Thermodynamics of Biological Systems

Thermodynamics of Biological Systems

Champion Deivanayagam

Center for Biophysical Sciences and Engineering

University of Alabama at Birmingham.

Outline:

Laws of thermodynamics

Enthalpy

Entropy

Gibbs free energy

some examples

What you need to know for your exam:

Definition of a thermodynamic system

Three laws of Thermodynamics

Definitions of Enthalpy, Entropy

Gibbs Free energy

ATP’s ionization states and its potential

Energy: 1. Kinetic Energy

2. Potential Energy

Energy is the capacity to do work

Kinetic energy is the form of energy expended by objects in motion

A resting object still possess energy in the form of potential energy

Energy can be converted from one form into another

Thermodynamics:

A study of energy changes in systems:

System:

1. Isolated

2.

Closed

3. Open

First law of thermodynamics:

Energy is neither created nor destroyed; the energy of the universe is a constant

The total internal energy of an isolated system in conserved.

E = E

2

– E

1

= q + w

q – heat absorbed by the system from surroundings

w – work done on the system by the surroundings

Mechanical work is defined as movement through some distance caused by the application of force

Internal energy is independent of path

and represents the present state of the

system and is referred to as a State function

Mechanical Work:

w

= -P

V where V = V

2

– V

1

Work may occur in multiple forms:

1. Mechanical

2 . Electrical

3. magnetic 4. Chemical

The calorie (cal, kcal) are traditional units

Joule’s is the recommended SI unit.

Table of important thermodynamic units and constants

At constant pressure

work can be defined as

Enthalpy:

H = E + PV

In a

constant pressure system

(as in most biological systems)

one can then define it as

H = E + PV

When you expand on this equation:

H = q (simply put the heat energy of the system)

Enthalpy changes can be measured using a calorimeter:

For a system at equilibrium for any process where A

B

the standard enthalpy can be determined from the temperature dependence

using:

R- is the gas constant

R= 8.314 J/mol . K

Notice the ° sign: These are used to denote standard state:

For solutes in a solution, the standard state is normally unit activity (simplified to 1M concentration)

Protein

denaturation

:

Study of temperature induced reversible denaturation

of

chymotrypsinogen

At pH 3.0

T(K) 324.4 326.6 327.5 329.0 330.7 332.0 333.8

K

eq

0.041 0.12 0.27 0.68 1.9 5.0 21.0

Native state (N)

 Denatured state (D)

K

eq = [D] / [N]H° at any given temperature is the negative

of the slope of the plot:

H° = -[14.42]/[-0.027] x 10-3 = +533 kJ/mol

van’t

Hoff Plot

Positive values for

H° would be expected to break bonds and expose hydrophobic groups

During the unfolding process and raise the energy of the protein in solution.

Second law of thermodynamics:Every energy transfer increases the entropy (disorder) of the universe

System tends to proceed from ordered states to disordered states

Some definitions:

Reversible: a process where transfer of energy happens in both directions

Irreversible: a process where transfer of energy flows in one direction

Equilibrium: A

 B

(all naturally occurring process tend to equilibrium)

Entropy:

Entropy changes measure the dispersal of energy in a process.

Relationship between entropy and temperature



S = k

ln

W

fina

l

– k

ln

W

initial

k- is the Boltzmann’s constant

W – number of microstates

dS

reversible

=

dq

/T

S = k

ln

W

Third law of thermodynamics:

Entropy of any crystalline substance must approach zero as temperature approaches 0° K

The absolute entropy can be calculated from this equation:

Cp is the heat capacity, defined as the amount of heat 1 mole of it can store as the

temperature of that substance is raised by 1 degree.

For biological systems entropy changes are more useful than absolute entropies

Gibb’s free energy ‘G’

Determines the direction of any reaction from the equation:

G = H – TS

For a

constant pressure and temperature

system (as most biological systems) then the

Equation becomes easier to handle

G = H - TS

The enthalpy and entropy are now defined in one equation.

G is negative for

exergonic

reactions (release energy in the form of work) is positive for endergonic

reactions (absorbing energy in the form of work)

Consider a reaction: A + B



C + D

At Equilibrium:

G° = RT

ln

K

eq

and

K

eq

= 10

-

G°/2.3RT

Example of chymotrypsinogen

denaturation

From the

van’t

Hoff plot we calculated

H° = +533 kJ/mol

At pH 3.0

T(K) 324.4 326.6 327.5 329.0 330.7 332.0 333.8

K

eq

0.041 0.13 0.27 0.68 1.9 5.0 21.0

The equilibrium constant at 54.5 °C (327.5K) is 0.27

Then



G

°

= (-8.314 J/

mol

·

K

) (327.5K)

ln

(0.27) = - 3.56 kJ/mol

Similarly calculating

S

° = - (

G - H°) / T = 1620 J/

mol

·K

For a process to occur spontaneously the system must either give up energy (decrease H) or give up order (increase in S)

or both

In general for the process to be spontaneous:

G must be negative

The more negative the G value, the greater the amount of work the process can perform

Exergonic

reactions:

G is negative and the reaction is spontaneous

Example: Cellular respiration

C

6

H12O6 + 6O2 6C02 + 6 H2

0

G = -686 kcal/mol (-2870 kJ/mol)

(For each molecule of glucose broken 686 kcal energy is made available for work)

Endergonic

reactions:

G is positive and requires large input of energy:

Example: Photosynthesis where the energy is derived from the sun.

Table: Variation of Reaction Spontaneity (Sign of

D

G

) with the signs of

D

H

and

DS

.

ATP: Adenosine triphosphate

A cell does three kinds of work:

1. Mechanical work: beating of cilia, muscle contraction etc.

2. Transport work: Moving substances across membranes

3. Chemical work: Enabling non-spontaneous reactions to occur spontaneously

e.g.

Protein synthesis.

The molecule that powers most kinds of work in the cell is ATP

Energy is released when one or more phosphate

groups are hydrolyzed

ATP + H

2

O

→ ADP + Pi (

G

°

= -35.7 kJ/mol)

G° = RT

ln

Keq

The activation energies for phosphoryl

group-transfer

reactions

(200 to 400 kJ/mol) are substantially larger than the free energy of hydrolysis of ATP (-30.5 kJ/mol).

ΔG

o

` = -30.5 kJ/mole

= -7.3 kcal/moleΔG` = -52 kJ/mole = -12.4 kcal/mole

Cellular conditions

:

[ADP][P

i] / [ATP] = 1/850

Ionization States of ATP

ATP has five dissociable protons

pK

a

values range from 0-1 to 6.95

Free energy of hydrolysis of ATP is relatively constant from pH 1 to 6, but rises steeply at high pH

Since most biological reactions occur near pH 7, this variation is usually of little consequence

The pH dependence of the free energy of hydrolysis of ATP. Because pH varies only slightly in biological environments, the effect on G is usually small.

The free energy of hydrolysis of ATP as a function of total Mg2+ ion concentration at 38°C and pH 7.0

.

(

Adapted from Gwynn

, R. W.,

and

Veech

, R. L., 1973. The equilibrium constants of the adenosine triphosphate hydrolysis and the adenosine

triphosphate

-citrate

lyase

reactions. Journal of Biological Chemistry 248:6966–6972.) 

The free energy of hydrolysis of ATP as a function of concentration at 38°C, pH 7.0. The plot follows the relationship described in Equation (3.36), with the concentrations [C] of ATP, ADP, and Pi assumed to be equal.

What is the Daily Human Requirement for ATP?

The average adult human consumes approximately 11,700 kJ of food energy per day

Assuming thermodynamic efficiency of 50%, about 5860 kJ of this energy ends up in form of ATP

Assuming 50 kJ of energy required to synthesize one mole of ATP, the body must cycle through 5860/50 or 117 moles of ATP per day

This is equivalent to 65 kg of ATP per day

The typical adult human body contains 50 g of ATP/ADP

Thus each ATP molecule must be recycled nearly 1300 times per day

Isothermal titration calorimetry

Reference and experimental cell

Heat energy required to maintain both of them

At the same level is measured and integrated.

This allows for the measurement of

Kd

,

G and S

A1 A2 A3

P1 P2 P3

S

V-region

W M C

1

39

201

448

578

828

840

960

1486

1561

A1 A2 A3

P1 P2 P3

V-region

ITC studies on

A123 +

VP3 regions

1:1

Stoichiometric

ratio

(

N=0.946

±

0.006) and

K

d

~ 40 nm

Large

release of Heat energy indicates

Ordering of structures

Hydrogen bonding

The

K

d

and the energy released indicate that the interaction between these two regions is strong.

What happens in a cell if G = 0 ?