What is Expression: Definition and 999 Discussions

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. S

    MHB An expression resembling Laguerre

    This was posted to calculus forum. I suppose it should have been posted here. I am trying to find a closed form expression/or limit as $n\implies\infty$ of ${S}_{n}=\sum_{k=0}^{n}{n \choose k} {a}^{k} \sum_{j=0}^{n}{n \choose j}\frac{{b}^{n-j}{c}^{j}}{(k+j)!}$ where $a$ , $b$ and $c$ are...
  2. olgerm

    Simplifying expression with vectors

    Homework Statement To simplify: ##\mid \vec b -\frac{\vec a*\vec b}{\vec a*\vec c} * \vec c \mid## ##\mid \vec b -\frac{(\vec a*\vec c)*(\vec b*\vec b)-(\vec a*\vec b)*(\vec b*\vec c)}{(\vec a*\vec b)*(\vec c*\vec c)-(\vec a*\vec c)*(\vec b*\vec c)} * \vec c \mid## Vectors may be any...
  3. X

    How can I represent this expression as a Fourier Transform?

    Hello, I hope I am posting this in the correct forum topic. It really is more of a "mathy" type of question, but I am posting it here because it deals with radar, and this type of math is used a lot in radar. To the mods, feel free to move it to a more suitable location if desired. I have...
  4. L

    Determining the complex expression using Thevnin's theorem

    I tried my best but I wasn't able to solve this can someone please provide me with a detailed solution. Here 's the question : Establish the expression of Vs/Ve (complex) using Thevnin's theorem Here is the circuit : I spent 4 hours trying to solve this but I had no clue how. I'am having...
  5. C

    Find expression for electric field from magnetic field

    Homework Statement In a region of space, the magnetic field depends on the co-ordinate ##z## and is given by $$\mathbf{B} = \hat{\jmath} B_0 \cos \left(kz - \omega t \right)$$ where ##k## is the wave number, ##\omega## is the angular frequency, and ##B_0## is a constant. The Electric Field in...
  6. S

    MHB Prove that the expression is a valid argument using the deduction method

    (∃x)[P(x) → Q(x)]∧(∀y)[Q(y) → R(y)]∧(∀x)P(x) → (∃x)R(x)
  7. S

    Math expression for a developing waveform?

    Hi all! I have a question about representing waves mathematically. I hope it will make sense. The waves I've been learning about are of the form F(x-vt), which represents a wave-form, every point of which is translated spatially with velocity v. I am wondering if there is a way to...
  8. Odious Suspect

    When to introduce absolute value in hyperbola expression?

    We begin with this definition of a hyperbola. \left(\overline{F_1 P}-\overline{F_2 P}=2 a\right)\land a>0 Perform a few basic algebraic manipulations. \sqrt{(c+x)^2+y^2}-\sqrt{(x-c)^2+y^2}=2 a \sqrt{(c+x)^2+y^2}=2 a+\sqrt{(x-c)^2+y^2} (c+x)^2+y^2=4 a^2+4 a \sqrt{(x-c)^2+y^2}+(x-c)^2+y^2...
  9. Taryn1

    MHB Write a trigonometric expression as an algebraic expression

    This problem probably should be easy, but I don't remember learning the basic way to do these problems: Write the trigonometric expression as an algebraic expression: cos(arccos x + arcsin x) The answer is zero, but I don't know how to get there...
  10. M

    Quantum 1D box obtain an expression for the normalization constant

    Homework Statement An electron in a one-dimensional box with walls at x =(o,a) is in the quantum state psi = A o<x<a/2 psi = -A a/2<x<a A) obtain an expression for the normalization constant, A. B) What is the lowest energy of the electron that will be measured in this state...
  11. C

    Symbolic Expression for Speed of Draining a Tank

    Hi, I've completed an experiment in which I measured the height of the water in the tank with time. I plotted my results on graph paper as a graph of height against time, resulting in a curve of decreasing gradient, slightly resembling that of the e^(-kx) graph. 1) I am asked to symbolically...
  12. F

    Finding a closed form expression given decimal approximation

    Good evening. Is there a way to take a decimal approximation and see if there is a relatively simple expression? I'm guessing there might be software for this, but I'm not sure I'm even asking the appropriate question. If it matters, the number I'm after is...
  13. phys-student

    Finding expression for non-uniform current density of a wire

    Homework Statement A long, straight wire, radius R, carries total current I. The current is distributed in the wire so that the current density is proportional to s, the distance from the center of the wire. (a) Write an expression for the current density J in the wire, as a function of s...
  14. K

    Ideal gas volume work expression (adiabatic)

    Homework Statement I have the following task: Homework EquationsThe Attempt at a Solution But I don't understand how to solve it. Can somebody help me?[/B]
  15. anemone

    MHB Find the maximum and minimum of an expression

    Find the maximum and minimum of $x^3+y^3+xy(x^2+y^2)$ given $x,\,y$ are two non-negative real numbers that satisfy $x+y+xy=3$.
  16. ognik

    MHB Check another visualise vector expression

    $ \left( \vec{r} - \vec{a} \right). \vec{r} = 0 $ Please check this: Then, $ r^2 - a.r = 0 $, then $ \left( r - \frac{a}{2} \right)^2 - \left(\frac{a}{2}\right)^2 = 0 $, then $ \left( x - \frac{a}{2}\right)^2 + \left(y - \frac{a}{2}\right)^2 + \left( z - \frac{a}{2}\right)^2 =...
  17. ognik

    MHB I want to visualise this vector expression

    The vector r, starting at the origin, terminates at and specifies the point in space (x, y, z). A surface is swept out by the tip of r if $ (\vec{r} −\vec{a}) · \vec{a} = 0 $. $\vec{a}$ is a constant vector... 1) I tried $ (r - a).a = 0, \therefore r.a = a^2$, but still can't 'see' what shape...
  18. P

    Deriving the Force-Position Relationship for a Spring Powered Model Car

    Homework Statement In your design of an experimental spring powered model car, you note that the speed of the car (mass Mc) increases as the car travels further. The exact relationship is that v(x) = C|x|, where C is a constant and x is the position of the car with respect to the starting...
  19. alexmahone

    MHB Find a closed-form expression for f(n)

    Find a closed-form expression for $f(n)$ where $f(n)=1+n+n(n-1)+n(n-1)(n-2)+...+n(n-1)\cdots2$ for $n>1$ and $f(1)=1$. (So, $f(2)=1+2=3$ $f(3)=1+3+3\cdot 2=10$ $f(4)=1+4+4\cdot 3+4\cdot 3\cdot 2=41$ and so on.)
  20. L

    How Does cos(θ)sin(θ+φ)-sinθcos(θ+φ) Simplify to sinφ?

    Can someone please show me, step-by-step, how cos(θ)sin(θ+φ)-sinθcos(θ+φ) simplifies to sinφ? I know I have to use trig identities, and I got to cos2θsinφ-sin2θcosφ but I'm not sure where to go from there. Thanks
  21. S

    Derive an expression for the acceleration of the ramp.

    Homework Statement Homework Equations The picture is all we know about the entire system, we need to derive an expression for the acceleration of ramp M. There is no friction anywhere. The ramp is free to move on the surface beneath it. The Attempt at a Solution I drew the free body...
  22. R

    Engineering Turning expression into circuit help?

    Homework Statement AC'D+ AB'D + BCD' + A'BC 2. Homework Equations The Attempt at a Solution Would I start by inverting all the inputs? Would there be 3 Or's to this? I get from the truth table, to simplifying expressions with k-map, but I don't know how to turn it into a circuit. Can someone...
  23. G

    Time derivative of tensor expression

    I was trying to compute the time derivative of the following expression: \mathbf{p_k} = \sum_i e_{ki}\sum_{n=0}^{\infty} \frac{(-1)^n}{(n+1)!} \mathbf{r_{ki}}(\mathbf{r_{ki}\cdot \nabla})^n \delta(\mathbf{R_k}-\mathbf{R}) I am following deGroot in his Foundations of Electrodynamics. He says...
  24. karush

    MHB What is the Limit of a Rational Expression?

    $$\lim_{{x}\to{\infty}}\frac{\sqrt{3x^2 - 1 }}{x-1}=\sqrt{3}$$ I tried dividing everything by ${x}^{2}$ but not
  25. caters

    Simplify Expression: (1/3 + 1/3y)/(1/y + 1/3) = 6y/(9 + 3y^2)

    Homework Statement Simplify (1/3 + 1/3y)/(1/y + 1/3) Homework Equations (1/3 + 1/3y)/(1/y + 1/3) = x In this case I am using x to represent the simplified expression The Attempt at a Solution (1/3 + 1/3 * 1/y)/(1/y+1/3) = (2/3 * 1/y)/(1/y + 1/3) = (2/3y)/(1/y+1/3) = (2/3y)/(3/3y + y/3y) =...
  26. C

    [Electromagnetism] Force on a moving charge expression

    Homework Statement [/B] The total force on a moving charge q with velocity v is given by \mathbf{F}=q(\mathbf{E}+\mathbf{v}\times\mathbf{B}) Using the scalar and vector potentials, show that \mathbf{F}=q[-\nabla\phi-\frac{d\mathbf{A}}{dt}+\nabla(\mathbf{A}\cdot\mathbf{v})]Homework Equations...
  27. Galbi

    Why need 4th order stiffness tensor expression?

    OK. First of all, I'm novice at Physics so this question may be weird. Above, there are 2 expressions for strain-stress relations. Let's assume that all components in the matrix are variables, not zero, not E, nor not G in the first picture. The first one is written in 2D matrix form, whereas...
  28. Mr Davis 97

    Finding the limit of a rational expression

    To find the horizontal asymptotes of a rational function, we find the limit as x goes to infinity. Given the rational function ##\displaystyle\frac{x + 1}{\sqrt{x^2+1}}##, we can find the limit by multiplying the numerator and the denominator by ##\frac{1}{x}##. This gives us ##\frac{1 +...
  29. Mr Davis 97

    Simplifying a rational expression

    Given that we have the expression ##\displaystyle-\frac{1}{(x-2)(x-2)(x-3)}~\cdot~\sqrt{\frac{(x-2)^{2}}{(x-3)(x-1)}} ##, how do we simplify it, step by step? Specifically, I am concerned about the ##\sqrt{(x-2)^{2}}## term. Are we allowed to cancel this with the ##(x-2)## in the denominator?
  30. S

    MHB How this exponent expression is reduced

    Initially the expression A has 8 terms. So how is it reduced in the second line to 5 terms? Could you show me, please? Thank you. \begin{align*} A&=10^{28} -10^{22} +61\times10^{14}+12\times10^{21}-12\times10^{15}+3\times10^{9}-36\times10^{8}+9\times10^{2}\\ &=10^{28}...
  31. anemone

    MHB Prove an expression is rational

    The rational numbers $a,\,b,\,c$ (for which $a+bc$, $b+ac$ and $a+b$ are all non-zero) satisfy the equality $\dfrac{1}{a+bc} =\dfrac{1}{a+b}-\dfrac{1}{b+ac}$. Prove that $\sqrt{(c−3)(c+1)}$ is rational.
  32. olgerm

    Simplify this expression please

    ##m*\frac{G*16*π*ρ*ω}{c^2}*\int_{a_0}^{a_{1}}(da*a*\int_{y}^{H+y} (\int_0^R (\int_0^{2*π} (\frac{(r-a*Cos(α))*r^2}{(a^2+r^2+h^2-2*r(a*Cos(α)))^{3/2}}* dα)dr)dh))## This equation is related with this post https://www.physicsforums.com/threads/gravitomagnetic-experiment.824048/. It where helpful...
  33. karush

    MHB Simplifying a Trigonometric Expression

    $$\frac{\cot^3\left({y}\right)-\tan^3\left({y}\right)} {\sec^2\left({y}\right)+\cot^2\left({y}\right)} =2\cot\left({2y}\right)$$ I tried the LHS but could get it to reduce.
  34. J

    How do I simplify this expression with a floor function?

    I would want to change this expression to another one that would have P easily accessible. \frac{\left \lceil (n+1)^{P} \right \rceil}{\left \lceil n^{P} \right \rceil} As an example of 'accessible'; given (n+1)^P / n^P, I can make P more accessible by using log(). Then it becomes P *...
  35. K

    Maple Partially Factor Lengthy Expression w/ Maple - Positive Real Numbers

    I need to show that the following expression, $$a^3b-a^3c+a^3z+a^3x+a^3y-a^2bx+a^2by+a^2cx-a^2cy-a^2zx+a^2zy-a^2x^2+a^2y^2-abcz-abcx-aczx-acx^2+b^2c^2+2bc^2x+c^2x^2-b^2c-2bcx-cx^2,$$ is positive given that: $1.$ $\ a,b,c,x,y,z$ are positive real numbers $2. \ \ a>b+x$ $3. \ \ c<b+y$ I...
  36. E

    Why is the expression for sheet resistance given without demonstration?

    Hello! I have in my notes an expression for the sheet resistance of a uniform conductor with length L, width W = L and thickness t. It is R_{\square} = \displaystyle \frac{\sqrt{\displaystyle \frac{\pi f \mu}{\sigma}}}{1 - e^{-t/\delta}} = \displaystyle \frac{1}{\sigma \delta} \frac{1}{1 -...
  37. S

    Heat transfer coeffcient expression

    Homework Statement Getting an expression for the convective heat tarnsfer coefficient. Homework Equations See attached images The Attempt at a Solution I have been reading about the boundary layers. Here is an extract of my notes corresponding to thermal boundary layer and consequently my...
  38. S

    Variation of a tensor expression with indices

    Say I want to find ##\delta \bigg( \sqrt{- \eta_{\mu \nu} \frac{dx^{\mu}}{d \tau} \frac{dx^{\nu}}{d \tau}} \bigg)##. Is the following alright: ##\delta \bigg( \sqrt{- \eta_{\mu \nu}} \bigg( \frac{dx^{\mu}}{d \tau} \bigg)^{-1/2} \bigg( \frac{dx^{\nu}}{d \tau} \bigg)^{1/2} \bigg)##?
  39. K

    MHB How to simplify a diabolical expression involving radicals

    A friend and I have been working on this problem for hours - how can the following expression be simplified analytically? It equals $\frac{1}{2},$ and we have tried the following to no avail: 1. Substitution of $x = \sqrt{5}$ 2. Substitution of $x = 2\sqrt{5}$ 3. Substitution of $x =...
  40. F

    Meaning of return expression in C

    Hello Forum, I am new to C programming and I have a few questions about the main() function. The main function does not take any arguments (nothing written between the round parentheses): main() or even main(void) . I have also seen the expression void main. Is that the same as main(void)...
  41. R

    Arc Length. Simplify expression

    Homework Statement I'm trying to find Arc Length of F(x) = (e^x + e^-x)/2 0< x < 2]Homework Equations L = integrate sqrt ( 1 + (dy/dx))^2)The Attempt at a Solution (dy/dx)^2 + 1 = 1/4e^2x + 1/4e^-2x + 1/2] I don't know how to take the square root of the above function so I can be able...
  42. binbagsss

    Differential commutator expression stuck

    Homework Statement I am trying to show that ##a(x)[u(x),D^{3}]=-au_{xxx}-3au_{xx}D-3au_{x}D^{2}##, where ##D=d/dx##, ##D^{2}=d^{2}/dx^{2} ## etc.Homework Equations [/B] I have the known results : ##[D,u]=u_{x}## ##[D^{2},u]=u_{xx}+2u_{x}D## The property: ##[A,BC]=[A,B]C+B[A,C] ##*The...
  43. M

    Trying to invert an expression

    I've come across an expression that looks like n(k) = ∫cos(x-y)f(x,y)dxdy Is there a name for this transform? I would like to invert it to obtain f(x,y) but I'm not used to the 2D integral on the RHS. I tried to turn it into a Fourier transform: n(k) = 1/2 ( ∫eixe-iyf(x,y)dxdy +...
  44. C

    Mathematica WolframAlpha miscalculates a simple arithmetic expression

    There is a crucial bug on both WolframAlpha and Mathematica. When we give the input "Floor(sqrt(11.44-10)/0.2)" it gives wrong answer. The actual answer is six (6) but wolframalpha gives five (5). The problem is Wolframalpha calculates 11.44-10 incorrectly. Although the answer is exactly 1.44...
  45. J

    Mathematica Mathematica: unable to format isomorphic expression

    I can't figure out how to format a variable isomorphic expression in Mathematica so that it will look nice. The best I can do will put parentheses around everything and expand powers. For example, given the array ##\{2,4,4,3,3\}##, I'd like Mathematica to write...
  46. D

    Derive the Gunn-Peterson optical depth expression....

    Homework Statement Derive an expression for the Gunn-Peterson optical depth Tau(λ) for Lyman limit absorption from smoothly distributed intergalactic neutral Hydrogen of comoving density n0 toward a QSO of emission redshift zem. Take the absorption cross section for Lyman-limit absorption to...
  47. X

    Is it possible to re-write this expression?

    Hello everyone, I am trying to develop a model for my PhD research, I don't want to get into specifics too much, but I have encountered the following problem. I need to write \psi \frac{\partial \psi^*}{\partial x} in the following form \frac{\partial}{\partial x}(\text{Some function}) This...
  48. B

    When is the expression real

    Homework Statement I have the expression ##a_2\overline{β} + a_3β## involving complex variables, where ##|β|≤1##. I was wondering, is it possible to determine for what ##a_2## and ##a_3## the expression is always real, for every ##β## satisfying ##|β|≤1##; or is there insufficient information...
  49. B

    For what values is the expression always real?

    Homework Statement I have the expression ##a_2 \overline{\beta} + a_3 \beta## involving complex variables, where ##|\beta| \le 1##. I was wondering, is it possible to determine for what ##a_2## and ##a_3## the expression is always real, for every ##\beta## satisfying ##|\beta| \le 1##; or is...
  50. CAH

    Calculating Variance: Sample vs Population

    See the photo of the question+ mark scheme! I don't understand a question on finding an expression for the variance of something... Attempt at solution: also I worked out c as (3/2) previously, which is correct Var(U) = (3/2)^2 x Var(Xbar) = 9/4n^2 x a^2/18 I'll attach a photo of this too if...
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