Lecture3 - UC Davis, BME BIM 162 Quantitative Concepts in...

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Unformatted text preview: UC Davis, BME BIM 162 Quantitative Concepts in Biomolecular Engineering Lecture 03 Interactions between biomolecules: Electrostatics Follow-up Things worth remembering (among others) “Special rules” for biomolecules Special rules size aqueous environment (role of water) e pe a u e (k ) temperature ( BT) strength flexibility Bond energies (typical values) : covalent “weak” bond weak Basic structure and structural components of biomolecules Boltzmann distribution/probability Energy minimization vs. force balance E Energy of attractive vs. repulsive i t f tt ti l i interactions ti Follow-up kBT in action Phospholipid vesicles Follow-up kBT in action Blood cells – Introduction Dr. I. Saurelius’ lab, U of Rochester S , Elastic cantilever beam Optical-lever method for deflection measurement Boltzmann distribution Confined Brownian motion Example: elastic cantilever beam k kBT var x Recall Gaussian distribution: x 2 1 g x , , exp 2 2 2 Boltzmann distribution Boltzmann distribution 3D Brownian motion of glass bead in water 3D Brownian motion of glass bead in water Interactions between biomolecules: Electrostatics Coulomb energy: 1 q1q2 e 2 z1 z2 E r 40 r 40 r e 1.602 1019 C … elementary charge p y p 0 8 854 1012 C 2 J -1m -1 … permittivity of free space 8.854 … relative permittivity, dielectric constant z1 2 … ionic valencies 1,2 Force: F dE r dr Born energy: ”self-energy” (vacuum) or “solvation energy” (medium) of an ion • work done in forming the ion (or charging it from 0 to q) q 1 qdq 1 q2 40 a 80 a 0 Interactions between biomolecules: Electrostatics Ion-dipole interaction: E r 1 q1q2 q1q2 1 q2 1 1 40 r r 40 r r q1 … dipole moment .85 030 C Example: H 2O 1.85 3.336 10 Cm 1D ("Debye") E r 1 q2 cos 40 r 2 How much more likely is the case =0 compared to =? 1 q2 4 r 2 cos 0 0 exp kBT 1 q2 4 r 2 cos 0 exp p kBT ...
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