GP2 Written assignment # 2 Muscle contractions are caused by the motor protein m
ID: 1406865 • Letter: G
Question
GP2 Written assignment # 2 Muscle contractions are caused by the motor protein myosin which consumes the high energy molecule ATP for fuel. The ATP molecules carry a negative charge of -4e, so the active site of the myosin has a positive charge to help the ATP find the correct place to bind. Consider t he following arrangement of an ATP molecule, a myosin binding site (q = + 3), a RNA molecule with a charge - 150e, and a protein carrying a charge -6e. Since these molecules are immersed in water, the dielectric constant is K = 80. Calculate to following showing all symbolic manipulations and unit conversions: a) The electric potential at the ATP molecule's position due to the other molecules. (Let V= 0 at infinite distance from all charges.) b) The force vector on the ATP. (Biological forces arc typically given in piconewtons or nanonewtons.) c) The energy required to move the ATP molecule from very far away to its present location. Express your answer in both kCal/mole and eV.Explanation / Answer
(ATP) q = -4e
q1 = -6e
q2 = +3e
q3 = -150e
(a)
Electric Potential at ATP due to other charges -
V = k (q1/r1 +q2/r2 +q3/r3)
V = (9 * 10^9 * 1.6 *10^-19)/(10^-9) ( -6/5 +3/3 -150/200) Volt
V = -1.368 Volt
(b)
Force due to q1 = k * q1*q /r^2
Force due to q1 = (9 * 10^9 * 6*1.6*10^-19 * 4 *1.6*10^-19) /(5 * 10^-9)^2
Force due to q1 = 2.21 * 10^-10
Fq1 in x direction = F * (4/5) i = 1.768 * 10^-10 i N
Fq1 in y direction = - F * (3/5) j = - 1.326 * 10^-10 j N
Force due to q2 = k * q2*q /r^2
Force due to q2 = - (9 * 10^9 * 3*1.6*10^-19 * 4 *1.6*10^-19) /(3 * 10^-9)^2 i
Force due to q2 = -3.072 * 10^-10 i N
Force due to q3 = k * q3*q /r^2
Force due to q3 = (9 * 10^9 *150*1.6*10^-19 * 4 *1.6*10^-19) /(200 * 10^-9)^2
Force due to q3 = - 0.03456 * 10^-10 i N
Force vector on ATP molecule due to charges = (1.768 -3.072 - 0.03456) * 10^-10 i N - 1.326 * 10^-10 j N
Force vector on ATP molecule due to charges = - 1.34* 10^-10 i N - 1.326 * 10^-10 j N
(c)
Energy required to move ATP Molecule to its present location = Charge * Electric potential
Energy required to move ATP Molecule to its present location = -4 * 1.6 * 10^-19 * -1.368 J
Energy required to move ATP Molecule to its present location = 8.75 *10^-19 J
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