# 8.8 Exploring the biochemical and mechanical effects of intestinal  (Page 5/6)

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## Myosin activation

The activation of the ${M}_{K}$ complex includes 4 $C{a}^{{2}^{+}}$ ions bonded to calmodulin and myosin light chain kinase. Side reactions include the disassociation of the kinase from the complex and interactions with binding proteins. These interactions were modeled using mass action kinetics summarized in 9 reactions from [link] .

$\begin{array}{cc}\hfill \frac{d\left[C\right]}{dt}& ={r}_{1}\left[C{a}_{2}C\right]+{r}_{3}\left[{C}_{{M}_{K}}\right]+{r}_{8}\left[{C}_{{B}_{P}}\right]-{f}_{1}{\left[C{a}^{{2}^{+}}\right]}^{2}\left[C\right]\hfill \\ & -{f}_{3}\left[C\right]\left[{M}_{K}\right]-{f}_{8}\left[C\right]\left[{B}_{P}\right]\hfill \\ \hfill \frac{d\left[{M}_{K}\right]}{dt}& ={r}_{3}\left[{C}_{{M}_{K}}\right]+{r}_{4}\left[C{a}_{2}{C}_{{M}_{K}}\right]+{r}_{5}\left[C{a}_{4}{C}_{{M}_{K}}\right]-{f}_{3}\left[C\right]\left[{M}_{K}\right]\hfill \\ & -{f}_{4}\left[{M}_{K}\right]\left[C{a}_{2}C\right]-{f}_{5}\left[{M}_{K}\right]\left[C{a}_{4}C\right]\hfill \\ \hfill \frac{d\left[C{a}_{2}C\right]}{dt}& ={f}_{1}{\left[C{a}^{{2}^{+}}\right]}^{2}\left[C\right]+{r}_{2}\left[C{a}_{4}C\right]+{r}_{4}\left[C{a}_{2}{C}_{{M}_{K}}\right]\hfill \\ & +{f}_{9}{\left[C{a}^{{2}^{+}}\right]}^{2}\left[{C}_{{B}_{P}}\right]-{r}_{1}\left[C{a}_{2}C\right]-{f}_{2}{\left[C{a}^{{2}^{+}}\right]}^{2}\left[C{a}_{2}C\right]\hfill \\ & -{f}_{4}\left[{M}_{K}\right]\left[C{a}_{2}C\right]-{r}_{9}\left[C{a}_{2}C\right]\left[{B}_{P}\right]\hfill \\ \hfill \frac{d\left[C{a}_{4}C\right]}{dt}& ={f}_{2}{\left[C{a}^{{2}^{+}}\right]}^{2}\left[C{a}_{2}C\right]+{r}_{5}\left[C{a}_{4}{C}_{{M}_{K}}\right]-{r}_{2}\left[C{a}_{4}C\right]\hfill \\ & -{f}_{5}\left[{M}_{K}\right]\left[C{a}_{4}C\right]\hfill \\ \hfill \frac{d\left[{C}_{{M}_{K}}\right]}{dt}& ={f}_{3}\left[C\right]\left[{M}_{K}\right]+{r}_{6}\left[C{a}_{2}{C}_{{M}_{K}}\right]-{r}_{3}\left[{C}_{{M}_{K}}\right]\hfill \\ & -{f}_{6}{\left[C{a}^{{2}^{+}}\right]}^{2}\left[{C}_{{M}_{K}}\right]\hfill \\ \hfill \frac{d\left[C{a}_{2}{C}_{{M}_{K}}\right]}{dt}& ={f}_{4}\left[{M}_{K}\right]\left[C{a}_{2}C\right]+{f}_{6}{\left[C{a}^{{2}^{+}}\right]}^{2}\left[{C}_{{M}_{K}}\right]+{r}_{7}\left[C{a}_{4}{C}_{{M}_{K}}\right]\hfill \\ & -{r}_{4}\left[C{a}_{2}{C}_{{M}_{K}}\right]-{r}_{6}\left[C{a}_{2}{C}_{{M}_{K}}\right]-{f}_{7}{\left[C{a}^{{2}^{+}}\right]}^{2}\left[C{a}_{2}{C}_{{M}_{K}}\right]\hfill \\ \hfill \frac{d\left[C{a}_{4}{C}_{{M}_{K}}\right]}{dt}& ={f}_{5}\left[{M}_{K}\right]\left[C{a}_{4}C\right]+{f}_{7}{\left[C{a}^{{2}^{+}}\right]}^{2}\left[C{a}_{2}{C}_{{M}_{K}}\right]\hfill \\ & -{r}_{5}\left[C{a}_{4}{C}_{{M}_{K}}\right]-{r}_{7}\left[C{a}_{4}{C}_{{M}_{K}}\right]\hfill \\ \hfill \frac{d\left[{B}_{P}\right]}{dt}& ={r}_{8}\left[{C}_{{B}_{P}}\right]+{f}_{9}{\left[C{a}^{{2}^{+}}\right]}^{2}\left[{C}_{{B}_{P}}\right]-{f}_{8}\left[C\right]\left[{B}_{P}\right]\hfill \\ & -{r}_{9}\left[C{a}_{2}C\right]\left[{B}_{P}\right]\hfill \\ \hfill \frac{d\left[{C}_{{B}_{P}}\right]}{dt}& ={f}_{8}\left[C\right]\left[{B}_{P}\right]+{r}_{9}\left[C{a}_{2}C\right]\left[{B}_{P}\right]-{r}_{8}\left[{C}_{{B}_{P}}\right]\hfill \\ & -{f}_{9}{\left[C{a}^{{2}^{+}}\right]}^{2}\left[{C}_{{B}_{P}}\right]\hfill \end{array}$
 ${\left[C\right]}_{0}=$ $0.9285\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial Calmodulin (C) concentration [link] ${\left[{M}_{K}\right]}_{0}=$ $9.6506\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial Myosin LC Kinase ( ${M}_{K}$ ) concentration [link] ${\left[C{a}_{2}C\right]}_{0}=$ $0.0015\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial $C{a}_{2}C$ complex concentration [link] ${\left[C{a}_{4}C\right]}_{0}=$ $0.00\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial $C{a}_{4}C$ complex concentration [link] ${\left[{C}_{{M}_{K}}\right]}_{0}=$ $0.3332\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial $C{M}_{K}$ complex concentration [link] ${\left[C{a}_{2}{C}_{{M}_{K}}\right]}_{0}=$ $0.2713\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial $C{a}_{2}C{M}_{K}$ complex concentration [link] ${\left[C{a}_{4}{C}_{{M}_{K}}\right]}_{0}=$ $0.013\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial $C{a}_{4}C{M}_{K}$ activated complex concentration [link] ${\left[{B}_{P}\right]}_{0}=$ $15.1793\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial Binding Protein ( ${B}_{P}$ ) concentration [link] ${\left[{C}_{{B}_{P}}\right]}_{0}=$ $2.8207\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial $C-{B}_{P}$ complex concentration [link] $\left[{f}_{1}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{r}_{1}\right]=$ $\left[12\phantom{\rule{0.277778em}{0ex}}\mu {M}^{-1}$ $12\right]{s}^{-1}$ Forward and reverse rates for reaction 1 [link] $\left[{f}_{2}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{r}_{2}\right]=$ $\left[480\phantom{\rule{0.277778em}{0ex}}\mu {M}^{-1}$ $1200\right]{s}^{-1}$ Forward and reverse rates for reaction 2 [link] $\left[{f}_{3}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{r}_{3}\right]=$ $\left[5\phantom{\rule{0.277778em}{0ex}}\mu {M}^{-1}$ $135\right]{s}^{-1}$ Forward and reverse rates for reaction 3 [link] $\left[{f}_{4}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{r}_{4}\right]=$ $\left[840\phantom{\rule{0.277778em}{0ex}}\mu {M}^{-1}$ $45.4\right]{s}^{-1}$ Forward and reverse rates for reaction 4 [link] $\left[{f}_{5}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{r}_{5}\right]=$ $\left[28\phantom{\rule{0.277778em}{0ex}}\mu {M}^{-1}$ $0.0308\right]{s}^{-1}$ Forward and reverse rates for reaction 5 [link] $\left[{f}_{6}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{r}_{6}\right]=$ $\left[120\phantom{\rule{0.277778em}{0ex}}\mu {M}^{-1}$ $4\right]{s}^{-1}$ Forward and reverse rates for reaction 6 [link] $\left[{f}_{7}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{r}_{7}\right]=$ $\left[7.5\phantom{\rule{0.277778em}{0ex}}\mu {M}^{-1}$ $3.75\right]{s}^{-1}$ Forward and reverse rates for reaction 7 [link] $\left[{f}_{8}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{r}_{8}\right]=$ $\left[5\phantom{\rule{0.277778em}{0ex}}\mu {M}^{-1}$ $25\right]{s}^{-1}$ Forward and reverse rates for reaction 8 [link] $\left[{f}_{9}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}{r}_{9}\right]=$ $\left[7.6\phantom{\rule{0.277778em}{0ex}}\mu {M}^{-1}$ $22.8\right]{s}^{-1}$ Forward and reverse rates for reaction 9 [link]

## Force generation

The interactions between myosin, actin, and the activated ${M}_{K}$ complex were modeled using Henri-Michaelis-Menten Enzyme Kinetics from [link] .

$\begin{array}{cc}\hfill \frac{d\left[M\right]}{dt}& =-\frac{{k}_{1}\left[C{a}_{4}{C}_{{M}_{K}}\right]\left[M\right]}{{k}_{2}+\left[M\right]}+\frac{{k}_{5}\left[{M}_{L}\right]\left[{M}_{p}\right]}{{k}_{6}+\left[{M}_{p}\right]}+{k}_{7}\left[{A}_{M}\right]\hfill \\ \hfill \frac{d\left[{M}_{p}\right]}{dt}& =\frac{{k}_{1}\left[C{a}_{4}{C}_{{M}_{K}}\right]\left[M\right]}{{k}_{2}+\left[M\right]}-\frac{{k}_{5}\left[{M}_{L}\right]\left[{M}_{p}\right]}{{k}_{6}+\left[{M}_{p}\right]}-{k}_{3}\left[{M}_{p}\right]+{k}_{4}\left[{A}_{{M}_{p}}\right]\hfill \\ \hfill \frac{d\left[{A}_{{M}_{p}}\right]}{dt}& ={k}_{3}\left[{M}_{p}\right]-{k}_{4}\left[{A}_{{M}_{p}}\right]+\frac{{k}_{1}\left[C{a}_{4}{C}_{{M}_{K}}\right]\left[{A}_{M}\right]}{{k}_{2}+\left[{A}_{M}\right]}\hfill \\ & -\frac{{k}_{5}\left[{M}_{L}\right]\left[{A}_{{M}_{p}}\right]}{{k}_{6}+\left[{A}_{{M}_{p}}\right]}\hfill \\ \hfill \frac{d\left[{A}_{M}\right]}{dt}& =-\frac{{k}_{1}\left[C{a}_{4}{C}_{{M}_{K}}\right]\left[{A}_{M}\right]}{{k}_{2}+\left[{A}_{M}\right]}+\frac{{k}_{5}\left[{M}_{L}\right]\left[{A}_{{M}_{p}}\right]}{{k}_{6}+\left[{A}_{{M}_{p}}\right]}-{k}_{7}\left[{A}_{M}\right]\hfill \\ \hfill F\left(t\right)& ={F}_{max}\frac{\left[{A}_{M}\left(t\right)\right]+\left[{A}_{{M}_{p}}\left(t\right)\right]}{\left[{M}_{T}\right]}\hfill \end{array}$
 ${\left[M\right]}_{0}=$ $23.9558\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial myosin concentration [link] ${\left[{M}_{p}\right]}_{0}=$ $0.0144\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial phosphorylated myosin concentration [link] ${\left[{A}_{{M}_{p}}\right]}_{0}=$ $0.0166\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial cross-bride concentration [link] ${\left[{A}_{M}\right]}_{0}=$ $0.0132\phantom{\rule{0.277778em}{0ex}}\mu M$ Initial latch-bridge concentration [link] $\left[{M}_{L}\right]=$ $7.5\phantom{\rule{0.277778em}{0ex}}\mu M$ Myosin light chain phosphatase concentration [link] $\left[{M}_{T}\right]=$ $24\phantom{\rule{0.277778em}{0ex}}\mu M$ Total myosin concentration [link] $F\left(t\right)=$ Force generated in $mN$ [link] ${F}_{max}=$ $70\phantom{\rule{0.277778em}{0ex}}mN$ Maximum force cell can generate [link] ${k}_{1}=$ $27{s}^{-1}$ Rate for reaction 10 [link] ${k}_{2}=$ $10\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\mu M$ Rate for reaction 11 [link] ${k}_{3}=$ $15{s}^{-1}$ Forward rate for reaction 12 [link] ${k}_{4}=$ $5{s}^{-1}$ Reverse rate for reaction 12 [link] ${k}_{5}=$ $16{s}^{-1}$ Rate for reaction 13 [link] ${k}_{6}=$ $15\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\mu M$ Rate for reaction 14 [link] ${k}_{7}=$ $10{s}^{-1}$ Rate for reaction 15 [link]

## Mechanical model

A variety of models which represent SMCs and other types of cells as mass-spring systems have been developed [link] , [link] , [link] , [link] , [link] , [link] . The most comparable of these models used a single contractile element and two passive elements: one to represent the elastic actin and myosin fibers and the other to represent the adjacent muscle cells and surroundings [link] . We present a novel mechanical model of the SMC which incorporates the previously described biochemical interactions to produce a comprehensive model of SMC contraction.

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I know this work
salma
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Abhi
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20/(×-6^2)
Salomon
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it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
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Abhi
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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