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Group: Deep Thought

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Transfer of Heat in Biological Systems

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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?

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Temperature Field Three-dimensional Non-uniform So A mathematical formulation of burns is difficult to obtain But. Difficult, but not impossible

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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 Distributions Thermal Protein Denaturation

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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

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Arrhenius Process Observed in thermally activated reactions Collision Theory: Molecules react if they collide with kinetic energy that exceeds E A Explains temperature dependence of reaction rates Boltzmann: probability of reactive collisions

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Application of Arrhenius How is Thermal Injury explained by Arrhenius? Two Hypotheses: 1. Statistical Mechanics. Central Limit Theorem 2. Specific Denaturation.

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Statistical Thermodynamics Free Energy Distribution in Proteins

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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

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

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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 proteins 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)

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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. K (F. Despa, 2005) Percent denaturation equation:Rate of unfolding and refolding:

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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)

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Table.1:Percent denaturation of proteins and cellular components after 20 seconds exposure to varying temperatures (40-66C) Table 2: Percent denaturation of proteins and cellular components at 80 C as a function of time.

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

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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

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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

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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

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Quickly heat collagen to a specific temperature Measure shrinkage over time isothermally Equation: is the shrinkage, K(T) is the specific reaction rate, is the time

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Denaturation of Collagen Via Heating: An Irreversible Rate Process Wright

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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. An initial heat distribution resulting from point exposure to a high temperature object Heat diffusion as experienced by a particular skin surface model.