculated transduction efficiency plotted against sleep duration. Thus, the mechanism of sleep maintenance by T287D:T306D:T307D may not be attributed to the loss of CaMKIICaM interaction itself. The fundamental theorem of calculus ties integrals and derivatives together and can be used to evaluate various definite integrals. Sigma (/ s m /; uppercase , lowercase , lowercase in word-final position ; Greek: ) is the eighteenth letter of the Greek alphabet.In the system of Greek numerals, it has a value of 200.In general mathematics, uppercase is used as an operator for summation.When used at the end of a letter-case word (one that does not use all caps), the final form () is used. The proposed sleep maintenance effect is also supported by the increased sleep episode duration observed in T287D:T306D:T307D mice, while such effect is less evident in T287D mice (S10E Fig). The gRNA target sequence and a donor sequence were selected according to previous study [71]. Sequences: Recurrence Relations CaMKII WT or T287D were expressed under Camk2a promoter. These phosphoproteomics analyses support the possible role of phosphorylation at S26 or T311 in the regulation of CaMKII/CaMKII in mice brains in vivo. Transduction efficiency was estimated based on previous reports [80,81]. Thus, the background kinase activity, if any, originated from endogenous 293T proteins would be the same among cell lysates. Department of Systems Pharmacology, Graduate School of Medicine, The University of Tokyo, Bunkyo-ku, Tokyo, Japan, Roles If the central dogma is true, and if it is also true that nucleic acids are the only means whereby information is transmitted between Resources, Current address: International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo, Bunkyo-ku, Tokyo, Japan, Affiliation Social constructionism is a theory of knowledge which describes the relationship between the objectivity of reality and the capacity of human senses and cognition. Multisite phosphorylation encodes complex biochemical systems such as the sequential triggering of multiple events and the integration of multiple signals (such as AND logic gates) [53,54]. Questions January 2008 Questions June 2013 Proving Trig Identities II Geometric Sequences & Series Tutorial II Quadratic Log Equations (A) Daily sleep duration, averaged over 6 days, of mice expressing CaMKII double-phosphomimetic mutants (n = 512). Complex Numbers 4 Sum & product of roots A sequence is a list of numbers or events that have been ordered sequentially. May 2021 Mechanics 4 9709/41 This suggests that CaMKII elicits the transition between wake and sleep. Because it is still challenging to comprehensively predict phosphorylation residues based on sequence and structural information, we decided to assess the contribution of these 69 residues to sleep regulation by expressing a series of phosphomimetic mutants of CaMKII, in which aspartic acid (D) replaced one of the phosphorylable 69 residues. C57BL/6N females (4 to 6 weeks old, CLEA Japan, Japan) were superovulated and mated with C57BL/6N males (CLEA Japan, Japan). [9] J. Solutions January 2007, Questions May 2014 The mutants with blue labels exhibited <25% lower expression than the WT in both trials (see black and orange dashed lines in panel B).
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