Ideal Gas Law

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Ideal Gas Law

• The number of gas molecules in a box at constant
  temperature is proportionate to its volume.
• pV NkBT, where p pressure, V volume,N
  number of molecules, and kB Boltzmann constant,
  and T temperature
• pV nRT chemistry formula where n number of
  moles, where R is the gas constant (8.314
  J?mole-1??K-1)
• Since 1 mole 6.022 x 1023 molecules kB
  R/6.022 x 1023 1.38 x 10-23 J?molecule-1??K-1

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The first law of thermodynamics
?E q-w, energy is neither created or
destroyed w P?V, work done at constant
pressure PV nRT, gas law w ?nRT, calculate
work at ideal conditions at constant-pressure PV
work is done therefore a greater amount of heat
is released to the surroundings than
constant-volume. q ?E w Most biochemical
reactions are at constant-pressure
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Free Energy The Second Law of Thermodynamics in
Open Systems G H TS
?G ? H T ?S ?G positive, thermodynamically
not favored, reverse process favored -
endergonic ?G negative, thermodynamically
favored - exergonic ?G zero, reversible, at
equilibrium
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Entropy and the Second Law of Thermodynamics

• The direction of processes. Irreversibility of
  processes
• -Reversible always at equilibrium
• -Irreversible far from equilibrium drive
  toward equilibrium state
• Entropy S klnW, where W number of
  substrates, and k boltzman constant
• The entropy of an isolated system will tend to
  increase to a maximum value. Things left alone
  will not get more orderly.
• Enthapy will tend to decrease to the lowest
  possible value.

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Mechanical Forces

• Chapter 2
• Mechanical Properties of Motor Proteins and the
  Cytoskeleton

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Mechanical Forces

• Force what is force, where does it come from
  and what effect does it have on proteins and
  cells?
• Fundamental mechanical elements spring,
  dashpot, and mass
• Difference between molecular biophysics and
  general physics

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Force

• Definition
• Forces acting on molecules Table 2.1
• Work F x Distance
• Net Force
• SI Units of Force - newtons

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Newtons 1st and 2nd Law

• 1st Law if an object has no net force acting on
  it will remain at rest. If it is moving it will
  remain at constant velocity.
• 2nd Law if an object is subjected to net force,
  then is will accelerate according the equation F
  ma.
• Forces can be transferred to biomolecules by
  direct contact of their atoms with other
  biomolecules, or by exposure to a gravitational,
  electrical, or magnetic field.

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Physical Forces

• Elastic Forces F kx
• Viscous Forces - F ?? , where ? 6??r
• Collisional and Thermal Forces - F d(mv)/dt
• Optical Forces - hv/c h/n?
• Gravity F mg, g 9.8 m/s2
• Centrifugal Forces - Fmac
• Electrostatic Forces - F qE
• Magnetic Forces

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Mass, Dashpot, Spring

• Biomolecules Atoms that have mass, connected
  with bonds that have elasticity like springs
• Individual mechanical elements move under applied
  force.

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Mass

• Force causes mass to undergo a constant
  acceleration equal to F/m. The greater the mass
  is the greater the inertia the smaller the
  acceleration. Acceleration is the rate of change
  of velocity (a dv/dt), a constant acceleration
  means the velocity increases linearly with time.

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Dashpot

• An idealized mechanical element that is fixed at
  one end and responds to a force applied at the
  other end by elongating at a constant velocity.
  The velocity of elongation of a dashpot is equal
  to F/?, where gamma is the drag coefficient. Drag
  coefficient is proportional to the viscosity of
  the solution according to Stokes Law.

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Spring

• A mechanical element whose length increases in
  response to an applied force. Like the dashpot,
  one end of the spring is held fixed while a force
  is applied to the other end. An increase in
  length of the spring above resting levels equals
  F/?, where ? is the spring constant. A stiffer
  spring is harder to extend, takes more force.

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Mass and Dashpot

• Mass and dashpot connected in series.
• Model of movement of a cell or protein through a
  liquid.
• The mass experiences an applied force, which is
  opposed by a drag force, Fd -?v. The net force
  is then F Fd F -?v. Since F ma, the ma F
  -?v. Acceleration is the rate of change of
  velocity over time, a dv/dt. We can rewrite
  this equation as m dv/dt ?v F
• V(t) F/?1-exp(-t/ ?) where (? m/?)
• Example inertia of bacterium

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Spring and Dashpot.

• A spring in parallel with a dashpot. A compliant
  object that is deformed in a liquid.
• Protein global conformational change
• Skin adopting a new shape
• Time constant depends on damping and stiffness (?
  ?/?)
• Timescale of protein conformational changes (ns)

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Mass and Spring

• Net Force applied elastic ma F Fs F-kx
• md2x/dt2 kx F
• Constant acceleration displacement increases
  parabolically
• When reach F/k net force is zero, as well as
  acceleration , but inertia keeps it moving
• New avg. displacement F/k, particle stops when
  reach 2F/k.
• Elastic restoring force acceleration back to
  original position. Sinusoidal oscillation or
  harmonic motion
• X(t) F/k1-cos(wt), where w (k/m)1/2
• Frequencies, f w/2?
• Higher mass lower frequency of oscillation,
  higher stiffness, higher frequency of oscillation
• Vibration of chemical bonds

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Motion of Mass and Spring with Damping

• Protein conformational changes damped by internal
  viscosity and viscosity of solution - 3
  mechanical elements
• Underdamped motion ?2 lt 4mk, mass on a spring
• Overdamped motion - ?2 gt 4mk, spring and dashpot
  relaxation time dominates, can drop inertial term
• Molecules are overdamped b/c intertial forces are
  small
• Example relaxation time of motor proteins

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Work, Energy and Heat

• W F x distance(x)
• Force is the negative of the gradient of
  potential energy , Fs -dU/dx
• Some energy stored as kinetic energy
• This energy is dissipated as heat or absorbed by
  the object
• W U Q, conservation of energy
• Example, Motor protein energy stored in
  conformational change