Expression Definition and 999 Threads

Gene expression is the process by which information from a gene is used in the synthesis of a functional gene product that enables it to produce end products, protein or non-coding RNA, and ultimately affect a phenotype, as the final effect. These products are often proteins, but in non-protein-coding genes such as transfer RNA (tRNA) and small nuclear RNA (snRNA), the product is a functional non-coding RNA. Gene expression is summarized in the central dogma of molecular biology first formulated by Francis Crick in 1958, further developed in his 1970 article, and expanded by the subsequent discoveries of reverse transcription and RNA replication.The process of gene expression is used by all known life—eukaryotes (including multicellular organisms), prokaryotes (bacteria and archaea), and utilized by viruses—to generate the macromolecular machinery for life.
In genetics, gene expression is the most fundamental level at which the genotype gives rise to the phenotype, i.e. observable trait. The genetic information stored in DNA represents the genotype, whereas the phenotype results from the "interpretation" of that information. Such phenotypes are often expressed by the synthesis of proteins that control the organism's structure and development, or that act as enzymes catalyzing specific metabolic pathways.
All steps in the gene expression process may be modulated (regulated), including the transcription, RNA splicing, translation, and post-translational modification of a protein. Regulation of gene expression gives control over the timing, location, and amount of a given gene product (protein or ncRNA) present in a cell and can have a profound effect on the cellular structure and function. Regulation of gene expression is the basis for cellular differentiation, development, morphogenesis and the versatility and adaptability of any organism. Gene regulation may therefore serve as a substrate for evolutionary change.

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  1. A

    How can the electron density expression be simplified using momenta?

    Suppose we have a system with M nuclei and N electrons the electron density is defined as: \rho(\mathbf{r}) = \sum\limits_{\sigma = \uparrow, \downarrow} \sum\limits_{i}^N \psi^{*}_{i}(\mathbf{r\sigma})\psi_{i}(\mathbf{r\sigma}) i would like to know if it is valid...
  2. U

    Find minimum value of the expression

    Homework Statement Let n be a positive integer. Determine the smallest possible value of $$|p(1)|^2+|p(2)|^2 + ...+ |p(n+3)|^2 $$ over all a monic polynomials p with degree n. The Attempt at a Solution Let the polynomial be x^n+c_{n-1} x^{n-1} +...+ c_1x+c_0 p(1) =...
  3. Y

    Rate law expression with solids and liquids

    Hello Forum! I was wondering: In the rate law expressions, I could never find an example with a solid or a liquid in the reactants in my textbook (Chemistry by Zumdahl). I searched Chemistry (Raymond Chang) and Principles of Molecular Chemistry, without any success. What happens to...
  4. Y

    MHB Drawing and finding the value of postfix expression

    I am ending with no operator in the end. So 1000 160 would be the answer or what. I do not know what to do from here. Please help!
  5. I

    MHB How Can You Find an Expression for t(n)?

    hi all, Would it be possible for you to explain how to reach a solution for this question, or explain the process that you need to find the solution thank you
  6. T

    Engineering (DC motor derive ω expression with respect time

    Homework Statement I try to derive the expression of ω with respect to t, but the problem is the armature current Ia or the flux is unknown. I don't know how to solve it. Anyone could give me ideas? Thanks a lotHomework Equations τ=J(ω/t) Vs=IaRa+Ea T=KEøIa Ea=KEøω
  7. Y

    MHB How to read this expression "A graph G = (V ,E)"

    How to read this expression "A graph G = (V ,E)"
  8. D

    How is Kp(T) Derived for Dissociation of H2O at High Temperatures?

    Hello I'm solving previous exams and there is this exercise that appears in almost every exam : Homework Statement Suppose v moles of a gas H2O are enclosed in a constant volume V at a low temperature so the gas is in aN undissociated state. At highest temperatureS, H2O molecules are...
  9. anemone

    MHB Factorization of an expression

    Factorize the expression $(1+a+\cdots+a^n)^2-a^n$.
  10. M

    An expression about kinetic energy

    Hi, all. Here is an expression about kinetic energy from analytical dynamics of Haim Baruh which confuses me. "Consider a particle and the case which the kinetic energy is only quadratic in terms of velocity of the particle. We take the differential form of work-energy principle and remove...
  11. B

    MHB Is this Tree of Algebraic Expression Correct?

    Hello I just wanted to see if I did this right. I've come up with two trees and I'm pretty sure one of them is correct, I'm just not sure. Construct the Tree of the algebraic expression: ((x - 2) + 3) / ((2 - (3 + y)) x (w - 8))
  12. A

    MHB State the differences between an expression and its simplified equivalent.

    State the differences between an expression and its simplified equivalent.
  13. S

    Proof of the nontrivial expression

    I'm looking for a proof of a validity of the inequation: (n-1)\sum_{i=1}^{n}x_{i}^{2}\neq 2\sum_{i=1,j=1,j<i}^{n}x_{i}x_{j} Assumptions: n\geq 2 \exists (i,j),x_{i}\neq x_{j} i=1,...,n j=1,...,n I have no idea how to prove those non-trivial expressions.
  14. gfd43tg

    AC Op-Amp output voltage expression in time domain

    Homework Statement For vi(t) =V0 cosωt, obtain an expression for vout(t) in the circuit below and then evaluate it for V0 = 4 V, ω = 400 rad/s, R = 5 kΩ, and C = 2.5 μF. Homework Equations The Attempt at a Solution For this problem, I am having difficulty taking that second term...
  15. S

    Summation of 'n' terms of the given expression

    Homework Statement find the general formula to calculate the sum Homework Equations 1+11+111+1111+11111+....upto n terms The Attempt at a Solution 100 + (101+100) + (102+101 + 100) + (103 + 102+101 + 100) + ... ==> (100+100+100+...upto n terms) + (101+101+101+...upto n-1 terms)...
  16. MarkFL

    MHB Simplifying tan(2arccotx) - Peter's Question at Yahoo Answers

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  17. K

    Expression for current through loop as a function of time

    Homework Statement An N-turn circular coil of radius r with a total resistance of R is placed such that the normal to its plane is parallel to the +z axis. A uniform magnetic field varies with time according to B=B0sin(\omegat) where the amplitude B0 and angular frequency ω are constants...
  18. K

    Derive the analytic expression of a function by its Taylor expansion

    Homework Statement Actually this is not from homework. It occurs in my brain this afternoon. Is it possible to derive the analytic expression of a function by its Taylor series expansion? For example, given the following expansion, how to derive the analytic expression of it? f(x) =...
  19. N

    Simplify this expression for an ellipse

    Homework Statement Simplify sqrt(x^2+(y-sqrt(5))^2) = 8 - sqrt(x^2 + (y+sqrt(5))^2) The Attempt at a Solution I know squaring both sides, collecting like terms and simplifying gets the equation but in my solution manual they do it a different way that is a lot shorter and I need help...
  20. anemone

    MHB Evaluate trigonometric expression

    Without the help of calculator, evaluate $\cos \dfrac{\pi}{7}\cos \dfrac{2\pi}{7}\cos \dfrac{4\pi}{7}$.
  21. T

    Arranging this expression into a laplace transform

    Hi Guys, I have an expression that i am struggling to manipulate into a laplace transform. This expression should fit one or a combination of the common transform pairs. I believe the transform the expression should be fitting is either a unit step 1/s a unit ramp 1/s^2 an exponential 1/s+a...
  22. A

    Evaluating a Finite Sum to a Closed Form Expression

    I have a finite sum of the form: ∑n=1Nexp(an+b√(n)) Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.
  23. J

    Extremely easy math, but need expression

    Okay, This could be the easiest math question on here... but I'm going to ask the dumb question anyway. I have several coordinate points to solve for, and in each case I subtract the same amount from the previous "x" to get the next "x" value (X2...3...4...5...). The only point where I...
  24. J

    MHB Solve Quadratic Equation: -2x^2-14x-49

    Q4.) Quadratic equation: \frac{-2x^2-14x-49}{x^3-7x^2}
  25. Albert1

    MHB What is the value of the expression given these equations?

    given : $\dfrac {x}{m}+\dfrac{y}{n} +\dfrac {z}{p}=1$ $\dfrac {m}{x}+\dfrac{n}{y} +\dfrac {p}{z}=0$ find: $\dfrac {x^2}{m^2}+\dfrac{y^2}{n^2} +\dfrac {z^2}{p^2}=?$
  26. Albert1

    MHB How to Simplify Radical Expressions with Multiple Radicals?

    simplify: $\sqrt {21-4 \sqrt 5 +8\sqrt 3 - 4\sqrt {15}}$
  27. evinda

    MHB How can I continue to find a regular expression?

    Hello! :) I have a question: Suppose that $\Sigma=\{0,1\}$.Is the language $\{0^{m}1^{n}:m+n \geq 2\}$ regular? I tried to find a regular expression.I checked the case $m+n=2$ and I found that the possible words are $00,01,11$ .But..how can I continue? :confused:
  28. F

    Help putting expression in form of miniterms (Boolean algebra)

    Homework Statement I need to obtain the minimum second order circuit of the function: Homework Equations The Attempt at a Solution I know that in order to get the minimum second order circuit, I need to use K-Map using both miniterms and maxiterm and compare them. My problem is to put the...
  29. H

    Dirac Expression for Vector Potential of a Magnetic Monopole Problem

    Hi, Homework Statement Consider the vector potential, \vec{A}(\vec{x}), below. The problem is to calculate \vec{A}(\vec{x}) explictly, and show that it has components A_{r}, A_{\theta} and A_{\phi} Homework Equations \vec{A}(\vec{x}) = \frac{g}{4\pi} \int_{-\infty}^{0} \frac{dz'...
  30. C

    Expression for volume as a function of pressure

    Homework Statement When pressure is applied to a liquid, its volume decreases. Assuming that the isothermal compressibility κ=-1/V(δV/δP) is independent of pressure, derive an expression for the volume as a function of pressure. Homework Equations The Attempt at a Solution I don't...
  31. M

    Simplifying an Expression with x>>a: Step-by-Step Guide

    Hi, I've attached a screenshot in which a solution simplifies an expression given x>>a. I have been trying to simplify and express the equation as shown, but keep failing to recognize how they reached their solution. If anyone could provide a step-by-step breakdown that would be greatly...
  32. E

    Expression of fields in Faraday rotation

    Hello! Talking about propagation of an electro-magnetic field in a non-isotropic medium, I've got some troubles with the expression in object, used to show the Faraday rotation of the polarization of a field. Homework Statement An electro-magnetic field enters a particular medium...
  33. B

    Is there a closed form of this expression?

    Hi, (not homework/academic) Is a closed form of the following expression possible? Either way, some pointers in the right direction would be really helpful. H(s)=\sum_{n=-\infty}^\infty \frac{k^n}{k^n+a/s} Thanks, D
  34. C

    Why this expression is time-reversal odd?

    P and k are four-momentum of two particles. I read in a paper which said that [\slashed{P},\slashed{k}]=\slashed{P}\slashed{k} - \slashed{k}\slashed{P} is time-reversal odd. Why?
  35. E

    How to determine Tchebysheff polynomial general expression

    Hello! Tchebysheff polynomials are often defined with trigonometric functions: T_m (x) = \begin{cases} \cos(m \arccos (x)) & -1 \le x \le 1\\ \mathrm{cosh} (m \mathrm{arccosh} (x)) & x > 1\\(-1)^m \mathrm{cosh} (m \mathrm{arccosh} |x|) & x < 1 \end{cases} But they are also polynomials, and...
  36. anemone

    MHB Finding Maximum Value of an Expression with Respect to $x$

    Hi MHB, I am completely clueless about how to tackle the problem below, given I noticed $y$ increases as $x$ increases, so there is no maximum point over the entire domain for that function, that is for $x \ge 0$, isn't that so?(Tmi) For what value of $x$ is the expression in...
  37. N

    Trying to understand an expression in Peano's Principia Arithmetices

    In the attached image, I am having trouble with point 66. I realize the notation is a bit archaic, so I'll explain as much as I can. [(x,y)∈]a means "the set of solutions of the proposition a(x,y)." For example, the set of solutions to the proposition x < y. -= means "is not equivalent to"...
  38. S

    MHB Question concerning simplification of numerical expression with square roots.

    how does \frac{5700}{\sqrt{15,300}} turn into \frac{570}{\sqrt{153}} ??
  39. T

    Theoretical expression for relationship between height and force

    Homework Statement I did an experiment investigating what effect height has on force and now i need a theoretical value to compare it to Homework Equations f=ma but i don't think acceleration is constant here The Attempt at a Solution f=ma f=0.104x9.8 f=1.01 i got 49 N with...
  40. D

    Limit of expression containing unknown function.

    I would like to get an answer or pointers to suitable material, on the following question: I know that ∫|f(x)|2dx is finite. Can we say that lim x→±∞ x*(d/dx)|f(x)|2 is zero? Are there any theorems about such limits with unknown functions that have some known properties? Basically this question...
  41. NATURE.M

    Rotational motion: Expression for Angular Velocity

    Homework Statement A solid flywheel of radius R and mass M is mounted on a light shaft of radius r so that the axis of rotation is horizontal. A light, inelastic rope is wound around the drive shaft and is connected, via a light, frictionless pulley to a mass m, which is suspended a height h...
  42. U

    Finding max value of this expression

    Homework Statement In a triangle ABC let A,B,C denote the angles of the triangle. Then maximum value of the expression sinA/A + sinB/B + sinC/C is Homework Equations The Attempt at a Solution Applying Cauchy Shwarz inequality \dfrac{sinA}{A} + \dfrac{sinB}{B} + \dfrac{sinC}{C} \leq...
  43. ajayguhan

    Expression of bulk modulus of a cube in terms of strain

    In my text it's given when a cube underwents a uniform unit tensile force be applied in all six faces, bulk module=1/3(α-2β) Where α is longitudinal strain and β is lateral strain.is there a derviation for it..? And it states in x direction there will be increase in length and in y, z...
  44. I

    Foundations of Quantum Mechanics: Unknown Expression

    Hi, I'm reading a paper on foundations of QM where the expression below appeared \frac{1}{2}m\left(\frac{d^2 \overrightarrow{r}^2}{dt^2}\right)=m\left(\frac{d^2 \overrightarrow{r}}{dt^2}\right).\overrightarrow{r}+m\left(\frac{d \overrightarrow{r}}{dt}\right)^2 I cannot identify where it...
  45. N

    Analytic expression to find the range of non-negative numbers in array

    Hello, I have an array of length M. Some of the indices are non-negative. I need to derive a function/analytic expression (preferably linear or convex) that finds the span of indices for which the indices are non-negative. Example: Let p denote the desired vector. Let, p = [0 0 0.3 2.6...
  46. L

    Making an expression an explicit function of time

    Hello, This actually isn't a homework question, more of a curiosity, but since its a book problem I decided to post it here. Homework Statement An object is released from rest at time t=0 and falls through the air, which exerts a resistive force such that the acceleration a of the the...
  47. B

    Evaluating expression (numerical analysis)

    Hello, using octave when I evaluate this expression (1+1/x)*x-x, with x = 10^(15) i get as result 1.125, I didn't undesrtood why, I know that octave show 15 digits in format long so when i evaluate (1+1/x)*x i get 1e15, the last digit is not visible and it is 1, so when i do substraction i get...
  48. F

    L'Hôpital's rule and weird expression

    Homework Statement Find, using l'Hôpital's rule: lim x-> ∞ ((tan(ax)-atanx)/(sin(ax)-asinx)) Where a is a non constant greater than ± 1. Homework Equations -The Attempt at a Solution I can't work out anything from this point. I don't know how to change or factorize the expression (is there a...
  49. Saitama

    Triangle problem - Evaluating the given expression

    Homework Statement In a triangle ABC, with usual notation, if ##a^2b^2c^2 (\sin 2A + \sin 2B + \sin 2C) = λ(∆)^x## where ∆ is the area of the triangle and x ##\in## Q, find (λx). Homework Equations The Attempt at a Solution The usual notation is: a,b,c are three sides of the...
  50. U

    Can Absolute Entropy Be Calculated Directly from State Variables?

    Homework Statement So as a part of a very long question on homework for thermodynamics, I and some of my friends got into a debate about how to write an expression for entropy at a particular state. Homework Equations delS(state 1 to 2)= Cv*ln(T2/T1)+R*ln(V2/V1) (from constitutive...
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