Examples of MreB in the following topics:
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- Also, bacteria that are naturally spherical do not have the gene encoding MreB.
- Prokaryotes carrying the mreB gene can also be helical in shape.
- MreB has long been thought to form a helical filament underneath the cytoplasmic membrane.
- Recent research shows that peptidoglycan precursors are inserted into cell wall following helical pattern which is dependent on MreB, and it's reported that MreB also promote the GT activity of PBPs.
- Procaryotic MreB in cartoon representation.
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- However, it is actually the MreB protein that facilitates cell shape.
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- P(A OR B) = P(A) + P(B) − P(A AND B)
- If A and B are mutually exclusive then P(A AND B) = 0 ; so P(A OR B) = P(A) + P(B).
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- If A and B are two events defined on a sample space, then: P(A AND B) = P(B) · P(A|B).
- $P ( A | B ) = \frac{P ( A \; AND \; B )}{P(B)} $
- (The probability of A given B equals the probability of A and B divided by the probability of B. )
- If A and B are independent, then P(A|B) = P(A).
- Then P(A AND B) = P(A|B) P(B) becomes P(A AND B) = P(A) P(B).
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- The average of a function $f(x)$ over an interval $[a,b]$ is $\bar f = \frac{1}{b-a} \int_a^b f(x) \ dx$.
- Therefore, the average of a function $f(x)$ over an interval $[a,b]$ (where $b > a$) is expressed as:
- The first mean value theorem for integration states that if $G : [a, b] \to R$ is a continuous function and $\varphi$ is an integrable function that does not change sign on the interval $(a, b)$, then there exists a number $x$ in $(a, b)$ such that:
- In particular, if $\varphi(t) = 1$ for all $t$ in $[a, b] $, then there exists $x$ in $(a, b)$ such that:
- The average of a function $f(x)$ that has area $S$ over the range $[a,b]$ is $\frac{S}{b-a}$.
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- If A and B are defined on a sample space, then: P(A OR B) = P(A) + P(B) − P(A AND B).
- Then P(A OR B) = P(A) + P(B) − P(A AND B) becomes P(A OR B) = P(A) + P(B).
- P(A OR B) = P(A) + P(B) − P(A AND B) = 0.65 + 0.65 − 0.585 = 0.715 (3.2)
- P(B AND N) = P(B) · P(N|B) = ( 0.143 ) · ( 0.02 ) = 0.0029
- P(B OR N) = P(B) + P(N) − P(B AND N) = 0.143 + 0.85 − 0.0029 = 0.9901
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- The multiplication rule states that the probability that $A$ and $B$ both occur is equal to the probability that $B$ occurs times the conditional probability that $A$ occurs given that $B$ occurs.
- That is, in the equation $\displaystyle P(A|B)=\frac{P(A\cap B)}{P(B)}$, if we multiply both sides by $P(B)$, we obtain the Multiplication Rule.
- The rule is useful when we know both $P(B)$ and $P(A|B)$, or both $P(A)$ and $P(B|A).$
- $\displaystyle
\begin{aligned}
P(A \cap B) &= P(A) \cdot P(B|A)\\
&= \frac { 4 }{ 52 } \cdot \frac { 3 }{ 51 } \\
&=0.0045
\end{aligned}$
- Note that when $A$ and $B$ are independent, we have that $P(B|A)= P(B)$, so the formula becomes $P(A \cap B)=P(A)P(B)$, which we encountered in a previous section.
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- Immature B cells are produced in the bone marrow and migrate to secondary lymphoid tissues where some develop into mature B cells.
- The immature B cells whose B-cell receptors (BCRs) bind too strongly to self antigens will not be allowed to mature.
- Once a B cell encounters its cognate antigen and receives an additional signal from a T helper cell, it can further differentiate into either plasma B cells or memory B cells.
- B cells exist as clones.
- B cells that encounter antigen for the first time are known as naive B cells.
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- The length of the component of $\mathbf{b}$ along $\mathbf{a}$ is $\|\mathbf{b}\| \cos \theta$ which is also $\mathbf{b}^T \mathbf{a}/\|\mathbf{a}\|$ .
- Now suppose we want to construct a vector in the direction of $\mathbf{a}$ but whose length is the component of $\mathbf{b}$ along $\|\mathbf{b}\|$ .
- As an exercise verify that in general $\mathbf{a}(\mathbf{a}^T \mathbf{b}) = (\mathbf{a}\mathbf{a}^T) \mathbf{b}$ .
- Let $\mathbf{a}$ and $\mathbf{b}$ be any two vectors.
- The length of the component of $\mathbf{b}$ along $\mathbf{a}$ is $\|\mathbf{b}\| \cos \theta$ which is also $\mathbf{b}^T \mathbf{a}/\|\mathbf{a}\|$ .
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- Exponential form, written $b^n$, represents multiplying the base $b$ times itself $n$ times.
- For example, the expression $b^3$ represents $b \cdot b \cdot b$.
- For example, $b^2$ is usually read as "$b$ squared" and $b^3$ as "$b$ cubed."
- That is to say, $b^1=b$.
- That is to say, $b^0=1$.