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1. ABSTRACT

Since the first major publication on thermodynamics of biochemical reactions by Hans Krebs in 1957, extensive research has been conducted in the field of biological thermodyamics. In this report, in the beginning the two thermodynamic laws were explained by considering two different biological systems. In addition, application of thermodynamics to biological systems was discussed with emphasis on the ATP-ADP cycle, enzyme catalysis reactions and DNA melting.

2. INTRODUCTION

Biological thermodynamics is a branch in thermodynamics which provides useful knowledge about living systems and biological processes considering the molecular and cellular mechanisms involved [1]. Essentially, a biological system is referred to a living system, contained by a boundary across which there is a transfer of energy, matter or work. Studying biological thermodynamics helps us better conceive the mechanisms involved during cell division in protein synthesis, finding out the thermodynamic considerations that cause the nucleic acids, proteins, and membranes to assume their active structures [2].

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Occasionally, it can be found that some biological mechanisms are inconsistent with the thermodynamic principles, but the importance of analysis in these cases is to better understand what really determines the equilibrium in biological systems and how the living systems are produced by coupling these equilibrium processes. In principle, thermodynamics provides a common framework for diverse biological systems [3].

3. RELATING THERMODYNAMIC LAWS TO BIOLOGICAL SYSTEMS

3.1 FIRST LAW OF THERMODYNAMICS

The first law of thermodynamics also called the "conservation of energy principle" is considered one of the fundamental laws of nature. According to this law during any interaction, energy cannot be created or destroyed but can be converted in to a different form while maintaining the total amount of energy constant. One of the practical applications of this first law is in the diet industry. For example, as seen in Fig 1, when a person takes excess input energy (over eating) compared to the amount of energy that he spends(exercise), that person will eventually gain weight which is stored as fat in our body. Alternatively, a person taking lesser energy input than energy output will lose weight. The change in the energy content in this particular body system is the difference between the energy input and the energy output, expressed as Ein - Eout = ?E (energy balance)

3.2 SECOND LAW OF THERMODYNAMICS

The second law of thermodynamics termed as the "law of increased entropy" states that spontaneous changes that do not require outside energy increase the entropy, or disorder, of the universe. Example for the second law is shown in Fig 2. In this context, entropy is added to the cheetah's surroundings in the form of heat and the small molecules (carbon dioxide and water (sweat)) that are the by-products of metabolism.

4. APPLICATIONS OF THERMODYNAMICS TO BIOLOGICAL SYSTEMS

4.1 HYDROLYSIS OF ATP TO ADP

Thermodynamic analysis of glycolysis is a good illustration of how thermodynamics can help in understanding the many coupled reactions occurring in biology. It also demonstrates how metabolism is utilized to produce molecules such as ATP that can be used to drive other physiological reactions, rather than converting most of the free energy to heat. The ATP-ADP cycle is part of the ten step glycolysis process which deals with the energy storage of our body. Adenosine triphosphate , known as ATP, contains the stored energy in our body, while Adenosine diphosphate known as ADP helps in intermediate cellular metabolism [4]. The mechanism of the hydrolysis of ATP to ADP and then back to ATP is shown as schematic in Fig 3. From the schematic we observe that the conversion of ATP to ADP is an exothermic process while the reverse process of ADP conversion back to ATP is an endothermic process.

Before going forward with deriving the free energy of hydrolysis of ATP, it is worth noting that when considering biochemical reactions, the exact nature of the standard state are different to the chemical reactions. In this example, for ATP, the standard state normally would be 1 M, but this includes taking into consideration all possible states of protonation, the sum of the metal complexs and uncomplexed species. The activity of water is set equal to 1 for reactions in dilute solutions. This assumption is justified since the concentration of water is essentially constant. Finally, pH 7 is usually selected as the standard condition, so that the activity of the hydrogen ion is set equal to 1 at pH 7, and the standard free energy of formation of the hydrogen ion is set equal to zero at pH 7.

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Considering the hydrolysis reaction of ATP to ADP and orthophosphate (Pi), the standard enthalpy change for this reaction can be calculated from the known enthalpies of hydrolysis and also the standard free energy change of the hexokinase reaction can be calculated since the standard free energies of hydrolysis are known.

In order to determine an equilibrium constant, a measurable amount of both reactants and products must be present. For reactions specified above that essentially go to completion, a sequence of reactions must be found with measurable equilibrium constants that can be summed to total the reaction of interest. The individual equilibrium constants calculated for the resultant reaction,

The resultant enthalpy of this reaction, ?H° = -30.88kJ/mol, finally, equilibrium constant at different temperatures can be found out by Eq.6

The standard Gibbs free energy of ATP hydrolysis, ?G&deg; = -32.48 kJ/mol < 0, is less than zero the reaction is thermodynamically favorable and spontaneous reaction.

4.2 DIRECT SYNTHESIS OF ATP FROM ADP

From the previous section we observe that, the standard free energy change for the hydrolysis of ATP to ADP and orthophosphate (Pi) is -32.5kJ/mol. This shows that the reverse reaction is thermodynamically unfavourable and it seems unlikely that ATP would be synthesized. Also the concentrations of reactants cannot be adjusted sufficiently to make the overall free energy favorable since the reaction takes place in physiological condition. Yet, it is well known fact that ATP is synthesized directly from ADP and orthophosphate (P), in the mitochondria present in our body [1].

For many years, people in this field grappled to find the mechanism on how this is possible. In 1961 Peter Mitchell proposed that the synthesis of ATP occurred due to a coupling of the chemical reaction with a proton gradient across the membrane. The enzyme responsible for ATP synthesis, ATP synthase, consists of a protein "ball," which carries out the catalytic function, coupled to membrane-bound proteins through which protons can be transported. The process of proton transfer in ATP synthesis is shown schematically in Figure 4.

Fig 4: Schematic representation of ATP synthase, E, in mitochondria. The enzyme inside the mithocondria contains the catalytic sites. Protons are pumped from the outside of the membrane to the inside as ATP is synthesized

According to the chemiosmotic hypothesis, a pH gradient is established across the membrane by a series of electron transfer reactions, and the ATP synthesis is accompanied by the simultaneous transport of protons across the membrane. The overall reaction can be written as the sum of two reactions(Eq.7):

For the above resultant reaction, experimentally the value of n was calculated to be 3. The free energy change for the transport of protons in this reaction is written as

The standard free energy for this process is , since the hydrogen ions concentration present inside and outside the membrane is the same. At 298K, pH differential of one unit gives a free energy change of -17.1kJ/mol. The actual physiological situation is even more favorable than the standard state as a membrane potential exists whereby the membrane is more negative on the inside relative to the outside. By utilizing the extended chemical potential equation an additional term is added equal to 3 F?, where 3 is the number of protons transported, F is the Faraday, and ? is the membrane potential.

The standard free energy for the synthesis of ATP from ADP and P in physiological conditions is +32.5 kJ/mol, but we need to know the free energy change under physiological conditions. Although the concentrations of the reactants are not known exactly, estimation of the ratio of ATP to ADP is taken as about 100, and the concentration of phosphate is 1-10 mM. This makes the ratio [ATP]/ ([ADP] [P]) equal to 100-1000.

Thus, the coupling of the synthesis of ATP to a modest proton gradient and membrane potential can readily provide the necessary free energy for the overall reaction to occur. It is important to note that the coupling of free energies is very general. It can involve chemical reactions only, as in glycolysis, or it can involve other processes such as ion transport across membranes, as in this example.

4.3 ENZYME CATALYSIS

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Enzyme catalysis is the process of increasing or decreasing the rate of the chemical reactions by means of specialized enzymes which in principle it is similar to chemical catalysis. Enzymes can be though as simple catalysts which drastically increase the rate of reaction. This rate of increase can often reach to a factor of 106 or more.

If we consider an example of the following reaction (Eq.10), the time taken for carbon dioxide to react with water occurs without any catalyst is 100sec, but in the presence of carbonic anhydrase as catalyst it only takes 10-5sec.

So, enzymes basically increase the reaction rate by providing an alternative reaction path which needs lesser energy to reach the highest energy transition state of the reaction. This reduction of activation energy (?G) gives a chance to more number of reactant molecules to reach the activation energy and form the product. The effect of catalyst on activation energy in a catalysis reaction is shown as Fig 5

The same concept of enzyme catalysis can also be explained by considering thermodynamic concepts and transition state theory (TST). TST is primarily used to understand the kinetics of the chemical reactions. This theory assumes quasi-equilibrium between the reactants and activated transition state complexes.

In1889, Svante Arrhenius put forward an expression for the rate constant of a reaction, given as

This Arrhenius equation was widely accepted, but the physical interpretation of A and E remained vague. In order to better correlate A and E to the molecular dynamics directly which are responsible for the chemical reactions.

K- Reaction rate constant; DGo‡ - Gibbs energy of activation/ Standard free energy of activation

rom the above equation, we observe that as the reaction rate constant increases, the standard free energy decreases exponentially. Thus, the increase in the reaction rate by the enzymes can be related to the fact that enzymes reduce the standard free energy of the reaction and thereby increasing the rate of the reaction. But, it is important to remark that enzymes can accelerate reactions in both directions, but do not change overall DG or Keq

4.4 DNA MELTING

Thermodynamic analyses of the melting of DNA are conducted extensively in biochemistry research labs, particularly those involved in determining nucleic acid structure. In addition to providing important information about the conformational properties of either DNA or RNA sequences (mismatched base pairs and loops have distinct effects on melting properties), thermodynamic data for DNA are also important for several basic biochemical applications [3].

4.4.1 STRUCTURE OF DNA

Deoxyribonucleic acid (DNA) (Fig 6), is a double stranded macromolecule with two polynucleotide chains (strands) held together by weak hydrogen bonding. The monomer units of DNA are called nucleotides, each of which consists of a nitrogen containing base attached to sugar, 5-carbon sugar (deoxyribose), and a phosphate group. The four different types of nucleotides found in DNA are called Adenine (A), Guanine (G), Cytosine(C) and Thymine (T). The four nucleotides are given one letter abbreviations as shorthand for the four bases.

4.4.2 MELTING OF DNA

The two strands in a DNA moleculecan be dissociatedinto single polydeoxyribonucleotide strands by heat or urea and this process is called melting or denaturing (Fig 7). This process proceeds by breaking the hydrogen bonds between complementary bases. Understanding of the denaturation process is important for understanding DNA replication and manipulation in the laboratory. Although there are several techniques of denaturing DNA like change in salt concentration, pH or other factors, denaturation by increasing temperature is the standard procedure, melting of DNA by heat is a very important method for preparing "single-stranded DNA"(ssDNA).

Fig 7: Illustration of hybridization of two single stranded DNA to complementary DNA and viceversa. The four nucleotides are shown as identical blocks

The simplest way of characterizing the denaturing of DNA is by melting temperature, Tm, the temperature at which half the melting has taken place.The Tm depends on several factors like DNA length, sequence, ionic environment, pH, etc.Because G-C (Guanine- cytosine) pairs consist of threehydrogen bonds, while A- T (Adenine-Thymine) pairs only have two, the temperature at which a particular DNA molecule "melts"usually will increase with higher percentage of GC pairs. The relationship between melting temperature (Tm) and G-C content for long DNA can be given as

During the denaturation process, as the ordered regions of stacked base pairs in the DNA duplex are disrupted, the UV absorbance increases. This difference in absorbance between the duplex and single strand states is due to an effect called hypochromicity. According to this effect, when the DNA is in the duplex state (dsDNA), interactions between base pairs decrease the UV absorbance relative to that of single strands. This can be attributed to when the DNA is in the single strand state the interactions are much weaker and the UV absorbance is higher than that in the duplex state. The profile of UV absorbance versus temperature is called a melting curve; the midpoint of the transition is defined as the melting temperature, Tm. Thedependence of the melting transition, Tm, on the strand concentration can be analyzed to yield quantitative thermodynamic data including DH&deg;, DS&deg;, DG&deg; for the transition from duplex to single strand DNA. Alternatively, one can get this information by analyzing the whole melting curve.

This thermodynamic information about the Tm can be used to determine the minimum length of a oligonucleotide probe needed to form a stable double helix with a target gene at a particular temperature. Thermodynamic analysis of the hybridization and subsequent denaturation of two small DNA is carried out below

4.4.3 THERMODYNAMIC ANALYSIS OF SMALL OLIGOMERS

The association constant at the midpoint (when half of the DNA is single stranded and the other half is helical) is K50 = 4/[C], where [C] is the sum of the concentrations of the two single strands which are non-self-complementary. (For self-complementary strands, K50 = 1/[C]) Since, for any process at equilibrium,

From the concentration dependence of the melting temperature, the standard enthalpy and entropy can be determined using so-called van't Hoff plot of 1/Tm versus ln [C]. The standard free energy of duplex formation, DGo, at any temperature can then be determined. Shown below is a table of different thermodynamic quantities for various DNA sequences

The calculated standard free energy will help in determining if the DNA hybridization will occur at the given concentrations.

5. CONCLUSION

In summary, biological thermodynamics helps us in quantitative study of several biological processes occurring in nature. Thermodynamic analysis of different internal biochemical dynamics like ATP-ADP cycle, DNA melting and enzyme catalysis was discussed to better explain the underlying mechanism of the processes.

6. REFERENCES

  1. Gordon G. Hammes (1934), Thermodynamics and Kinetics for the biological sciences, John Wiley & sons, England
  2. Donald T.Haynie (2001), Biological Thermodynamics, Cambridge university press, England
  3. Olivier Toussaint, Eric D. Schneider (1998), The thermodynamics and evolution of complexity in biological systems, C
  4. Reza Karimi (2005), Teaching Glycolysis with the Student's Perspective in Mind, American Journal of Pharmaceutical Education, 69, (5) Article 85.
  5. Llya Prigogine, Gregoire Nicolis and Agnes Babloyantz, (1972), Thermodynamics of evolution, Physics today
  6. Georgi P. Gladyshev (1999), On Thermodynamics, Entropy and Evolution of Biological Systems: What Is Life from a Physical Chemist's Viewpoint, Entropy 1: 9-20
  7. Ioulia Rouzina, Victor A. Bloomfield (1999), Heat Capacity Effects on the Melting of DNA. 1. General Aspects, Biophysical Journal Volume 77: 3242- 3251