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How to calculate or know by experiment the entropy of enzymes or protein?

How to calculate or know by experiment the entropy of enzymes or protein?


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How do you calculate or experimentally determine the entropy of enzymes or protein? In particular, I am interested in Boltzmann and conformational entropy, and Gibbs free energy. Any references are welcome.


In practice, like Energy calculations, Entropy is a relative numbers and difficult to get. Computational chem and bio have been working on this problem with mixed success. The summary of what I'm going to say here is that when you try to calculate the differences in entropy (or energy for that matter), the Gibbs Free Energy differences in most biological processes such as enzyme/substrate binding, protein/protein or protein/DNA interactions or protein folding etc is so small compared to the errors in these calculations that the computations are hard to believe.

Entropy is ultimately a term one would use in calculating the Gibb's free energy which will tell whether a given chemical or molecular process will occur. So it's a valuable number to have. Gibbs Free Energy (G) equals Enthalpy (heat) minus the temperature (T) times the change in entropy.

G = H - T$Delta$S

The Entropic term, $Delta$S is described in chemical systems often as a change in the combinatorial change of the system and the change in the heat capacity of the system. The first of these could broadly described as a 'mixing' term. When more than one solvents or a solvent and a solute diffuse into each other mix completely, the number of possible states is maximized.

The heat capacity of the system is a more often the focus of entropy calculations for proteins and biological molecules. This is because the conformations of the biological molecules, especially how free they are to move around are thought to contribute to the entropic part of G.

So attempts have been made to estimate from NMR and crystallography as well as molecular dynamics how much domains and side chains are free to move. Unfortunately this is only an insufficient proxy for biological entropy. A substantial if not dominant contribution to the T$Delta$S term comes from solvent.

How is this so? Water molecules form structures around proteins which are not static, but do involve many water molecules residing there on the average to see them in crystal structures and NMR experiments. While the individual waters are exchanging rapidly, they are not in the same entropic state in water solution as they are when they form a hydration shell around an aromatic or charged side chain.

Attempts have been made to parametrize the solvent entropy by looking at the buried nonpolar surface in a folded protein, looking at the mobility of sidechains before and after folding/binding, but these metrics appear to be configuration dependent to the point that they can't calculate the protein entropy via these efforts, at least heretofore.

Conventionally, molecular dynamics tries to calculate this by surrounding the proteins or other molecules with water molecules and some approximation of the overall entropy is calculated on the entire system. It turns out that small differences between the water molecular models and the simplifications in ball and stick/Hooke potential water models we make are also problematic approximations when there are hundreds or thousands of water molecules in the simulation.


19.4: Entropy Changes in Chemical Reactions

We have seen that the energy given off (or absorbed) by a reaction, and monitored by noting the change in temperature of the surroundings, can be used to determine the enthalpy of a reaction (e.g. by using a calorimeter). Tragically, there is no comparable easy way to experimentally measure the change in entropy for a reaction. Suppose we know that energy is going into a system (or coming out of it), and yet we do not observe any change in temperature. What is going on in such a situation? Changes in internal energy, that are not accompanied by a temperature change, might reflect changes in the entropy of the system.

For example, consider water at °0C at 1 atm pressure

  • This is the temperature and pressure condition where liquid and solid phases of water are in equilibrium (also known as the melting point of ice)

[ce label] At such a temperature and pressure we have a situation (by definition) where we have some ice and some liquid water If a small amount of energy is input into the system the equilibrium will shift slightly to the right (i.e. in favor of the liquid state) Likewise if a small amount of energy is withdrawn from the system, the equilibrium will shift to the left (more ice) However, in both of the above situations, the energy change is not accompanied by a change in temperature (the temperature will not change until we no longer have an equilibrium condition i.e. all the ice has melted or all the liquid has frozen) Since the quantitative term that relates the amount of heat energy input vs. the rise in temperature is the heat capacity, it would seem that in some way, information about the heat capacity (and how it changes with temperature) would allow us to determine the entropy change in a system. In fact, values for the "standard molar entropy" of a substance have units of J/mol K, the same units as for molar heat capacity. Slideshow

Hydrogen peroxide is a toxic product of many chemical reactions that occur in living things. Although it is produced in small amounts, living things must detoxify this compound and break down hydrogen peroxide into water and oxygen, two non-harmful molecules. The organelle responsible for destroying hydrogen peroxide is the peroxisome using the enzyme catalase. Both plants and animals have peroxisomes with catalase. The catalase sample for today’s lab will be from a potato.


Structure of Catalysts and Enzymes

A catalyst is any substance that can cause significant alterations to the rate of a chemical reaction. Thus it could be a pure element like nickel or platinum, a pure compound like Silica, Manganese Dioxide, dissolved ions like Copper ions or even a mixture like Iron-Molybdenum. The most commonly used catalysts are proton acids in hydrolysis reaction. Redox reactions are catalyzed by transition metals and platinum is used for reactions involving hydrogen. Some catlaysts occur as precatalysts and get converted to catalysts in the course of reaction. The typical example is that of Wilkinson’s catalyst – RhCl(PPh3)3 which loses one triphenylphosphine ligand while catalyzing the reaction.

Enzymes are globular proteins and can consist of 62 amino acids (4-oxalocrotonate) to a size of 2,500 amino acids (fatty acid synthase). There also exists RNA based enzymes called ribozymes. Enzymes are substrate specific and usually are larger than their respective substrates. Only a small part of an enzyme takes part in a enzymatic reaction. The active site is where substrates bind to enzyme for facilitating the reaction. Other factors like co factors, direct products, etc also have specific binding sites on enzyme. Enzymes are made of long chains of amino acids that fold over each other giving rise to a globular structure. The amino acid sequence gives enzymes their substrate specificity. Heat and chemical can denature an enzyme.


Protocol

1. Designing Primers

Designing appropriate primers is essential to the successful outcome of a PCR experiment. When designing a set of primers to a specific region of DNA desired for amplification, one primer should anneal to the plus strand, which by convention is oriented in the 5' → 3' direction (also known as the sense or nontemplate strand) and the other primer should complement the minus strand, which is oriented in the 3' → 5' direction (antisense or template strand). There are a few common problems that arise when designing primers: 1) self-annealing of primers resulting in formation of secondary structures such as hairpin loops (Figure 1a) 2) primer annealing to each other, rather then the DNA template, creating primer dimers (Figure 1b) 3) drastically different melting temperatures (Tm) for each primer, making it difficult to select an annealing temperature that will allow both primers to efficiently bind to their target sequence during themal cycling (Figure 1c) (See the sections CALCULATING MELTING TEMPERATURE (Tm) and MODIFICATIONS TO CYCLING CONDITIONS for more information on Tms).

Below is a list of characteristics that should be considered when designing primers.

Primer length should be 15-30 nucleotide residues (bases).

Optimal G-C content should range between 40-60%.

The 3' end of primers should contain a G or C in order to clamp the primer and prevent "breathing" of ends, increasing priming efficiency. DNA "breathing" occurs when ends do not stay annealed but fray or split apart. The three hydrogen bonds in GC pairs help prevent breathing but also increase the melting temperature of the primers.

The 3' ends of a primer set, which includes a plus strand primer and a minus strand primer, should not be complementary to each other, nor can the 3' end of a single primer be complementary to other sequences in the primer. These two scenarios result in formation of primer dimers and hairpin loop structures, respectively.

Optimal melting temperatures (Tm) for primers range between 52-58 ଌ, although the range can be expanded to 45-65 ଌ. The final Tm for both primers should differ by no more than 5 ଌ.

Di-nucleotide repeats (e.g., GCGCGCGCGC or ATATATATAT) or single base runs (e.g., AAAAA or CCCCC) should be avoided as they can cause slipping along the primed segment of DNA and or hairpin loop structures to form. If unavoidable due to nature of the DNA template, then only include repeats or single base runs with a maximum of 4 bases.

Notes:

There are many computer programs designed to aid in designing primer pairs. NCBI Primer design tool http://www.ncbi.nlm.nih.gov/tools/primer-blast/ and Primer3 http://frodo.wi.mit.edu/primer3/ are recommended websites for this purpose.

In order to avoid amplification of related pseudogenes or homologs it could be useful to run a blast on NCBI to check for the target specificity of the primers.

2. Materials and Reagents

When setting up a PCR experiment, it is important to be prepared. Wear gloves to avoid contaminating the reaction mixture or reagents. Include a negative control, and if possible a positive control.

Arrange all reagents needed for the PCR experiment in a freshly filled ice bucket, and let them thaw completely before setting up a reaction (Figure 2). Keep the reagents on ice throughout the experiment.

Standard PCR reagents include a set of appropriate primers for the desired target gene or DNA segment to be amplified, DNA polymerase, a buffer for the specific DNA polymerase, deoxynucleotides (dNTPs), DNA template, and sterile water.

Additional reagents may include Magnesium salt Mg 2+ (at a final concentration of 0.5 to 5.0 mM), Potassium salt K + (at a final concentration of 35 to 100 mM), dimethylsulfoxide (DMSO at a final concentration of 1-10%), formamide (at a final concentration of 1.25-10%), bovine serum albumin (at a final concentration of 10-100 μg/ml), and Betaine (at a final concentration of 0.5 M to 2.5 M). Additives are discussed further in the trouble shooting section.

Organize laboratory equipment on the workbench.

Materials include PCR tubes and caps, a PCR tube rack, an ethanol-resistant marker, and a set of micropipettors that dispense between 1 - 10 μl (P10), 2 - 20 μl (P20), 20 - 200 μl (P200) and 200 - 1000 μl (P1000), as well as a thermal cycler.

When setting up several PCR experiments that all use the same reagents, they can be scaled appropriately and combined together in a master mixture (Master Mix). This step can be done in a sterile 1.8 ml microcentrifuge tube (see Notes).

To analyze the amplicons resulting from a PCR experiment, reagents and equipment for agarose gel electrophoresis is required. To approximate the size of a PCR product, an appropriate, commercially available molecular weight size standard is needed.

3. Setting up a Reaction Mixture

Start by making a table of reagents that will be added to the reaction mixture (see Table 1).

Next, label PCR tube(s) with the ethanol-resistant marker.

Reaction volumes will vary depending on the concentrations of the stock reagents. The final concentrations (CF) for a typical 50 μl reaction are as follows.

X buffer (usually supplied by the manufacturer of the DNA polymerase may contain 15 mM MgCl2). Add 5 μl of 10X buffer per reaction.

200 μM dNTPs (50 μM of each of the four nucleotides). Add 1 μl of 10 mM dNTPs per reaction (dATP, dCTP, dTTP and dGTP are at 2.5 mM each).

1.5 mM Mg 2+ . Add only if it is not present in the 10X buffer or as needed for PCR optimization. For example, to obtain the 4.0 mM Mg 2+ required for optimal amplicon production of a conserved 566 bp DNA segment found in an uncharacterized Mycobacteriophage add 8 μl of 25 mM MgCl2 to the reaction (Figure 3).

20 to 50 pmol of each primer. Add 1 μl of each 20 μM primer.

Add 10 4 to 10 7 molecules (or about 1 to 1000 ng) DNA template. Add 0.5 μl of 2ng/μl genomic Mycobacteriophage DNA.

Add 0.5 to 2.5 units of DNA polymerase per 50 μl reaction (See manufacturers recommendations) For example, add 0.5 μl of Sigma 0.5 Units/μl Taq DNA polymerase.

Add Q.S. sterile distilled water to obtain a 50 μl final volume per reaction as pre-determined in the table of reagents (Q.S. is a Latin abbreviation for quantum satis meaning the amount that is needed). Thus, 33 μl per reaction is required to bring the volume up to 50 μl. However, it should be noted that water is added first but requires initially making a table of reagents and determining the volumes of all other reagents added to the reaction.

4. Basic PCR Protocol

Place a 96 well plate into the ice bucket as a holder for the 0.2 ml thin walled PCR tubes. Allowing PCR reagents to be added into cold 0.2 ml thin walled PCR tubes will help prevent nuclease activity and nonspecific priming.

Pipette the following PCR reagents in the following order into a 0.2 ml thin walled PCR tube (Figure 4): Sterile Water, 10X PCR buffer, dNTPs, MgCl2, primers, and template DNA (See Table 1). Since experiments should have at least a negative control, and possibly a positive control, it is beneficial to set up a Master Mix in a 1.8 ml microcentrifuge tube (See explanation in Notes).

In a separate 0.2 ml thin walled PCR tubes (Figure 4) add all the reagents with the exception of template DNA for a negative control (increase the water to compensate for the missing volume). In addition, another reaction (if reagents are available) should contain a positive control using template DNA and or primers previously known to amplify under the same conditions as the experimental PCR tubes.

Taq DNA polymerase is typically stored in a 50% glycerol solution and for complete dispersal in the reaction mix requires gentle mixing of the PCR reagents by pipetting up and down at least 20 times. The micropipettor should be set to about half the reaction volume of the master mix when mixing, and care should be taken to avoid introducing bubbles.

Put caps on the 0.2 ml thin walled PCR tubes and place them into the thermal cycler (Figure 5). Once the lid to the thermal cycler is firmly closed start the program (see Table 2).

When the program has finished, the 0.2 ml thin walled PCR tubes may be removed and stored at 4 ଌ. PCR products can be detected by loading aliquots of each reaction into wells of an agarose gel then staining DNA that has migrated into the gel following electrophoresis with ethidium bromide. If a PCR product is present, the ethidium bromide will intercalate between the bases of the DNA strands, allowing bands to be visualized with a UV illuminator.

Notes:

When setting up multiple PCR experiments, it is advantageous to assemble a mixture of reagents common to all reactions (i.e., Master Mix). Usually the cocktail contains a solution of DNA polymerase, dNTPs, reaction buffer, and water assembled into a 1.8 ml microcentrifuge tube. The amount of each reagent added to the Master Mix is equivalent to the total number of reactions plus 10% rounded up to the nearest whole reaction. For instance, if there are 10 x 0.1 = 1 reaction, then (10 + 1) x 5 μl 10X buffer equals 55 μl of 10X buffer for the Master Mix. The reagents in the Master Mix are mixed thoroughly by gently pumping the plunger of a micropipettor up and down about 20 times as described above. Each PCR tube receives an aliquot of the Master Mix to which the DNA template, any required primers, and experiment-specific reagents are then added (see Tables 1 and 7).

The following website offers a calculator for determining the number of copies of a template DNA (http://www.uri.edu/research/gsc/resources/cndna.html). The total number of copies of double stranded DNA may be calculated using the following equation: Number of copies of DNA = (DNA amount (ng) x 6.022x10 23 ) / (length of DNA x 1x10 9 ng/ml x 650 Daltons) Calculating the number of copies of DNA is used to determine how much template is needed per reaction.

False positives may occur as a consequence of carry-over from another PCR reaction which would be visualized as multiple undesired products on an agarose gel after electrophoresis. Therefore, it is prudent to use proper technique, include a negative control (and positive control when possible).

While ethidium bromide is the most common stain for nucleic acids there are several safer and less toxic alternatives. The following website describes several of the alternatives including Methylene Blue, Crystal Violet, SYBR Safe, and Gel Red along with descriptions of how to use and detect the final product (http://bitesizebio.com/articles/ethidium-bromide-the-alternatives/).

While most modern PCR machines use 0.2 ml tubes, some models may require reactions in 0.5 ml tubes. See your thermal cyclers manual to determine the appropriate size tube.

5. Calculating Melting Temperature (Tm)

Knowing the melting temperature (Tm) of the primers is imperative for a successful PCR experiment. Although there are several Tm calculators available, it is important to note that these calculations are an estimate of the actual Tm due to lack of specific information about a particular reaction and assumptions made in the algorithms for the Tm calculators themselves. However, nearest-neighbor thermodynamic models are preferred over the more conventional calculation: Tm ≈ 4(G-C) + 2(A-T). The former will give more accurate Tm estimation because it takes into account the stacking energy of neighboring base pairs. The latter is used more frequently because the calculations are simple and can be done quickly by hand. See Troubleshooting section for information about how various PCR conditions and additives affect melting temperature. For calculating the Tm values by nearest-neighbor thermodynamic models, one of the following calculators is recommended: http://www6.appliedbiosystems.com/support/techtools/calc/ http://www.cnr.berkeley.edu/

6. Setting Up Thermal Cycling Conditions

PCR thermal cyclers rapidly heat and cool the reaction mixture, allowing for heat-induced denaturation of duplex DNA (strand separation), annealing of primers to the plus and minus strands of the DNA template, and elongation of the PCR product. Cycling times are calculated based on the size of the template and the GC content of the DNA. The general formula starts with an initial denaturation step at 94 ଌ to 98 ଌ depending on the optimal temperature for DNA polymerase activity and G-C content of the template DNA. A typical reaction will start with a one minute denaturation at 94 ଌ. Any longer than 3 minutes may inactivate the DNA polymerase, destroying its enzymatic activity. One method, known as hot-start PCR, drastically extends the initial denaturation time from 3 minutes up to 9 minutes. With hot-start PCR, the DNA polymerase is added after the initial exaggerated denaturation step is finished. This protocol modification avoids likely inactivation of the DNA polymerase enzyme. Refer to the Troubleshooting section of this protocol for more information about hot start PCR and other alternative methods.

The next step is to set the thermal cycler to initiate the first of 25 to 35 rounds of a three-step temperature cycle (Table 2). While increasing the number of cycles above 35 will result in a greater quantity of PCR products, too many rounds often results in the enrichment of undesirable secondary products. The three temperature steps in a single cycle accomplish three tasks: the first step denatures the template (and in later cycles, the amplicons as well), the second step allows optimal annealing of primers, and the third step permits the DNA polymerase to bind to the DNA template and synthesize the PCR product. The duration and temperature of each step within a cycle may be altered to optimize production of the desired amplicon. The time for the denaturation step is kept as short as possible. Usually 10 to 60 seconds is sufficient for most DNA templates. The denaturation time and temperature may vary depending on the G-C content of the template DNA, as well as the ramp rate, which is the time it takes the thermal cycler to change from one temperature to the next. The temperature for this step is usually the same as that used for the initial denaturation phase (step #1 above e.g., 94 ଌ). A 30 second annealing step follows within the cycle at a temperature set about 5 ଌ below the apparent Tm of the primers (ideally between 52 ଌ to 58 ଌ). The cycle concludes with an elongation step. The temperature depends on the DNA polymerase selected for the experiment. For example, Taq DNA polymerase has an optimal elongation temperature of 70 ଌ to 80 ଌ and requires 1 minute to elongate the first 2 kb, then requires an extra minute for each additional 1 kb amplified. Pfu DNA Polymerase is another thermostable enzyme that has an optimal elongation temperature of 75 ଌ. Pfu DNA Polymerase is recommended for use in PCR and primer extension reactions that require high fidelity and requires 2 minutes for every 1 kb to be amplified. See manufacturer recommendations for exact elongation temperatures and elongation time indicated for each specific DNA polymerase.

The final phase of thermal cycling incorporates an extended elongation period of 5 minutes or longer. This last step allows synthesis of many uncompleted amplicons to finish and, in the case of Taq DNA polymerase, permits the addition of an adenine residue to the 3' ends of all PCR products. This modification is mediated by the terminal transferase activity of Taq DNA polymerase and is useful for subsequent molecular cloning procedures that require a 3'-overhang.

Termination of the reaction is achieved by chilling the mixture to 4 ଌ and/or by the addition of EDTA to a final concentration of 10 mM.

7. Important Considerations When Troubleshooting PCR

If standard PCR conditions do not yield the desired amplicon, PCR optimization is necessary to attain better results. The stringency of a reaction may be modulated such that the specificity is adjusted by altering variables (e.g., reagent concentrations, cycling conditions) that affect the outcome of the amplicon profile. For example, if the reaction is not stringent enough, many spurious amplicons will be generated with variable lengths. If the reaction is too stringent, no product will be produced. Troubleshooting PCR reactions may be a frustrating endeavor at times. However, careful analysis and a good understanding of the reagents used in a PCR experiment can reduce the amount of time and trials needed to obtain the desired results. Of all the considerations that impact PCR stringency, titration of Mg 2+ and/or manipulating annealing temperatures likely will solve most problems. However, before changing anything, be sure that an erroneous result was not due to human error. Start by confirming all reagents were added to a given reaction and that the reagents were not contaminated. Also take note of the erroneous result, and ask the following questions: Are primer dimers visible on the gel after electrophoresis (these run as small bands 𼄀 b near the bottom of the lane)? Are there non-specific products (bands that migrate at a different size than the desired product)? Was there a lack of any product? Is the target DNA on a plasmid or in a genomic DNA extract? Also, it is wise to analyze the G-C content of the desired amplicon.

First determine if any of the PCR reagents are catastrophic to your reaction. This can be achieved by preparing new reagents (e.g., fresh working stocks, new dilutions), and then systematically adding one new reagent at a time to reaction mixtures. This process will determine which reagent was the culprit for the failed PCR experiment. In the case of very old DNA, which often accumulates inhibitors, it has been demonstrated that addition of bovine serum albumin may help alleviate the problem.

Primer dimers can form when primers preferentially self anneal or anneal to the other primer in the reaction. If this occurs, a small product of less than 100 bp will appear on the agarose gel. Start by altering the ratio of template to primer if the primer concentration is in extreme excess over the template concentration, then the primers will be more likely to anneal to themselves or each other over the DNA template. Adding DMSO and or using a hot start thermal cycling method may resolve the problem. In the end it may be necessary to design new primers.

Non-specific products are produced when PCR stringency is excessively low resulting in non-specific PCR bands with variable lengths. This produces a ladder effect on an agarose gel. It then is advisable to choose PCR conditions that increase stringency. A smear of various sizes may also result from primers designed to highly repetitive sequences when amplifying genomic DNA. However, the same primers may amplify a target sequence on a plasmid without encountering the same problem.

Lack of PCR products is likely due to reaction conditions that are too stringent. Primer dimers and hairpin loop structures that form with the primers or in the denatured template DNA may also prevent amplification of PCR products because these molecules may no longer base pair with the desired DNA counterpart.

If the G-C content has not been analyzed, it is time to do so. PCR of G-C rich regions (GC content 㹠%) pose some of the greatest challenges to PCR. However, there are many additives that have been used to help alleviate the challenges.

8. Manipulating PCR Reagents

Understanding the function of reagents used on conventional PCR is critical when first deciding how best to alter reaction conditions to obtain the desired product. Success simply may rely on changing the concentration of MgCl2, KCl, dNTPs, primers, template DNA, or DNA polymerase. However, the wrong concentration of such reagents may lead to spurious results, decreasing the stringency of the reaction. When troubleshooting PCR, only one reagent should be manipulated at a time. However, it may be prudent to titrate the manipulated reagent.

Magnesium salt Mg 2+ (final reaction concentration of 0.5 to 5.0 mM) Thermostable DNA polymerases require the presence of magnesium to act as a cofactor during the reaction process. Changing the magnesium concentration is one of the easiest reagents to manipulate with perhaps the greatest impact on the stringency of PCR. In general, the PCR product yield will increase with the addition of greater concentrations of Mg 2+ . However, increased concentrations of Mg 2+ will also decrease the specificity and fidelity of the DNA polymerase. Most manufacturers include a solution of Magnesium chloride (MgCl2) along with the DNA polymerase and a 10X PCR buffer solution. The 10 X PCR buffer solutions may contain 15 mM MgCl2, which is enough for a typical PCR reaction, or it may be added separately at a concentration optimized for a particular reaction. Mg 2+ is not actually consumed in the reaction, but the reaction cannot proceed without it being present. When there is too much Mg 2+ , it may prevent complete denaturation of the DNA template by stabilizing the duplex strand. Too much Mg 2+ also can stabilize spurious annealing of primers to incorrect template sites and decrease specificity resulting in undesired PCR products. When there is not enough Mg 2+ , the reaction will not proceed, resulting in no PCR product.

Potassium salt K + (final reaction concentration of 35 to 100 mM) Longer PCR products (10 to 40 kb) benefit from reducing potassium salt (KCl) from its normal 50 mM reaction concentration, often in conjunction with the addition of DMSO and/or glycerol. If the desired amplicon is below 1000 bp and long non-specific products are forming, specificity may be improved by titrating KCl, increasing the concentration in 10 mM increments up to 100 mM. Increasing the salt concentration permits shorter DNA molecules to denature preferentially to longer DNA molecules.

Deoxynucleotide 5'-triphosphates (final reaction concentration of 20 and 200 μM each) Deoxynucleotide 5'-triphosphates (dNTPs) can cause problems for PCR if they are not at the appropriate equivalent concentrations (i.e., [A] = [T] = [C] = [G]) and/ or due to their instability from repeated freezing and thawing. The usual dNTP concentration is 50 μM of EACH of the four dNTPs. However, PCR can tolerate concentrations between 20 and 200 μM each. Lower concentrations of dNTPs may increase both the specificity and fidelity of the reaction while excessive dNTP concentrations can actually inhibit PCR. However, for longer PCR-fragments, a higher dNTP concentration may be required. A large change in the dNTP concentration may necessitate a corresponding change in the concentration of Mg 2+ .

Thermal stable DNA polymerases PCR enzymes and buffers associated with those enzymes have come a long way since the initial Taq DNA polymerase was first employed. Thus, choosing an appropriate enzyme can be helpful for obtaining desired amplicon products. For example the use of Taq DNA polymerase may be preferred over Pfu DNA polymerase if processivity and/or the addition of an adenine residue to the 3' ends of the PCR product is desired. The addition of a 3' adenine has become a useful strategy for cloning PCR products into TA vectors whit 3' thymine overhangs. However, if fidelity is more important an enzyme such as Pfu may be a better choice. Several manufactures have an array of specific DNA polymerases designed for specialized needs. Take a look at the reaction conditions and characteristics of the desired amplicon, and then match the PCR experiment with the appropriate DNA polymerase. Most manufactures have tables that aid DNA polymerase selection by listing characteristics such as fidelity, yield, speed, optimal target lengths, and whether it is useful for G-C rich amplification or hot start PCR.

Template DNA DNA quality and purity will have a substantial effect on the likelihood of a successful PCR experiment. DNA and RNA concentrations can be determined using their optical density measurements at 260 nm (OD260). The mass of purified nucleic acids in solution is calculated at 50 μg/ml of double stranded DNA or 40 μg/ml for either RNA or single stranded DNA at an OD260 =1.0. DNA extraction contaminants are common inhibitors in PCR and should be carefully avoided. Common DNA extraction inhibitors of PCR include protein, RNA, organic solvents, and detergents. Using the maximum absorption of nucleic acids OD260 compared to that of proteins OD280 (OD260/280), it is possible to determine an estimate of the purity of extracted DNA. Ideally, the ratio of OD260/280 is between 1.8 and 2.0. Lower OD260/280 is indicative of protein and/ or solvent contamination which, in all probability, will be problematic for PCR. In addition to the quality of template DNA, optimization of the quantity of DNA may greatly benefit the outcome of a PCR experiment. Although it is convenient to determine the quantity in ng/μl, which is often the output for modern nanospectrophotometers, the relevant unit for a successful PCR experiment is the number of molecules. That is, how many copies of DNA template contain a sequence complementary to the PCR primers? Optimal target molecules are between 10 4 to 10 7 molecules and may be calculated as was described in the notes above.

9. Additive Reagents

Additive reagents may yield results when all else fails. Understanding the reagents and what they are used for is critical in determining which reagents may be most effective in the acquisition of the desired PCR product. Adding reagents to the reaction is complicated by the fact that manipulation of one reagent may impact the usable concentration of another reagent. In addition to the reagents listed below, proprietary commercially available additives are available from many biotechnology companies.

10. Additives That Benefit G-C Rich Templates

Dimethylsulfoxide (final reaction concentration of 1-10% DMSO) In PCR experiments in which the template DNA is particularly G-C rich (GC content 㹠%), adding DMSO may enhance the reaction by disrupting base pairing and effectively lowering the Tm. Some Tm calculators include a variable entry for adding the concentration of DMSO desired in the PCR experiment. However, adding more than 2% DMSO may require adding more DNA polymerase as it has been demonstrated to inhibit Taq DNA polymerase.

Formamide (final reaction concentration of 1.25-10%) Like DMSO, formamide also disrupts base pairing while increasing the stringency of primer annealing, which results in less non-specific priming and increased amplification efficiency. Formamide also has been shown to be an enhancer for G-C rich templates.

7-deaza-2'-deoxyguanosine 5'-triphosphate (final reaction concentration of dc 7 GTP 3 dc 7 GTP:1 dGTP 50 μM) Using 3 parts, or 37.5 μM, of the guanosine base analog dc 7 GTP in conjunction with 1 part, or 12.5 μM, dGTP will destabilize formation of secondary structures in the product. As the amplicon or template DNA is denatured, it will often form secondary structures such as hairpin loops. Incorporation of dc 7 GTP into the DNA amplicon will prohibit formation of these aberrant structures.

dc 7 GTP attenuates the signal of ethidium bromide staining which is why it is used in a 3:1 ratio with dGTP.

Betaine (final reaction concentration of 0.5M to 2.5M) Betaine (N,N,N-trimethylglycine) is a zwitterionic amino acid analog that reduces and may even eliminate the DNA melting temperature dependence on nucleotide composition. It is used as an additive to aid PCR amplification of G-C rich targets. Betaine is often employed in combination with DMSO and can greatly enhance the chances of amplifying target DNA with high G-C content.

11. Additives That Help PCR in the Presence of Inhibitors

Non ionic detergents function to suppress secondary structure formation and help stabilize the DNA polymerase. Non ionic detergents such as Triton X-100, Tween 20, or NP-40 may be used at reaction concentrations of 0.1 to 1% in order to increase amplicon production. However, concentrations above 1% may be inhibitory to PCR. The presence of non ionic detergents decreases PCR stringency, potentially leading to spurious product formation. However, their use will also neutralize the inhibitory affects of SDS, an occasional contaminant of DNA extraction protocols.

Addition of specific proteins such as Bovine serum albumin (BSA) used at 400 ng/μl and/ or T4 gene 32 protein at 150 ng/μl aid PCR in the presence of inhibitors such as FeCl3, hemin, fulvic acid, humic acid, tannic acids, or extracts from feces, fresh water, and marine water. However, some PCR inhibitors, including bile salts, bilirubin, EDTA, NaCl, SDS, or Triton X-100, are not alleviated by addition of either BSA or T4 gene 32 protein.

12. Modifications to Cycling Conditions

Optimizing the annealing temperature will enhance any PCR reaction and should be considered in combination with other additives and/ or along with other modifications to cycling conditions. Thus, in order to calculate the optimal annealing temperature the following equation is employed: Ta OPT = 0.3 Tm Primer + 0.7 Tm Product -14.9 Tm Primer is calculated as the Tm of the less stable pair using the equation: Tm Primer = ((ΔH/(ΔS+R x ln(c/4)))-273.15 + 16.6 log[K + ] Where ΔH is the sum of the nearest neighbor enthalpy changes for hybrids ΔS is the sum of the nearest neighbor entropy changes R is the Gas Constant (1.99 cal K-1 mol-1) C is the primer concentration and [K + ] is the potassium concentration. The latter equation can be computed using one of the Tm calculators listed at the following website: http://protein.bio.puc.cl/cardex/servers/melting/sup_mat/servers_list.html Tm Product is calculated as follows: Tm Product = 0.41(%G-C) + 16.6 log [K + ] - 675/product length For most PCR reactions the concentration of potassium ([K + ]) is going to be 50 mM.

Hot start PCR is a versatile modification in which the initial denaturation time is increased dramatically (Table 4). This modification can be incorporated with or without other modifications to cycling conditions. Moreover, it is often used in conjunction with additives for temperamental amplicon formation. In fact, hot start PCR is increasingly included as a regular aspect of general cycling conditions. Hot start has been demonstrated to increase amplicon yield, while increasing the specificity and fidelity of the reaction. The rationale behind hot start PCR is to eliminate primer-dimer and non-specific priming that may result as a consequence of setting up the reaction below the Tm. Thus, a typical hot start reaction heats the sample to a temperature above the optimal Tm, at least to 60 ଌ before any amplification is able to occur. In general, the DNA polymerase is withheld from the reaction during the initial, elongated, denaturing time. Although other components of the reaction are sometimes omitted instead of the DNA polymerase, here we will focus on the DNA polymerase. There are several methods which allow the DNA polymerase to remain inactive or physically separated until the initial denaturation period has completed, including the use of a solid wax barrier, anti-DNA polymerase antibodies, and accessory proteins. Alternatively, the DNA polymerase may simply be added to the reaction after the initial denaturation cycle is complete.

Touchdown PCR (TD-PCR) is intended to take some of the guess work out of the Tm calculation limitations by bracketing the calculated annealing temperatures. The concept is to design two phases of cycling conditions (Table 5). The first phase employs successively lower annealing temperatures every second cycle (traditionally 1.0 ଌ), starting at 10 ଌ above and finishing at the calculated Tm or slightly below. Phase two utilizes the standard 3-step conditions with the annealing temperature set at 5 ଌ below the calculated Tm for another 20 to 25 cycles. The function of the first phase should alleviate mispriming, conferring a 4-fold advantage to the correct product. Thus, after 10 cycles, a 410-fold advantage would yield 4096 copies of the correct product over any spurious priming.

Stepdown PCR is similar to TD-PCR with fewer increments in the first phase of priming. As an example, the first phase lowers annealing temperatures every second cycle by 3 ଌ, starting at 10 ଌ above and finishing at 2 ଌ below the calculated Tm. Like TD-PCR, phase two utilizes the standard 3-step conditions with the annealing temperature set at 5 ଌ below the calculated Tm for another 20 to 25 cycles. This would allow the correct product a 256-fold advantage over false priming products.

Slowdown PCR is simply a modification of TD-PCR and has been successful for amplifying extremely G-C rich (above 83%) sequences (Table 6). The concept takes into account a relatively new feature associated with modern thermal cyclers, which allows adjustment of the ramp speed as well as the cooling rate. The protocol also utilizes dc 7 GTP to reduce 2 °structure formation that could inhibit the reaction. The ramp speed is lowered to 2.5 ଌ s -1 with a cooling rate of 1.5 ଌ s -1 for the annealing cycles. The first phase starts with an annealing temperature of 70 ଌ and reduces the annealing temperature by 1 ଌ every 3 rounds until it reaches 58 ଌ. The second phase then continues with an annealing temperature of 58 ଌ for an additional 15 cycles.

Nested PCR is a powerful tool used to eliminate spurious products. The use of nested primers is particularly helpful when there are several paralogous genes in a single genome or when there is low copy number of a target sequence within a heterogeneous population of orthologous sequences. The basic procedure involves two sets of primers that amplify a single region of DNA. The outer primers straddle the segment of interest and are used to generate PCR products that are often non-specific in 20 to 30 cycles. A small aliquot, usually about 5 μl from the first 50 μl reaction, is then used as the template DNA for another 20 to 30 rounds of amplification using the second set of primers that anneal to an internal location relative to the first set.

Other PCR protocols are more specialized and go beyond the scope of this paper. Examples include RACE-PCR, Multiplex-PCR, Vectorette-PCR, Quantitative-PCR, and RT-PCR.

13. Representative Results

Representative PCR results were generated by following the basic PCR protocols described above. The results incorporate several troubleshooting strategies to demonstrate the effect of various reagents and conditions on the reaction. Genes from the budding yeast Saccharomyces cerevisiae and from an uncharacterized Mycobacteriophage were amplified in these experiments. The standard 3-step PCR protocol outlined in Table 2 was employed for all three experiments described below.

Before setting up the PCR experiment, the genomic DNA from both S. cerevisiae and the Mycobacteriophage were quantified and diluted to a concentration that would allow between 10 4 and 10 7 molecules of DNA per reaction. The working stocks were prepared as follows. A genomic yeast DNA preparation yielded 10 4 ng/μl. A dilution to 10 ng/μl was generated by adding 48 μl into 452 μl of TE pH 8.0 buffer. Since the S. cerevisiae genome is about 12.5 Mb, 10 ng contain 7.41 X 10 5 molecules. The genomic Mycobacteriophage DNA preparation yielded 313 ng/μl. A dilution to 2 ng/μl was generated by adding 6.4 μl into 993.6 μl of TE pH 8.0 buffer. This phage DNA is about 67 Kb. Thus, 1 ng contains 2.73 X 10 7 molecules, which is at the upper limit of DNA generally used for a PCR. The working stocks were then used to generate the Master Mix solutions outlined in Table 7. Experiments varied cycling conditions as described below.

In Figure 3a, genomic DNA from S. cerevisiae was used as a template to amplify the GAL3 gene, which encodes a protein involved in galactose metabolism. The goal for this experiment was to determine the optimal Mg 2+ concentration for this set of reagents. No MgCl2 was present in the original PCR buffer and had to be supplemented at the concentrations indicated with a range tested from 0.0 mM to 5.0 mM. As shown in the figure, a PCR product of the expected size (2098 bp) appears starting at a Mg 2+ concentration of 2.5 mM (lane 6) with an optimal concentration at 4.0 mM (lane 9). The recommended concentration provided by the manufacturer was 1.5 mM, which is the amount provided in typical PCR buffers. Perhaps surprisingly, the necessary concentration needed for product formation in this experiment exceeded this amount.

A different DNA template was used for the experiment presented in Figure 3b. Genomic DNA from a Mycobacteriophage was used to amplify a conserved 566 bp DNA segment. Like the previous experiment, the optimal Mg 2+ concentration had to be determined. As shown in Figure 3b, amplification of the desired PCR product requires at least 2.0 mM Mg 2+ (lane 5). While there was more variability in the amount of product formed at increasing concentrations of MgCl2, the most PCR product was observed at 4 mM Mg 2+ (lane 9), the same concentration observed for the yeast GAL3 gene.

Notice that in the experiments presented in Figures 3A and 3B, a discrete band was obtained using the cycling conditions thought to be optimal based on primer annealing temperatures. Specifically, the denaturation temperature was 95 ଌ with an annealing temperature of 61 ଌ, and the extension was carried out for 1 minute at 72 ଌ for 30 cycles. The final 5 minute extension was then done at 72 ଌ. For the third experiment presented in Figure 3c, three changes were made to the cycling conditions used to amplify the yeast GAL3 gene. First, the annealing temperature was reduced to a sub-optimal temperature of 58 ଌ. Second, the extension time was extended to 1 minute and 30 seconds. Third, the number of cycles was increased from 30 to 35 times. The purpose was to demonstrate the effects of sub-optimal amplification conditions (i.e., reducing the stringency of the reaction) on a PCR experiment. As shown in Figure 3c, what was a discrete band in Figure 3a, becomes a smear of non-specific products under these sub-optimal cycling conditions. Furthermore, with the overall stringency of the reaction reduced, a lower amount of Mg 2+ is required to form an amplicon.

All three experiments illustrate that when Mg 2+ concentrations are too low, there is no amplicon production. These results also demonstrate that when both the cycling conditions are correctly designed and the reagents are at optimal concentrations, the PCR experiment produces a discreet amplicon corresponding to the expected size. The results show the importance of performing PCR experiments at a sufficiently high stringency (e.g., discreet bands versus a smear). Moreover, the experiments indicate that changing one parameter can influence another parameter, thus affecting the reaction outcome.

Table 1. PCR reagents in the order they should be added.

*Units may vary between manufacturers

** Add all reagents to the Master Mix excluding any in need of titration or that may be variable to the reaction. The Master Mix depicted in the above table is calculated for 11 reactions plus 2 extra reactions to accommodate pipette transfer loss ensuring there is enough to aliquot to each reaction tube.

 Standard 3-step PCR Cycling 
Cycle stepTemperatureTimeNumber of Cycles
Initial Denaturation94 ଌ to 98 ଌ1 minute1
Denaturation Annealing Extension94 ଌ 5 ଌ below Tm 70 ଌ to 80 ଌ 10 to 60 seconds 30 seconds Amplicon and DNA polymerase dependent 25-35
Final Extension70 ଌ to 80 ଌ5 minutes1
Hold*4 ଌ1

Table 2. Standard 3-step PCR Cycling.

* Most thermal cyclers have the ability to pause at 4ଌ indefinitely at the end of the cycles.

 2-step PCR Cycling 
Cycle stepTemperatureTimeNumber of Cycles
Initial Denaturation94 ଌ to 98 ଌ1 minute1
Denaturation Annealing/Extension94 ଌ 70 ଌ to 80 ଌ10 to 60 seconds Amplicon and DNA polymerase dependent 25-35
Final Extension70 ଌ to 80 ଌ5 minutes1

Table 3. 2-step PCR Cycling.

 Hot Start PCR Cycling 
Cycle stepTemperatureTimeCycles
Initial Denaturation60 ଌ to 95 ଌ5 minute then add DNA polymerase1
Denaturation Annealing Extension94 ଌ 5 ଌ below Tm 70 ଌ to 80 ଌ10 to 60 seconds 30 seconds Amplicon and DNA polymerase dependent 25-35
Final Extension70 ଌ to 80 ଌ5 minutes1

Table 4. Hot Start PCR Cycling.

 Touchdown PCR Cycling 
Cycle stepTemperatureTimeCycles
Initial Denaturation94 ଌ to 98 ଌ1 minute1
Denaturation Annealing Extension94 ଌ X =10 ଌ above Tm 70 ଌ to 80 ଌ10 to 60 seconds 30 seconds Amplicon and DNA polymerase dependent 2
Denaturation Annealing Extension94 ଌ X-1 ଌ reduce 1 ଌ every other cycle 70 ଌ to 80 ଌ10 to 60 seconds 30 seconds Amplicon and polymerase dependent 28
Denaturation Annealing Extension94 ଌ 5 ଌ below Tm 70 ଌ to 80 ଌ10 to 60 seconds 30 seconds Amplicon and DNA polymerase dependent 20-25
Final Extension70 ଌ to 80 ଌ5 minutes1

Table 5. Touchdown PCR Cycling.

 Slowdown PCR Cycling 
Cycle stepTemperatureTimeCycles
Initial Denaturation94 ଌ to 98 ଌ1 minute1
Denaturation Annealing Extension94 ଌ X ଌ =10 ଌ above Tm 70 ଌ to 80 ଌ10 to 60 seconds 30 seconds Amplicon and polymerase dependent 2
Denaturation Annealing Extension94 ଌ X-1 ଌ reduce 1 ଌ every other cycle 70 ଌ to 80 ଌ*10 to 60 seconds 30 seconds Amplicon and polymerase dependent 28
Denaturation Annealing Extension94 ଌ 5 ଌ below Tm 70 ଌ to 80 ଌ10 to 60 seconds 30 seconds Amplicon and polymerase dependent 20-25
Final Extension70 ଌ to 80 ଌ5 minutes1

Table 6. Slowdown PCR Cycling.

*For slowdown PCR, the ramp speed is lowered to 2.5 ଌ s -1 with a cooling rate of 1.5 ଌ s -1 for the annealing cycles.

Table 7. Titration of Mg 2+ used in Figure 3.

Figure 1. Common problems that arise with primers and 3-step PCR amplification of target DNA. (a) Self-annealing of primers resulting in formation of secondary hairpin loop structure. Note that primers do not always anneal at the extreme ends and may form smaller loop structures. (b) Primer annealing to each other, rather than the DNA template, creating primer dimers. Once the primers anneal to each other they will elongate to the primer ends. (c) PCR cycles generating a specific amplicon. Standard 3-step PCR cycling include denaturation of the template DNA, annealing of primers, and extension of the target DNA (amplicon) by DNA polymerase.

Figure 2. Ice bucket with reagents, pipettes, and racks required for a PCR. (1.) P-200 pipette, (2.) P-1000 pipette, (3.) P-20 pipette, (4.) P-10 pipette, (5.) 96 well plate and 0.2 ml thin walled PCR tubes, (6.) Reagents including Taq polymerase, 10X PCR buffer, MgCl2, sterile water, dNTPs, primers, and template DNA, (7.) 1.8 ml tubes and rack.

Figure 3. Example of a Mg 2+ titrations used to optimize a PCR experiment using a standard 3-step PCR protocol. (a) S. cerevisiae Yeast genomic DNA was used as a template to amplify a 2098 bp GAL3 gene. In lanes 1 - 6, where the Mg 2+ concentration is too low, there either is no product formed (lanes 1-5) or very little product formed (lane 6). Lanes 7 - 11 represent optimal concentrations of Mg 2+ for this PCR experiment as indicated by the presence of the 2098 bp amplicon product. (b) An uncharacterized mycobacteriophage genomic DNA template was used to amplify a 566 bp amplicon. Lanes 1 - 4, the Mg 2+ concentration is too low, as indicated by the absence of product. Lanes 5 - 11 represent optimal concentrations of Mg 2+ for this PCR as indicated by the presence of the 566 kb amplicon product. (c) . S. cerevisiae Yeast genomic DNA was used as a template to amplify a 2098 bp GAL3 gene as indicated in panel a. However, the annealing temperature was reduced from 61 ଌ to 58 ଌ, resulting in a non-specific PCR bands with variable lengths producing a smearing effect on the agarose gel. Lanes 1 - 4, where the Mg 2+ concentration is too low, there is no product formed. Lanes 5 - 8 represent optimal concentrations of Mg 2+ for this PCR as seen by the presence of a smear and band around the 2098 kb amplicon product size. Lanes 9 - 11 are indicative of excessively stringent conditions with no product formed. (a-c) Lanes 12 is a negative control that did not contain any template DNA. Lane M (marker) was loaded with NEB 1kb Ladder.

Figure 4. Sterile tubes used for PCR. (1.) 1.8 ml tube (2.) 0.2 ml individual thin walled PCR tube, (3.) 0.2 ml strip thin walled PCR tubes and caps.

Figure 5. Thermal cycler. Closed thermal cycler left image. Right image contains 0.2 ml thin walled PCR tubes placed in the heating block of an open thermal cycler.


7.6.3 Explain that enzymes lower the activation energy of the chemical reactions that they catalyse.

Reactants of a chemical reaction need to gain energy before they can undergo the reaction. This required energy is called the activation energy of the reaction and it is needed to break bonds within the reactants. At a later stage in the reaction energy will be released as new bonds form. The majority of biological reactions are exothermic. In exothermic reactions the energy released by the new bonds formed is greater than the activation energy. In other words, the reaction releases energy. Enzymes make it easier for reactions to occur by decreasing the activation energy required in the reactions that they catalyse.

Figure 7.6.2 - Activation energy of an exothermic reaction


How to calculate or know by experiment the entropy of enzymes or protein? - Biology

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Enthalpy changes associated with a chemical reaction can be measured with a calorimeter, but the entropy change associated with a reaction cannot be directly measured.

Entropy is a state function, which means that the change in entropy depends solely on the initial and final states of a system. So, like enthalpy changes, entropy changes can be from calculated reference tables of standard molar entropies. 

For a reaction occurring under standard conditions, the associated entropy change is determined by the difference between the sum of the standard molar entropies of the products multiplied by their stoichiometric coefficients and the sum of the standard molar entropies of the reactants multiplied by their stoichiometric coefficients.

Consider the combustion of ethylene under standard conditions, where 1 mole of ethylene gas reacts with 3 moles of oxygen gas to produce 2 moles of carbon dioxide gas and 2 moles of water.

The standard entropy change for the reaction equals the sum of 2 times the standard entropy of carbon dioxide gas and 2 times the standard entropy of water, minus the sum of the standard entropy of ethylene gas and 3 times the standard entropy of oxygen. 

Note that, unlike standard enthalpies of formation of elements, which are zero, standard molar entropies of all substances are greater than zero at 298 K.

Substituting the values for molar entropies of reactants and products from the reference table yields [(2 × 213.8) + (2 × 70.0)] − [(219.5 + 3) × (205.3)]. The net entropy of the products equals 567.6 J/K, and the net entropy of the reactants is 835.4 J/K.

The difference between the products and the reactants equals negative 268 J/K for the standard entropy change of the combustion of ethylene. The negative value indicates there is a decrease in entropy.

Even without calculating the exact entropy change, the decrease in entropy can be predicted by examining the reaction. Recall that gases are more disordered than liquids.

There are more moles of gas in the reactants, 4 moles of gas (with 1 mole of ethylene and 3 moles of oxygen) compared to the products (only 2 moles of carbon dioxide gas), while the other product is a liquid.

Thus, in this reaction, the reactants are more disordered than the products. Therefore, entropy decreases as the reaction proceeds.

17.5: Standard Entropy Change for a Reaction

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

where np and nr represent the stoichiometric coefficients in the balanced equation of the products and reactants, respectively.

For example, ΔS°rxn for the following reaction at room temperature

A partial listing of standard entropies is provided in the table.

Substance   S° (J/mol·K)  
C (s, graphite) 5.740
  C (s, diamond)   2.38
CO (g) 197.7
CO2 (g) 213.8
CH4 (g) 186.3
C2H4 (g) 219.5
C2H6 (g) 229.5
CH3OH (l) 126.8
 C2H5OH (l 160.7
H2 (g) 130.57
H (g) 114.6
H2O (g) 188.71
H2O (l) 69.91
HCI (g) 186.8
H2S (g) 205.7
O2 (g) 205.03

Determination of ΔS°

Consider the condensation of water, in which 1 mole of gaseous H2O changes into 1 mole of liquid H2O.

The standard entropy changes for the reaction, ΔS°rxn is calculated using the standard molar entropies and stoichiometric coefficients.

The value for ΔS°rxn is negative, as expected for this phase transition (condensation).
As a second example, consider the combustion of methanol, CH3OH:

The same procedure is followed to calculate the standard entropy change of the reaction:


AP Lab 2 Report 2001

Introduction
Enzymes are proteins produced by living cells that act as catalysts, which affect the rate of a biochemical reaction. They allow these complex biochemical reactions to occur at a relatively low temperature and with less energy usage.

In enzyme-catalyzed reactions, a substrate, the substance to be acted upon, binds to the active site on an enzyme to form the desired product. Each active site on the enzyme is unique to the substrate it will bind with causing each to have an individual three-dimensional structure. This reaction is reversible and is shown as following:

Enzymes are recyclable and unchanged during the reaction. The active site is the only part of the enzyme that reacts with the substrate. However, its unique protein structure under certain circumstances can easily be denatured. Some of the factors that affect enzyme reactions are salt concentration, pH, temperature, substrate and product concentration, and activators and inhibitors.

Enzymes require a very specific environment to be affective. Salt concentration must be in an intermediate concentration. If the salt concentration is too low, the enzyme side chains will attract each other and form an inactive precipitate. Likewise, if the salt concentration is too high, the enzyme reaction is blocked by the salt ions. The optimum pH for an enzyme-catalyzed reaction is neutral (7 on the pH scale). If the pH rises and becomes basic, the enzyme begins losing its H+ ions, and if it becomes too acidic, the enzyme gains H+ ions. Both of these conditions denature the enzyme and cause its active site to change shape.

Enzymes also have a temperature optimum, which is obtained when the enzyme is working at its fastest, and if raised any further, the enzyme would denature. For substrate and product concentrations, enzymes follow the law of mass action, which says that the direction of a reaction is directly dependent on the concentration. Activators make active sites better fit a substrate causing the reaction rate to increase. Inhibitors bind with the enzymes’ active site and block the substrate from bonding causing the reaction to subside.

The enzyme in this lab is catalase, which produced by living organisms to prevent the accumulation of toxic hydrogen peroxide. Hydrogen peroxide decomposes to form water and oxygen as in the following equation:

This reaction occurs spontaneously without catalase, but the enzyme speeds the reaction considerably. This lab’s purpose is to prove that catalase does speed the decomposition of hydrogen peroxide and to determine the rate of this reaction.

Hypothesis
The enzyme catalase, under optimum conditions, effectively speeds the decomposition of hydrogen peroxide.

Materials
Exercise 2A: Test of Catalase Activity

In Part 1, the materials used were 10mL of 1.5% H2O2, 50-mL glass beaker, 1 mL catalase, and 2 10-mL pipettes and pipette pumps. In Part 2, the materials used were 5 mL of catalase, a boiling water bath, 1 test tube, a test tube rack, 10 mL of 1.5% H2O2, 50-mL beaker, and 2 10-mL pipettes and pipette pumps. In Part 3, the materials used were 10 mL of 1.5% H2O2, 50-mL beaker, liver, and a syringe.

Exercise 2B: The Baseline Assay

This part of the lab required 10 mL of 1.5% H2O2, 1 mL distilled H2O, 10 mL of H2SO4, 2 50-mL beakers, a sheet of white paper, 5 mL KMnO4, 2 5-mL syringes, and 2 10-mL pipettes and pumps.

Exercise 2C: The Uncatalyzed Rate of H2O2 Decomposition

The materials used for this section were 15 mL of 1.5% H2O2, 1 mL distilled H2O, 10 mL H2SO4, 2 50-mL beakers, a sheet of white paper, 5 mL KMnO4, 2 5-mL syringes, and 2 10-mL pipettes and pumps.

Exercise 2D: An Enzyme-Catalyzed Rate of H2O2 Decomposition

The materials required for Exercise 2D were 70 mL of 1.5% H2O2, 70 mL of H2SO4, 6 mL of catalase solution, 13 plastic, labeled cups, 3 100-mL beakers, 1 50-mL beaker, 1 10-mL syringe, 1 5-mL syringe, 1 60-mL syringe, a sheet of white paper, a timer, and 30 mL of KMnO4.

Method
Exercise 2A: Test of Catalase Activity

In Part 1, 10 mL of 1.5% H2O2 were transferred into a 50-mL beaker. Then, 1 mL of fresh catalase solution was added and the reaction was observed and recorded. In Part 2, 5 mL of catalase was placed in a test tube and put in a boiling water bath for five minutes. 10 mL of 1.5% H2O2 were transferred to a 50-mL beaker and 1 mL of the boiled catalase was added. The reaction was observed and recorded. In Part 3, 10mL of 1.5% H2O2 were transferred to a 50 mL beaker. 1 cm3 of liver was added to the beaker and the reaction was observed and recorded.

Exercise 2B: The Baseline Assay

10 mL of 1.5% H2O2 were transferred to a 50-mL beaker. 1 mL of H2O was added instead of catalase, and then, 10 mL of H2SO4 were added. After mixing well, a 5 mL sample was removed and placed over a white sheet of paper. A 5-mL syringe was used to add KMnO4, 1 drop at a time until a persistent brown or pink color was obtained. The solution was swirled after every drop, and the results were observed and recorded. The baseline assay was calculated.

Exercise 2C: The Uncatalyzed Rate of H2O2 Decomposition

A small quantity of H2O2 was placed in a beaker and stored uncovered for approximately 24 hours. To determine the amount of H2O2 remaining, 10 mL of 1.5% H2O2 were transferred to a 50-mL beaker. 1 mL of H2O was added instead of catalase, and then, 10 mL of H2SO4 were added. After mixing well, a 5 mL sample was removed and placed over a white sheet of paper. A 5-mL syringe was used to add KMnO4, 1 drop at a time until a persistent brown or pink color was obtained. The solution was swirled after every drop, and the results were observed and recorded. The percent of the spontaneously decomposed H2O2 was calculated.

Exercise 2D: An Enzyme-Catalyzed Rate of H2O2 Decomposition

The baseline assay was reestablished following the directions of Exercise 2B. Before starting the actual experiment a lot of preparation was required. Six labeled cups were set out according to their times and 10 mL of H2O2 were added to each cup. 6 mL of catalase were placed in a 10-mL syringe, and 60 mL of H2SO4 were placed in a 60-mL syringe. To start the actual lab, 1 mL of catalase was added to each of the cups, while simultaneously, the timer was started. Each of the cups were swirled. At 10 seconds, 10 mL of H2SO4 were added to stop the reaction. The same steps were repeated for the 30, 60, 120, 180, and 360 second cups, respectively.

Afterwards, a five 5 mL sample of each of the larger cups were moved to the corresponding labeled smaller cups. Each sample was assayed separately by placing each over a white sheet of paper. A 5-mL syringe was used to add KMnO4, 1 drop at a time until a persistent brown or pink color was obtained. The solution was swirled after every drop, and the results were observed and recorded.


Molecular Biology 02: 'Thermodynamics of protein folding'

Continued from lecture 01. ω is always 0 or +180°. If you plot Φ and Ψ you find only a few clusters are well-represented: a range of α-helix combinations, a β-sheet area, and a third rarer area (called Lα and populated by left-handed α-helices). ω is ususally found in the trans conformation due to steric hindrance of the consecutive side chains, however, proline because it is anchored to the backbone has a unique twist that enables a cis conformation.

Secondary structure

α-helices and β-sheets are two ways of allowing the NH and C=O groups on the backbone to form hydrogen bonds. α-helices contain 3.6 residues per rotation, or in other words, each residue spans 100° of rotation. Consecutive rungs of an α-helix turns are separated by 5.4Å. α-helices are almost exclusively right-handed. In a right-handed α-helix, you turn counter-clockwise as you go up. In a left-handed α-helix you turn clockwise as you go up. Side chains point outward from the helix. If you plot out where each residue falls on the helix based on the 3.6 residues/turn rule, you find that amphipathic, half-buried helices have all the hydrophobic residues on one side and the hydrophilic ones on the other side. A fully buried helix will be all hydrophobic residues and a fully exposed helix will be all hydrophilic residues.

In β-sheets, all potential H-bonds are satisfied except for the “flanking” strands at either end of the sheet. About 20% of β-sheets found in nature are mixed parallel and anti-parallel, the other 80% are pure one or the other. β-sheets are not flat, but pleated.

Tertiary structure

A single sheet or helix is not stable in water. Tertiary structure is the packing of these elements, and loops connecting them, onto each other.

Thermodynamics of protein folding

There are two fundamental problems in protein folding:

  1. Can we predict a protein’s structure from its sequence? is that sampling all possible possible conformations of a polypeptide chain to find the lowest-energy state would take millions of years rather than a few seconds, so how do proteins fold so quickly?

As an example, consider the metalloprotease cleaveage of Notch to create the Notch intracellular domain (NICD), which then translocates to the nucleus and affects transcription. The proteolytic site of Notch is protected by Lin12/Notch repeats which are connected to the EGF repeats that interact with Notch’s ligand. The ligand is believed to apply a force that unfolds this region, allowing cleavage. Mutations which destabilize this fold and result in constitutive activation cause tumors.

Thermodynamics can only describe whether a chemical reaction will occur spontaneously or not, not how fast it will occur (see Biochemistry 01).

The energy of a system is its capacity to do work.

Where U is internal energy, q is heat and w is work.

Where C is the heat capacity and f and i mean final and initial.

Where F is force and Δx is displacement along the x axis.

If you dissolve urea in water at a 4M solution, it will dissolve spontaneously and the solution will become cold (just like guanidine, as I learned here).

Gibb’s free energy is defined as:

Where G, H, T and S are Gibb’s free energy, enthalpy, temperature and entropy respectively.

If ΔG < 0 the reaction will proceed spontaneously.

In the urea example, ΔH > 0 because energy is required to pull apart the interacting urea molecules, using heat from the water. Yet the reaction still occurs spontaneously because ΔS > 0 by a lot - the urea solution is much more entropic than urea and water separately.

For the reaction A + B ↔ C + D, we define:

ATP is a special molecule: its hydrolysis into ADP is spontaneous at physiological concentrations of the reactants and products, i.e. ΔG < 0 for this reaction:

Le Chatelier’s principle says you could drive the reaction in reverse, making ATP spontaneously, simply by increasing the concentrations of the procuts. However [Pi] never gets high enough in the cell for ATP to be spontaneously generated from ADP. The unfavorable production of ATP is instead created via a coupled reaction with favorable reactions such as the release of protons across the mitochondrial membrane (see Biochemistry 08).

Enthalpy

Where U, P and V are internal energy, pressure and volume.

In physiological conditions, changes in pressure and volume are almost always negligible, so H and U are closely coupled. In other words, in most biological systems, the enthalpy is equal to the internal energy.

People have developed molecular dynamics simulations of the fundamental atomic forces that determine a protein’s enthalpy (dihedral angles, Van der Waals interactions, electrostatic interactions, etc) and attempt to minimize the energy to determine a protein’s fold. But there are so many degrees of freedom that computational expense prohibits running the simulation long enough to find the lowest energy state. Still there are attempts, such as [email protected], Foldit, and D.E. Shaw’s Anton. Anton holds the record for the longest molecular dynamics simulation - it ran for some untold amount of time, calculating the energy a protein would have at every femtosecond or something, in order to simulate 1 millisecond of the protein’s movement. Obviously, the time that Anton took to simulate that millisecond was more than a millisecond.

Entropy

Where kb is Boltzmann’s constant and W is the number of microstates that give rise to the macrostate of interest.

My favorite explanation of this is that given by Richard Feynman. When I read it, I understood for the first time how physical entropy and information entropy are the same concept:

So we now have to talk about what we mean by disorder and what we mean by order. … Suppose we divide the space into little volume elements. If we have black and white molecules, how many ways could we distribute them among the volume elements so that white is on one side and black is on the other? On the other hand, how many ways could we distribute them with no restriction on which goes where? Clearly, there are many more ways to arrange them in the latter case. We measure “disorder” by the number of ways that the insides can be arranged, so that from the outside it looks the same. The logarithm of that number of ways is the entropy. The number of ways in the separated case is less, so the entropy is less, or the “disorder” is less.

— Richard Feynman, quoted here

In biology, entropy is very often the driving force, for instance for the burial of hydrophobic protein domains. Imagine a water molecule in a tetrahedron. The tetrahedron has four corners, and the water has two hydrogens, so you can place the molecule in 4 choose 2 = 6 orientations. If you add a nonpolar group of a neighboring molecule at one corner of the tetrahedron, only three of the six states remain favorable (by still allowing hydrogen bonding). So ΔShydrophobic = kbln(3) - kbln(6) < 0, meaning that entropy has decreased.

Consider the mixing of epoxy and hardener into cured epoxy. This reaction has ΔS < 0 because the solid has fewer microstates than the liquids did. Yet the reaction occurs spontaneously at room temperature, so it must be true that ΔH < 0. Heat is therefore released - in fact, the reaction is extremely exothermic. Joe measured the temperature of “5-minute epoxy” and it rose from 21°C to >40°C at the 5 minute mark.

An incorrect and simplistic view of protein folding is as follows. An unfolded protein has high configurational entropy but also high enthalpy because it has few stabilizing interactions. A folded protein has far less entropy, but also far less enthalpy. There is a tradeoff between H and S here. Note that because ΔG = ΔH - TΔS, increased temperature weights the S term more heavily, meaning that higher temperature favors unfolding.

That entire explanation only considers the energy of the protein and not that of the solvent. In fact, hydrophobic domains of a protein constrain the possible configurations of surrounding water (see explanation above), and so their burial upon folding increases the water’s entropy. Moreover, it turns out that the hydrogen bonding of polar residues and the backbone is satisfied both in an unfolded state (by water) and in a folded state (by each other). Therefore enthalpy is “zero sum,” and protein folding is driven almost entirely by entropy.

Here is a description of a technique called differential scanning calorimetry. You apply equal amounts of heat to two solutions, one with only buffer and the other with buffer and protein, and you measure the temperature in each solution. Eventually the protein reaches its melting temperature Tm, where the protein is 50% folded and 50% unfolded and ΔG = 0. At Tm, the melting of the protein aborbs lots of the applied heat, and so the temperature does not rise as much as it does in the buffer-only solution.

Another technique for measuring protein stability is the force required to unfold it using single molecule atomic force microscopy.

Common denaturants are urea and guanidine hydrochloride. Amazingly, we still do not know how they work. It is thought that they stabilize all constituent parts of the unfolded protein. Guanidine may surround those unfavorable hydrophobic domains of the protein but then expose its own hydrophilic side to water, so that the movement of the water is not constrained.

About Eric Vallabh Minikel

Eric Vallabh Minikel is on a lifelong quest to prevent prion disease. He is a scientist based at the Broad Institute of MIT and Harvard.


Restriction Enzyme Digestion

Preparation of DNA for traditional cloning methods is dependent upon restriction enzyme digestion to generate compatible ends capable of being ligated together. The DNA to be cloned can vary widely, from genomic DNA extracted from a pure bacterial culture or a mixed population, to a previously cloned gene that needs to be moved from one vector to another (subcloning). Restriction enzymes can also be used to generate compatible ends on PCR products. In all cases, one or more restriction enzymes are used to digest the DNA resulting in either non-directional or directional insertion into the compatible plasmid.

Genomic DNA, regardless of the source, is typically digested with restriction enzymes that recognize 6-8 consecutive bases, as these recognition sites occur less frequently in the genome than 4-base sites, and result in larger DNA fragments. The desired insert size for the clone library determines which enzymes are selected, as well as the digestion conditions. Most often, a serial dilution of the selected restriction enzyme(s) is used to digest the starting material and the desired insert size range is isolated by electrophoresis followed by gel extraction of the DNA. This method of preparation provides DNA fragments of the desired size with ends compatible to the selected vector DNA.

Subcloning requires the use of 1-2 restriction enzymes that cut immediately outside the insert fragment without cutting within the insert itself. Restriction enzymes that have a recognition site within the multiple cloning site (MCS) are commonly used since they do not cut elsewhere in the vector DNA and typically produce two easily resolved DNA fragments. The gene of interest is most commonly subcloned into an expression vector for improved protein expression and/or addition of a purification tag. In this case, it is essential that the gene be inserted in the correct orientation and in frame with the transcription promoter.

The Polymerase Chain Reaction (PCR) is commonly used to amplify a gene or DNA fragment of interest, from any source of DNA, to be cloned. In order to generate compatible ends, it is common to add restriction sites to the 5&rsquo end of both PCR primers. When adding restriction sites to a PCR primer, it is recommended to include 6 bases between the recognition site and the 5&rsquo end of the primer. These additional bases provide sufficient DNA for the restriction enzyme to bind the recognition site and cut efficiently. When selecting a restriction site(s) to add to the primers, it is important to determine which site(s) will be compatible with your selected vector, whether directional cloning is desired and, most importantly, confirm that the recognition site(s) does not occur within the gene or DNA fragment.


Calculation of enthalpy and entropy of fusion of an unknown solid.

The molar volume of a certain solid is 142.0 cm3/mol at 1.00 atm and 427.15 K, its melting temperature.
The molar volume of the liquid at this temperature and pressure is 152.6 cm3/mol.
At 1.2 MPa the melting temperature changes to 429.26 K. Calculate the enthalpy and entropy of fusion of the solid.

1 Answer

#DeltaS_"fus" = "5.52 J/mol K"#
#DeltaH_"fus" = "2.36 kJ/mol"#

Explanation:

Your tool of choice for this problem will be the Clapeyron equation used in the form

Now, you know that the following relationship exists between the enthalpy change of fusion, #DeltaH_f# , and the entropy change of fusion, #DeltaS_f#

This is derived from the Gibbds free energy change at equilibrium

Since at equilibrium #DeltaG = 0# , it follows that you have

#DeltaH = T * DeltaS implies DeltaS = (DeltaH)/T#

Now, in your case, #T# would represent the meting temperature. A good rule of thumb to go by here is that you can use the average of the two given melting temperatures

Now, you should rearrange equation #color(purple)((1))# to solve for #dT# , and then integrate, but you could skip that step if you go by the assumption that the temperature change, #dT# , is small enough.

You can get away with such an approximation because you're operating on the solid - liquid phase line, so you're bound to have small changes in temperature in such cases.

Now, if you take this route, you can say that

At this point, you have everything you need to solve for #DeltaS_"fus"# . More specifically, you know that

Here comes the tricky part - you need to convert #DeltaV_"fus"# and #DeltaP# to cubic meters per mole, #"m"^3"/mol",# and pascals, #"Pa"# - you'll see why in a minute!

#DeltaV_"fus" = V_2 - V_1 = "152.6 cm"^3 - "142.0 cm"^3 = "10.6 cm"^3#

#10.6color(red)(cancel(color(black)("cm"^3)))/"mol" * "1 m"^3/(10^6color(red)(cancel(color(black)("cm"^3)))) = 10.6 * 10^(-6)"m"^3"/mol"#

#DeltaP = 1.2 * 10^6"Pa" - 1.01325 * 10^5"Pa" = 10.987 * 10^5"Pa"#

So, plug in these values and solve for #DeltaS_"fus"#

#DeltaS_"fus" = (DeltaP)/(DeltaT) * DeltaV_"fus"#

#DeltaS_"fus" = (10.987 * 10^5"Pa")/"2.11 K" * 10.6 * 10^(-6)"m"^3/"mol"#

But #"Pa" xx "m"^3 = "J"# , so the answer will be

Now use equation #color(purple)((2))# to get

#DeltaH_"fus" = DeltaS_"fus" * T_"average"#

#DeltaH_"fus" = 5.52"J"/("mol" * color(red)(cancel(color(black)("K")))) * 428.21color(red)(cancel(color(black)("K"))) = 2363.72 "J"/"mol"#

I'll leave this value rounded to three sig figs as well, but expressed in kilojoules per mole



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