Life, Order, Thermodynamics...Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material

Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material is meant just as a guide, it does not substitute the books suggested for the Course.

Life, Order, Thermodynamics

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A key question about order… How order is created and maintained in biological systems?

Through energy fluxes

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Biological Physics, updated 1st ed. (© Philip C. Nelson)


Energy: conservation and conversion •  Mechanical energy (kinetic + potential):

conserved in absence of friction.

•  Thermal energy (heat): due to friction forces.

•  Total energy (mechanical + thermal): always conserved!

Indeed energy can be converted into different forms:

–  potential into kinetic (e.g. dynamics in a force-field).

–  mechanical into thermal (e.g. viscous friction).

Principles of Thermo-dynamics (valid also for chemical energy)

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Principles of thermodynamics 1. Variation of total energy (internal+kinetic+potential) in an open system (allows flux of matter and energy) is equal to heat absorbed minus work

done on surrounding environment:

2. Different ways of expressing the 2nd theorem: 1.  Heat never flows spontaneously from one body to another with higher temperature

(Clausius formulation).

2.  In a isolated system (no flux of energy or matter) entropy is a not-decreasing function of time, and its variation is maximal during a reversible process:

3.  In minimum-energy state entropy has a well-defined value which only depends on degeneracy of this fundamental state.

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dSdt

≥ 0 dS = dQrev

T≥dQT

Definition of irreversible process, linked to time arrow

ΔE =Q−W


Energies of different quality?

•  Heat is a particular form of mechanical energy, namely kinetic energy due to random motions of atoms and molecules building-up matter.

•  The mechanical energy producing work is “ordered” (fall of a stone, functioning of a turbine, etc…).

•  Is “organization” the key parameter to distinguish between high-quality energy (which can be used to produce work) and

low-quality energy (coming out from a – partial – conversion of high-quality energy)?

•  If so, how to mathematize this concept?

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Free energy •  Defines high-quality energy as total minus that “due to disorder”,

which is proportional to temperature times the entropy:

•  A system at a given temperature T can change spontaneously its status (evolve) only if free energy change ΔF is negative.

•  Can happen either through a reduction in E (e.g. fall of a stone) or through an increase in S (e.g. during isothermal expansion of a gas, or during formation of a solution).

•  High quality when TS E F ≈ E

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F = E −TS


How to create order in living world?

•  In a process leading to a reduction in F, TS could also drop if a larger reduction in E occurs.

•  This does not violate second principle of thermodynamics if system is not isolated (e.g. can exchange heat with surroundings).

Examples are:

–  Vapour condensation (ΔS < 0, ΔE < 0).

–  Interaction of matter with electromagnetic fields.

–  Formation of a chemical bond.

–  Appearance of organized life on Earth.

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F = E −TS


Free energy and order

Thus, an energy flux crossing a given system

could lead to an increase in order of system!

Principle of free energy transductions (anabolism) in

animals and plants.

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Osmosis and energy transduction

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A mechanism of energy transduction that is shared among living and non-living systems is that known as osmosis.


Osmotic flux

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•  Just after the solution is formed, flux of water through semipermeable membrane towards region with highest solute concentration.

•  An osmotic flux can be exploited to perform mechanical work (ΔUload > 0).

•  Associated to increase in entropy of system (spontaneous process), and heat adsorption if work is performed.

• Osmotic pressure does not depend on type of solute, only on its concentration (colligative property).


A mechanism of energy transduction that is shared among living and non-living systems is that known as osmosis.


Osmotic flux Inverse osmosis

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•  If we pull left end we increase concentration of solute in region on right side of semipermeable membrane.

•  This process is called inverse osmosis or ultrafiltration.

•  Mechanical work performed leads to increase in order of system (reduction of entropy), although part of it is dissipated as heat to surrounding environment.



Osmosis in living organisms

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Osmosis in living organisms

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Hypertonic Isotonic Hypotonic


References •  Books

•  Nelson, chap. 1

•  Online resources •  http://www.life.illinois.edu/crofts/bioph354/

•  http://www.fisicamente.net/DIDATTICA/index-1350.htm

•  http://online.scuola.zanichelli.it/chimicafacile/files/2011/02/app13.pdf

•  Movies •  https://www.youtube.com/watch?v=7-QJ-

UUX0iY&list=PL933F4D318515DDD0&index=11 14


Exercise

Demonstrate that the Van’t Hoff equation for a mixture of ideal gases particles, which relates the osmotic pressure Π to the molarity M and to the temperature T of the solution, reads:

Π = R T M

Hint

you need to evaluate the entropy of mixing of an ideal gas, and to recall the form of the first law of thermodynamics for an ideal gas

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Documents

Life, Order, Thermodynamics...Biophysics Course held at Physics Department, University of Cagliari, Italy. Academic Year: 2016/2017. Dr. Attilio Vittorio Vargiu PLEASE NOTE! This material