The Thermodynamicsof Burns

Group: Deep Thought

Macro Level

Transfer of Heat in Biological Systems

Biological System?

• Tissue– Skin• 3 layers:

– A thin outer Epidermis– A thicker layer of Dermis– A thick subcutaneous fatty tissue (Hypodermis)

• First-, Second-, and Third-Degree Burns

• How is heat transferred in the system?

Difficulties in Obtaining an Accurate Model

• Temperature Field– Three-dimensional– Non-uniform

• So…– A mathematical formulation of burns is

difficult to obtain• But….– Difficult, but not impossible

Bio-Heat Transfer Model

Bio-Heat Transfer Equation

• is density• is heat capacity• is the conductivity of tissue• is an index for the physical properties of blood• is the normalized blood perfusion of tissue• is the heat from metabolism• is the body core or deep tissue temperature• is the temperature of the skin at the burn site

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Cellular Level

Free Energy DistributionsThermal Protein Denaturation

Burn Trauma at the Cellular Level

• Which cellular structures are most vulnerable?

• Which are most critical in cell viability?

• Kinetics of damage ought to depend on multiple factors in the chemical environment

• Moritz and Henriques (1947): Time – Temperature relationship for

scald burning of forearm skin was Arrhenius

Arrhenius Process

• Observed in thermally activated reactions• Collision Theory:

Molecules react if they collide with kinetic energy that exceeds EA

• Explains temperature dependence of reaction rates

• Boltzmann: probability of reactive collisions RTEAekk /

0

Application of Arrhenius

• How is Thermal Injury explained by Arrhenius?• Two Hypotheses:

1. Statistical Mechanics. “Central Limit Theorem”

2. Specific Denaturation.

Statistical Thermodynamics

Free Energy Distribution in Proteins

Energetics of Denaturation

• Thermodynamics forces drive changes in protein conformations

• Central Limit Theorem: infinite number of different processes behave like single Arrhenius process

• Gibbs Free Energy (G): max energy available for work

Free Energy Distribution in Proteins

• Douglas Poland• Protein in aqueous solutions – Fluctuations in conformation and molecular

vibrations broad distribution of enthalpy states– Approximate distribution function using

maximum – entropy method from moments

• Gm becomes the central function: describes thermal behavior of a protein in the enthalpy neighborhood of the denaturation maximum.

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Burn Injuries Cause Protein Denaturation

• At normal physiological temperatures, proteins are in a folded, three-dimensional conformation.

• When a burn injury occurs, tissue is heated to well above physiological pH, and components of a protein’s 3-D structures are damaged, resulting in an unfolding and eventual denaturing of the protein.

• Denaturation is irreversible.

• A simple example of protein denaturation is the cooking of an egg white. (F. Despa, 2005)

The Rate of Protein Denaturationis Arrhenius-like

• The process of protein denaturation and aggregation can be modeled as a statistical process

• Rate of protein unfolding similar to the Arrhenius equation• As the temperature increases, a protein is unable to remain in its normal, folded

conformation and begins to transition into its unfolded state. • At the melting temperature of the protein, it can unfold and refold at the same

rate. • The protein can also reach its denatured state by transitioning irreversibly from its

unfolded state • If the rate of conversion from the unfolded state to the denatured state is faster

than the transition from the unfolded state to the refolded state, then the rate of denaturation becomes independent of the rate of irreversible unfolding and refolding.

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(F. Despa, 2005)

Percent denaturation equation:Rate of unfolding and refolding:

Why does protein denaturation followthe Arrhenius equation?

• The kinetics of protein denaturation is affected by so many different factors: density, solvent, bond strengths, interactions with surrounding molecules.

• Since every protein is different, then clearly each protein should have a different rate of denaturation.

• How, then, is it possible that the rate of protein denaturation follows a single, Arrhenius-like equation?

• 2 hypotheses:1. Cell denaturation depends on an infinite number of different processes that, when

combine, behaves like a single Arrhenius process. 2. Lethal burn injury is dominated by only a few molecular processes i.e., there are

one or two key structures that are critical to cell survival in a burn injury.

• The relative stability of a variety of different types of tissues was investigated by F. Despa et al. to determine if cell denaturation is dependent on only a few molecular processes.

(F. Despa, 2005)

(F. Despa, 2005)

Table.1:Percent denaturation of proteins and cellular components after 20 seconds exposure to varying temperatures (40-66ºC)

Table 2: Percent denaturation of proteins and cellular components at 80 ºC as a function of time.

Damage to Components of the Plasma Membrane are the Most Significant Cause of Tissue Necrosis in Burn Injury

• As can be seen from the graphs, most of proteins in the study denature at around 60 ºC.

• The lipid bilayer and the membrane bound ATPases, the Na+/K+ pump (NKP) and Ca2+ pump (PMCP), are the first to denature.

• As a result of these findings, this study suggests that alteration of the plasma membrane and its components as a result of high temperatures “is likely to be the most significant cause of tissue necrosis.”

(F. Despa, 2005)

http://academic.brooklyn.cuny.edu/biology/bio4fv/page/cotrans.htm

Developing Models

• Heating therapies that intentionally incite protein denaturation are being used in a variety of medical fields

• Most of these therapies are refined by trial and error

• Developing theoretical models– Reduces need for extensive clinical trials– Makes therapies more effective

What Do We Need to DevelopTheoretical Models?

• Determine rate of denaturation– As a function of temperature– As a function of mechanical load

• Determine the values of thermophysical properties– Specific Heat– Thermal Conductivity– Thermal Diffusivity

Collagen• Target of many heating therapies• Triple-helix structure• Moderate heating– Induces reversible local unfolding– Breaking of a few hydrogen bonds– Regains shape upon cooling

• Severe heating– Time-dependent irreversible changes– Breaking of many hydrogen bonds– Random, coiled structure

• Shrinks upon heating

Temperature-Jump Tests

• Quickly heat collagen to a specific temperature

• Measure shrinkage over time isothermally

• Equation:

• ξ is the shrinkage, K(T) is the specific reaction rate, τ is the time

)(TKw e

Collagen Shrinkage Over Time

“Denaturation of Collagen Via Heating: An Irreversible Rate Process” Wright

Developing Models• Actually developing a working

mathematical model is beyond the scope of this project• Requires fairly extensive empirical

validation and assigning meaningful values to constants

• Our proposal for animal testing fell through, so we were unable to gather our own data on this front

• Solve:

• For temperatures, then plug that result into the Arrhenius

• Both equations must be integrated numerically.

• As the reaction proceeds heat is absorbed and released by the proteins folding and unfolding.

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An initial heat distribution resulting from point exposure to a high temperature object

Heat diffusion as experienced by a particular skin surface model.