Physical Biology
LES 1: H5
Sorts of energy: (can translate into each other)
- Chemical (often how cells store energy)
o ATP, NAD(P)H, proton motive force (H+)
- Mechanical
- Electromagnetic
- Thermal
!!! kBT:
- Represents thermal energy
o kB = Boltzmann cte = 1,38*10-23 J/K
Relates temperature to energy
o T = temperature (K)
- Gives a measure of the average kinetic energy of particles in a
system
- Often used as energy scale: as reference point to compare different
forms of energy in a system
Equilibrium state:
System will return to its original state after a distortion
- Thermal forces: forces that arise due to temperature changes
resuting in motion of particles
- Deterministic forces: produce a predictable and reproducible effect
on a system
o Outcome will always be the same with given initial conditions
(always lead to the same result)
Bv gravity will always pull objects down to the earth
- Ratio E/kBT used to compare both forces
Energies at nanometer scale:
o Deterministic: forces become stronger due to shorter
distances between particles (bv electrostatic forces
between 2 charged particles)
o Thermal: motion of molecules due to T fluctuations
becomes more prominent
Can be comparable: kBT can be close to the magnitude of
intermolecular forces
, - Mechanical equilibrium: net force and net torque acting on an object
are zero (object is not accelerating)
o Static: object is at rest
o Dynamic: object moves at a constant speed
- Chemical equilibrium: rates of the forward and reverse reactions are
equal
Work:
Transfer of energy when a force is applied to an object and it
makes a displacement (it moves) in the direction of the applied
force
- Positive work: force & displacement in the same direction you
deliver energy TO the system
- Work done by all the forces acting on a system = change in energy
of the system
o Work = sum of change in kinetic energy & change in potential
energy
o Kinetic energy = energy of an object in motion
o Potential energy = energy stored in an object due to its
position/state
Strain/stress:
- Strain (= eenheidsvervorming): ε = deltaL/L0
- Stress (= force applied per unit area = spanning): σ = F/A
o σ/E = ε F/A = E*ε
E = Young’s modulus = stress/strain = (F/A)/(deltaL/L0)
Energy function:
Describes the energy of a system in terms of its configuration
relationship between the state of a system & the total energy
- Energetic cost: energy required to deform a material
o Bv when an elastic material deforms: work done on the
material is stored as elastic potential energy
Free energy:
- Entropy = number of different ways of rearranging the system
o Equilibrium state: state that has minimum free energy (out of
all the possible states the system can be in)
- ‘Entropy provides a measure of the microscopic degeneracy of a
macroscopic state’
o Degeneracy of a macroscopic state: number of different
microscopic configurations (microstates) that could lead to the
same microstate
, - 2nd law of thermodynamics: the universe will always increase entropy
until it’s reached its maximum
o Bv. molecules flow from higher to lower concentrations
Lower concentrations there are less molecules so more
space for the molecules to move and spread out leads
to more possible configurations = increase in entropy
- Free energy is dependent on energy of the system & entropy
o To minimize free energy: minimize energy & maximize entropy
LES 2: H6
Boltzmann distribution:
- Probability (pi) of a system being in a particular energetic state Ei at
a given T
o Exponential factor: probability of occupying a state decreases
exponentially with increasing energy
Lower energy states are more likely to be occupied than
higher energy states (especially at low T)
o T: when T increases, the probability distribution spreads out
more system is more likely to also occupy higher energetic
states
At lower T’s it looks more like this and the system will
mostly occupy lower energetic states
- Partition function Z:
o A sum over all possible energetic states weighted by their
Boltzmann factors
o = normalization factor = makes sure that the sum of all the
probabilities equals to 1
- Average energy (<E>) = sum of the energies of all possible states,
each weighted by the probability of the system to be in each state
, o Sum of Ei*Pi energy of one state & probability that the
system is in this state
- BOLTZMANN EQUATION: describes how mobile ions in a system
distribute themselves in response to the electrostatic potential (zie
H9)
States & weights diagrams:
Represent the possible energetic states of a system and their
relative probabilities (weigths) according to the Boltzmann
distribution
- Multiplicity = among of microstates with the same energy
o Multiplicity = 1 when a macrostate can only be formed by 1
microstate
- Binomial coefficient = number of ways to choose L elements from a
set of omega elements without considering order
Chemical potential (µ):
Measure o how the energy of a system changes when the number
of particles changes
o How much energy is required to add/remove a particle
while keeping other variables cte
- Higher chemical potential: molecules have a higher tendency to
spread out system has more energy available
Law of mass action:
States that the rate of a chemical reaction is proportional to the
product of the concentrations of the reactants, each raised to the
power of their respective stoichiometric coefficients.
Hill function:
Models how the response of a system depends on the
concentration of a ligand
o Binding o one molecule influences the binding of others
o = cooperativity
o Higher Hill coefficient = more switch-like behavior
LES 3: H7
Two-state systems:
System that can exist in 1 of 2 possible states
Two-state variable: σ
- Gating = mechanism that regulates the transition between different
states of a system
LES 1: H5
Sorts of energy: (can translate into each other)
- Chemical (often how cells store energy)
o ATP, NAD(P)H, proton motive force (H+)
- Mechanical
- Electromagnetic
- Thermal
!!! kBT:
- Represents thermal energy
o kB = Boltzmann cte = 1,38*10-23 J/K
Relates temperature to energy
o T = temperature (K)
- Gives a measure of the average kinetic energy of particles in a
system
- Often used as energy scale: as reference point to compare different
forms of energy in a system
Equilibrium state:
System will return to its original state after a distortion
- Thermal forces: forces that arise due to temperature changes
resuting in motion of particles
- Deterministic forces: produce a predictable and reproducible effect
on a system
o Outcome will always be the same with given initial conditions
(always lead to the same result)
Bv gravity will always pull objects down to the earth
- Ratio E/kBT used to compare both forces
Energies at nanometer scale:
o Deterministic: forces become stronger due to shorter
distances between particles (bv electrostatic forces
between 2 charged particles)
o Thermal: motion of molecules due to T fluctuations
becomes more prominent
Can be comparable: kBT can be close to the magnitude of
intermolecular forces
, - Mechanical equilibrium: net force and net torque acting on an object
are zero (object is not accelerating)
o Static: object is at rest
o Dynamic: object moves at a constant speed
- Chemical equilibrium: rates of the forward and reverse reactions are
equal
Work:
Transfer of energy when a force is applied to an object and it
makes a displacement (it moves) in the direction of the applied
force
- Positive work: force & displacement in the same direction you
deliver energy TO the system
- Work done by all the forces acting on a system = change in energy
of the system
o Work = sum of change in kinetic energy & change in potential
energy
o Kinetic energy = energy of an object in motion
o Potential energy = energy stored in an object due to its
position/state
Strain/stress:
- Strain (= eenheidsvervorming): ε = deltaL/L0
- Stress (= force applied per unit area = spanning): σ = F/A
o σ/E = ε F/A = E*ε
E = Young’s modulus = stress/strain = (F/A)/(deltaL/L0)
Energy function:
Describes the energy of a system in terms of its configuration
relationship between the state of a system & the total energy
- Energetic cost: energy required to deform a material
o Bv when an elastic material deforms: work done on the
material is stored as elastic potential energy
Free energy:
- Entropy = number of different ways of rearranging the system
o Equilibrium state: state that has minimum free energy (out of
all the possible states the system can be in)
- ‘Entropy provides a measure of the microscopic degeneracy of a
macroscopic state’
o Degeneracy of a macroscopic state: number of different
microscopic configurations (microstates) that could lead to the
same microstate
, - 2nd law of thermodynamics: the universe will always increase entropy
until it’s reached its maximum
o Bv. molecules flow from higher to lower concentrations
Lower concentrations there are less molecules so more
space for the molecules to move and spread out leads
to more possible configurations = increase in entropy
- Free energy is dependent on energy of the system & entropy
o To minimize free energy: minimize energy & maximize entropy
LES 2: H6
Boltzmann distribution:
- Probability (pi) of a system being in a particular energetic state Ei at
a given T
o Exponential factor: probability of occupying a state decreases
exponentially with increasing energy
Lower energy states are more likely to be occupied than
higher energy states (especially at low T)
o T: when T increases, the probability distribution spreads out
more system is more likely to also occupy higher energetic
states
At lower T’s it looks more like this and the system will
mostly occupy lower energetic states
- Partition function Z:
o A sum over all possible energetic states weighted by their
Boltzmann factors
o = normalization factor = makes sure that the sum of all the
probabilities equals to 1
- Average energy (<E>) = sum of the energies of all possible states,
each weighted by the probability of the system to be in each state
, o Sum of Ei*Pi energy of one state & probability that the
system is in this state
- BOLTZMANN EQUATION: describes how mobile ions in a system
distribute themselves in response to the electrostatic potential (zie
H9)
States & weights diagrams:
Represent the possible energetic states of a system and their
relative probabilities (weigths) according to the Boltzmann
distribution
- Multiplicity = among of microstates with the same energy
o Multiplicity = 1 when a macrostate can only be formed by 1
microstate
- Binomial coefficient = number of ways to choose L elements from a
set of omega elements without considering order
Chemical potential (µ):
Measure o how the energy of a system changes when the number
of particles changes
o How much energy is required to add/remove a particle
while keeping other variables cte
- Higher chemical potential: molecules have a higher tendency to
spread out system has more energy available
Law of mass action:
States that the rate of a chemical reaction is proportional to the
product of the concentrations of the reactants, each raised to the
power of their respective stoichiometric coefficients.
Hill function:
Models how the response of a system depends on the
concentration of a ligand
o Binding o one molecule influences the binding of others
o = cooperativity
o Higher Hill coefficient = more switch-like behavior
LES 3: H7
Two-state systems:
System that can exist in 1 of 2 possible states
Two-state variable: σ
- Gating = mechanism that regulates the transition between different
states of a system
