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

Page 5 / 6

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{matrix} \frac{d [C]}{d t} & = r_{1} [C a_{2} C] + r_{3} [C_{M_{K}}] + r_{8} [C_{B_{P}}] - f_{1} {[C a^{2^{+}}]}^{2} [C] \\ - f_{3} [C] [M_{K}] - f_{8} [C] [B_{P}] \\ \frac{d [M_{K}]}{d t} & = r_{3} [C_{M_{K}}] + r_{4} [C a_{2} C_{M_{K}}] + r_{5} [C a_{4} C_{M_{K}}] - f_{3} [C] [M_{K}] \\ - f_{4} [M_{K}] [C a_{2} C] - f_{5} [M_{K}] [C a_{4} C] \\ \frac{d [C a_{2} C]}{d t} & = f_{1} {[C a^{2^{+}}]}^{2} [C] + r_{2} [C a_{4} C] + r_{4} [C a_{2} C_{M_{K}}] \\ + f_{9} {[C a^{2^{+}}]}^{2} [C_{B_{P}}] - r_{1} [C a_{2} C] - f_{2} {[C a^{2^{+}}]}^{2} [C a_{2} C] \\ - f_{4} [M_{K}] [C a_{2} C] - r_{9} [C a_{2} C] [B_{P}] \\ \frac{d [C a_{4} C]}{d t} & = f_{2} {[C a^{2^{+}}]}^{2} [C a_{2} C] + r_{5} [C a_{4} C_{M_{K}}] - r_{2} [C a_{4} C] \\ - f_{5} [M_{K}] [C a_{4} C] \\ \frac{d [C_{M_{K}}]}{d t} & = f_{3} [C] [M_{K}] + r_{6} [C a_{2} C_{M_{K}}] - r_{3} [C_{M_{K}}] \\ - f_{6} {[C a^{2^{+}}]}^{2} [C_{M_{K}}] \\ \frac{d [C a_{2} C_{M_{K}}]}{d t} & = f_{4} [M_{K}] [C a_{2} C] + f_{6} {[C a^{2^{+}}]}^{2} [C_{M_{K}}] + r_{7} [C a_{4} C_{M_{K}}] \\ - r_{4} [C a_{2} C_{M_{K}}] - r_{6} [C a_{2} C_{M_{K}}] - f_{7} {[C a^{2^{+}}]}^{2} [C a_{2} C_{M_{K}}] \\ \frac{d [C a_{4} C_{M_{K}}]}{d t} & = f_{5} [M_{K}] [C a_{4} C] + f_{7} {[C a^{2^{+}}]}^{2} [C a_{2} C_{M_{K}}] \\ - r_{5} [C a_{4} C_{M_{K}}] - r_{7} [C a_{4} C_{M_{K}}] \\ \frac{d [B_{P}]}{d t} & = r_{8} [C_{B_{P}}] + f_{9} {[C a^{2^{+}}]}^{2} [C_{B_{P}}] - f_{8} [C] [B_{P}] \\ - r_{9} [C a_{2} C] [B_{P}] \\ \frac{d [C_{B_{P}}]}{d t} & = f_{8} [C] [B_{P}] + r_{9} [C a_{2} C] [B_{P}] - r_{8} [C_{B_{P}}] \\ - f_{9} {[C a^{2^{+}}]}^{2} [C_{B_{P}}] \end{matrix}

${[C]}_{0} =$	$0.9285 μ M$		Initial Calmodulin (C) concentration	[link]
${[M_{K}]}_{0} =$	$9.6506 μ M$		Initial Myosin LC Kinase ( $M_{K}$ ) concentration	[link]
${[C a_{2} C]}_{0} =$	$0.0015 μ M$		Initial $C a_{2} C$ complex concentration	[link]
${[C a_{4} C]}_{0} =$	$0.00 μ M$		Initial $C a_{4} C$ complex concentration	[link]
${[C_{M_{K}}]}_{0} =$	$0.3332 μ M$		Initial $C M_{K}$ complex concentration	[link]
${[C a_{2} C_{M_{K}}]}_{0} =$	$0.2713 μ M$		Initial $C a_{2} C M_{K}$ complex concentration	[link]
${[C a_{4} C_{M_{K}}]}_{0} =$	$0.013 μ M$		Initial $C a_{4} C M_{K}$ activated complex concentration	[link]
${[B_{P}]}_{0} =$	$15.1793 μ M$		Initial Binding Protein ( $B_{P}$ ) concentration	[link]
${[C_{B_{P}}]}_{0} =$	$2.8207 μ M$		Initial $C - B_{P}$ complex concentration	[link]
$[f_{1} r_{1}] =$	$[12 μ M^{- 1}$	$12] s^{- 1}$	Forward and reverse rates for reaction 1	[link]
$[f_{2} r_{2}] =$	$[480 μ M^{- 1}$	$1200] s^{- 1}$	Forward and reverse rates for reaction 2	[link]
$[f_{3} r_{3}] =$	$[5 μ M^{- 1}$	$135] s^{- 1}$	Forward and reverse rates for reaction 3	[link]
$[f_{4} r_{4}] =$	$[840 μ M^{- 1}$	$45.4] s^{- 1}$	Forward and reverse rates for reaction 4	[link]
$[f_{5} r_{5}] =$	$[28 μ M^{- 1}$	$0.0308] s^{- 1}$	Forward and reverse rates for reaction 5	[link]
$[f_{6} r_{6}] =$	$[120 μ M^{- 1}$	$4] s^{- 1}$	Forward and reverse rates for reaction 6	[link]
$[f_{7} r_{7}] =$	$[7.5 μ M^{- 1}$	$3.75] s^{- 1}$	Forward and reverse rates for reaction 7	[link]
$[f_{8} r_{8}] =$	$[5 μ M^{- 1}$	$25] s^{- 1}$	Forward and reverse rates for reaction 8	[link]
$[f_{9} r_{9}] =$	$[7.6 μ M^{- 1}$	$22.8] s^{- 1}$	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{matrix} \frac{d [M]}{d t} & = - \frac{k_{1} [C a_{4} C_{M_{K}}] [M]}{k_{2} + [M]} + \frac{k_{5} [M_{L}] [M_{p}]}{k_{6} + [M_{p}]} + k_{7} [A_{M}] \\ \frac{d [M_{p}]}{d t} & = \frac{k_{1} [C a_{4} C_{M_{K}}] [M]}{k_{2} + [M]} - \frac{k_{5} [M_{L}] [M_{p}]}{k_{6} + [M_{p}]} - k_{3} [M_{p}] + k_{4} [A_{M_{p}}] \\ \frac{d [A_{M_{p}}]}{d t} & = k_{3} [M_{p}] - k_{4} [A_{M_{p}}] + \frac{k_{1} [C a_{4} C_{M_{K}}] [A_{M}]}{k_{2} + [A_{M}]} \\ - \frac{k_{5} [M_{L}] [A_{M_{p}}]}{k_{6} + [A_{M_{p}}]} \\ \frac{d [A_{M}]}{d t} & = - \frac{k_{1} [C a_{4} C_{M_{K}}] [A_{M}]}{k_{2} + [A_{M}]} + \frac{k_{5} [M_{L}] [A_{M_{p}}]}{k_{6} + [A_{M_{p}}]} - k_{7} [A_{M}] \\ F (t) & = F_{m a x} \frac{[A_{M} (t)] + [A_{M_{p}} (t)]}{[M_{T}]} \end{matrix}

${[M]}_{0} =$	$23.9558 μ M$	Initial myosin concentration	[link]
${[M_{p}]}_{0} =$	$0.0144 μ M$	Initial phosphorylated myosin concentration	[link]
${[A_{M_{p}}]}_{0} =$	$0.0166 μ M$	Initial cross-bride concentration	[link]
${[A_{M}]}_{0} =$	$0.0132 μ M$	Initial latch-bridge concentration	[link]
$[M_{L}] =$	$7.5 μ M$	Myosin light chain phosphatase concentration	[link]
$[M_{T}] =$	$24 μ M$	Total myosin concentration	[link]
$F (t) =$		Force generated in $m N$	[link]
$F_{m a x} =$	$70 m N$	Maximum force cell can generate	[link]
$k_{1} =$	$27 s^{- 1}$	Rate for reaction 10	[link]
$k_{2} =$	$10 μ M$	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]
$k_{6} =$	$15 μ M$	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.

Questions & Answers

how do you get the 2/50

Abba Reply

number of sport play by 50 student construct discrete data

Aminu Reply

width of the frangebany leaves on how to write a introduction

Theresa Reply

Solve the mean of variance

Veronica Reply

Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ... Step 2: Find each score's deviation from the mean. ... Step 3: Square each deviation from the mean. ... Step 4: Find the sum of squares. ... Step 5: Divide the sum of squares by n – 1 or N.

kenneth

what is error

Yakuba Reply

Is mistake done to something

Vutshila

anas

What is the life teble

anas

Jibrin

statistics is the analyzing of data

Tajudeen Reply

what is statics?

Zelalem Reply

how do you calculate mean

Gloria Reply

diveving the sum if all values

Shaynaynay

let A1,A2 and A3 events be independent,show that (A1)^c, (A2)^c and (A3)^c are independent?

Fisaye Reply

what is statistics

Akhisani Reply

data collected all over the world

Shaynaynay

construct a less than and more than table

Imad Reply

The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.

Aschalew Reply

Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400 a. what is the probability of getting more than 12,000 hits? b. what is the probability of getting fewer than 9,000 hits?

Akshay Reply

Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400. a. What is the probability of getting more than 12,000 hits

Akshay

Bright

Sorry i want to learn more about this question

Bright

Someone help

Bright

a= 0.20233 b=0.3384

Sufiyan

Shaynaynay

How do I interpret level of significance?

Mohd Reply

It depends on your business problem or in Machine Learning you could use ROC- AUC cruve to decide the threshold value

Shivam

how skewness and kurtosis are used in statistics

Owen Reply

yes what is it

Taneeya

Got questions? Join the online conversation and get instant answers!

Jobilize.com Reply

<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'The art of the pfug' conversation and receive update notifications?

Ask

©flickr: Jovial	Video Mid Term By Dewey Compton Start Exam
©flickr: Luis	Final Exam Review By Madison Christian Start Exam
	2011 Dynamics CRM By Danielrosenberger Start Quiz
	1 Neuroscience Exam 2004 1 By David Corey Start Exam
	6 Physiotherapy Flashcards Set 6 By Rhodes Start Flashcards
	28 AP 28 Development Inheritance Essay By OpenStax Start Flashcards
©flickr:	Math for Economists MCQ By Tony Pizur Start Quiz
	11 Neuroanatomy 11 The Cerebellum By Stephen Voron Start Quiz
	MAPEH Test G9 (Physical Education) By Angelica Lito Start Quiz
	Nutrition Exam By Hannah Sheth Start Quiz