Lecture 9

Conservation of Energy – Enthalpy and Heat Capacity

Reading: Lecture 9, today: Chapter 6, section A Lecture 10, Wednesday: Chapter 6, section B

MCB65 2/12/15 1 Energy in biological systems Example of a reaction releasing energy:

Example of a reaction performing work: Heat Work

Thermodynamics helps us understand and describe these types of biological processes. MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 2 Thermodynamics

In this course, we will discuss thermodynamics as it applies to biological molecules

We will first cover concepts of classical thermodynamics, which cover macroscopic properties (temperature, volume, pressure, etc)

We will then bring in concepts of statistical mechanics, which will enable us to relate the macroscopic properties to the microscopic view of biological molecules in action

MCB65 2/12/15 3 Classical Thermodynamics

DG = DH – TDS

What is thermodynamics?

Science of heat and temperature Laws governing the conversion of thermal energy into mechanical, electrical or other forms of energy

Concerns bulk properties like pressure, temperature, volume Not based on a specific description of molecules

Helps us predict the direction and extent of chemical and biological reactions (but not the rate) MCB65 2/12/15 4 Math – make sure you understand

We’re entering the more math-intensive part of the course

Work it through on your own as you do the readings and review the lecture If there are things that you don’t know or don’t understand, use the resources available to you Ask in class, section, office hours Review your math textbooks

No need to get stuck on a concept because the math used doesn’t make sense to you!

MCB65 2/12/15 5 Laws of Thermodynamics

The first law of thermodynamics, which mandates conservation of energy.

The second law of thermodynamics, which states that the entropy of the universe always increases.

MCB65 2/12/15 6 Today’s goals

Develop elements of the First law of thermodynamics – conservation of energy

Delineate the system under observation

Understand the concepts of heat and work

Define Enthalpy, H

MCB65 2/12/15 7 Defining the field of observation – the closed system is most useful in biology Closed system most commonly used to study chemical reactions

Closed

MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 8 Defining the field of observation

Two other types of systems are more extreme:

Open Isolated Three different kinds of systems: open, isolated, or closed MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 9 Change in energy of a system

.

U = Energy of the system

ΔU = U(final) – U(initial)

Negative ΔU means an exothermic reaction

Positive ΔU means endothermic reaction

How do we measure these changes in energy? MCB65 2/12/15 10 Calorimetry

Calorimetry is a method to study energetic changes, commonly used in biochemistry

Measures the heat released or taken up by a chemical reaction under study

Isothermal titration calorimetry (ITC) How much heat to keep the temperature constant? Differential scanning calorimetry (DSC) How much heat to increase the temperature by a given amount?

MCB65 2/12/15 11 Isothermal Titration Calorimetry

Uses a closed system

The instrument has a feedback loop that maintains constant temperature in the system (both reference and test cells). Records how much more or less energy is required each time more reagent is added from the syringe. MCB65 Figure adapted from The Molecules of Life (© Garland Science 2008) 2/12/15 12 ITC to measure binding of NC protein to RNA

NC protein

needle

buffer dropwise injection

RNA

Packaging sequence from MLV virus binding to the nucleocapsid (NC)

MCB65 D’Souza and Summers (2004) Nature 2/12/15 13 ITC – an example

Binding reaction is exothermic and maintaining temperature requires less energy during an injection

Packaging sequence from MLV virus binding to the nucleocapsid (NC)

MCB65 D’souza and Summers (2004) Nature 2/12/15 15 Extensive and intensive properties

Doubling the system size

Doubles the energy released

Energy is an extensive property of a system Depends on its size Amount of material is often Volume? specified for extensive Temperature? properties, e.g. kJ mol-1

Density? MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 16 Energy transfer as heat or work

Heat Work

Energy transferred as work is “stored” and can be brought back into the system Mechanical Chemical Electrical

… MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 17 Example of a chemical reaction producing work

Figure from The Molecules of Life (© Garland Science 2008)

Expansion work – energy could be returned to the system by pushing the piston back down

MCB65 2/12/15 18 First Law of Thermodynamics

Law of conservation of energy

dU = dUsystem + dUsurroundings = 0 dU is an infinitesimally small change in energy

dUsystem = -dUsurroundings

A change in energy in the system should always be matched by a change in energy in the surroundings

MCB65 2/12/15 19 Change in energy through heat and work

dUsystem can come about through heat and/or work q denotes heat and w denotes work

Change in energy of the system can be written out as:

dUsystem = dq + dw

Increment of heat = dq Increment of work = dw

MCB65 2/12/15 20 Sign conventions

Changes that increase the Usystem have a positive sign negative sign if they decrease the Usystem

dUsystem = dq + dw

“positive in, dw will have negative out” negative value

Here, heat transferred to the system increases its energy, therefore dq will be positive Work done by the system to move the piston up decreases its energy, therefore dw will be negative MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 21 Reactions under constant volume have no expansion work

dUsystem = dq + dw

If there is no change in volume, then dw = 0 and

dUsystem = dq

MCB65 2/12/15 22 Biological reactions - under constant pressure

dUsystem = dq + dw If a reaction produces a gas, the gas will cause expansion work of magnitude PEXTdV: negative because the dUsystem = dq − PEXTdV work is done by the system

The heat transferred to the system will be:

dq = dUsystem + PEXTdV

When the volume changes in reactions at constant pressure, the heat transferred to the system is NOT equal to the change in energy

MCB65 2/12/15 23 Defining Enthalpy

Hsystem = Usystem + PVsystem H = Enthalpy Enthalpy is the total energy of a system, the sum of its internal energy (U) and the energy required to make room for it in its surroundings (PV) Change in enthalpy is then:

dHsystem = dUsystem + PdVsystem + VsystemdP

For biological reactions, which happen under constant pressure,

VsystemdP = 0:

dHsystem = dUsystem + PdVsystem And therefore

dHsystem = dq (at constant pressure)

MCB65 2/12/15 24 Enthalpy is useful in biology

Under constant pressure:

dHsystem = dUsystem + PdVsystem Most biological reactions do not cause a change in volume and therefore PdVsystem = 0 and

dHsystem = dUsystem

That is why enthalpy is such an important concept – change in enthalpy often reflects change in energy, and is easy to measure

E.g. protein + ligand ↔ protein-ligand complex By measuring dq (e.g. through ITC), we can determine the difference in energy between bound and unbound MCB65 2/12/15 25 State variables

State variables are properties of the system that are independent of the history of the system

U = Energy  P = Pressure  V = Volume  H = Enthalpy  q = Heat “path” or “process” w = Work functions

MCB65 2/12/15 27 Energy vs. direction of spontaneous change

But those are single, macroscopic objects. What about molecular reactions and populations of molecules?

MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 28 Energy vs. direction of spontaneous change

Setting up the experiment: Reminder: Ideal Gas Law PV = nRT

Reminder: An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The idea of an ideal gas is often used in thermodynamics to develop concepts with minimal real life complications MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 29 Adiabatic - In the absence of heat exchange

Starting from dU = dq + dw In this case, dq = 0 therefore dU = dw dw is negative because the gas does work on the piston For an ideal gas U = kinetic energy = (3/2)nRT (Box 6.3) dU = (3/2)nRdT therefore dU and dT are negative and temperature decreases and the kinetic energy of the gas also decreases MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 30 Isothermal expansion

Here dU = dq + dw = 0 because T = constant Ideal gas: dU = (3/2)nRdT In this case, dq = -dw Even though dU = 0, there is a change in the system. What is driving this change?

MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 31 Some key concepts

First law of thermodynamics: energy (U) is conserved Heat transferred to the system (dq) has a (+) value Work done by the system (dw) has a (-) value

Change in enthalpy (dH) = change in heat (dq) at constant pressure

Extensive properties depend on the size of the observed system whereas intensive properties do not

State variables depend only on the current state of the system, not its history

It’s important to fully delineate the system under observation MCB65 2/12/15 32