Dealing in the area of Mathematics,Algorithms,Physics, chemistry,Bio chemistry, Biology.Providing multiple solutions for one problem with the help of domain of mathematics like Algebra,Vector Calculus,Calculus,Coordinate Geometry,Trigonometry etc .Providing the basics and Advanced concept and creating Alternative solution paths for problems with the help of different domain of mathematics.Thus providing different views and interpretation for same phenomenon.
Today i will start from Stereoisomers and we will see how spatial orientation of a substituent attached to the central atom can lead to this type of isomers and how this spatial orientation can lead to optical activity of of this kind of isomers ,this optical activity is the only way to differentiate between chiral and achiral organic compound.We will see What type /mechanism of an organic reaction can lead to such optical activity. First let's start with spacial orientation of a carbon compound. Three-Dimensional Representation of Organic Molecules.
Hydrogen Attached by Dashed wedge is telling that H is having Spacial orientation and is pointing inside the paper and the H represented by solid wedge is telling that H is having a spacial orientation and pointing towards you ie above the paper. If we try representing this on 2d Euclidean plane then the H that is pointing Above the paper is represented on the Right side of the vertical line formed by carbon chain and the H that is pointing inside the page is represented to the left of the vertical line formed by carbon chain and this Spacial orientation of substituent group is responsible for two types of sterioisomers. 1.Enantiomers: 2.Diastereomers: Enantiomers are two stereoisomers that are related to each other by a reflection:They are mirror image of each other, which are non-superimposable. Human hands are a macroscopic analog of stereoisomerism. Every stereogenic center
in one has the opposite configuration in the other. Two compounds that
are enantiomers of each other have the same physical properties, except
for the direction in which they rotate polarized light and how they interact with different optical isomers
of other compounds. As a result, different enantiomers of a compound
may have substantially different biological effects. Pure enantiomers
also exhibit the phenomenon of optical activity and can be separated only with the use of a chiral agent. In nature, only one enantiomer of most chiral biological compounds, such as amino acids (except glycine, which is achiral), is present. Diastereomers are stereoisomers not related through a reflection operation. They are not mirror images of each other. These include meso compounds, cis–trans (E-Z) isomers, and non-enantiomeric optical isomers.
Diastereomers seldom have the same physical properties. In the example
shown below, the meso form of tartaric acid forms a diastereomeric pair
with both levo and dextro tartaric acids, which form an enantiomeric
pair.
As an another example we can consider Glucose and Fructose as optically Active this as Sterio isomers. Thus the figure for this is as following:
Isomers and stereoisomers. Glucose, fructose, and galactose are isomers with the empirical formula C6H12O6. A structural isomer of glucose, such as fructose, has identical chemical groups bonded to different carbon atoms, while a stereoisomer of glucose, such as galactose, has identical chemical groups bonded to the same carbon atoms but in different orientation
Geometrical isomerism:
Stereoisomerism about double bonds arises because rotation about the
double bond is restricted, keeping the substituents fixed relative to
each other. If the two substituents on at least one end of a double bond
are the same, then there is no stereoisomer and the double bond is not a
stereocenter, e.g. propene, CH3CH=CH2 where the two substituents at one end are both H. The isomer of the type (a), in which two identical atoms or groups lie on the same side of the double bond is called cis isomer and the other isomer of the type (b), in which identical atoms or groups lie on the opposite sides of the double bond is called trans isomer . Thus cis and trans isomers have the same structure but have different configuration (arrangement of atoms or groups in space). Due to different arrangement of atoms or groups in space, these isomers differ in their properties like melting point, boiling point, dipole moment, solubility etc. Geometrical or cis-trans isomers of but-2-ene are as following
Streric effect ,Dipole effect etc is cancelled out in Trans form according to vector law of Subtraction since the two methyl group are vertically opposite to each other. Noe you can appreciate why? Cis form of alkene is found to be more polar than the trans form. For example, dipole moment of cis-but-2-ene is 0.33 Debye, whereas, dipole moment of the trans form is almost zero or it can be said that trans-but-2-ene is non-polar. This can be understood by drawing geometries of the two forms as given below from which it is clear that in the trans-but-2-ene, the two methyl groups are in opposite directions,Threfore, dipole moments of C-CH3 bonds cancel, thus making the trans form non-polar. Applying vector law of addition is equivalent ti vector subtraction of two dipole effect created by vertically opposite placed methyl group Diagrammatically this vector substraction can be shown as
Conformers:Conformational isomerism is a form of isomerism that describes the
phenomenon of molecules with the same structural formula but with
different shapes due to rotations about one or more bonds. Different
conformations can have different energies, can usually interconvert, and
are very rarely isolatable.
The Eclipsed is least stable with Gibb's energy change as positive and Staggered as the most stable as with change in Gibb's energy negative thus high equilibrium constant.
The Staggered form obtained by 180 degree of rotation of eclipsed form is the most stable because the two methyl/Substituent group are vertically opposite to each other thus providing least steric repulsion to each other making Gibb's free energy change negative and you can appreciate this change as the difference in the Enthalpy change in Eclipsed and staggered is 12KJ/mole.
This can well be represented by Figure as shown below.
Enzyme Cofactors: A co factor is a non protein chemical compound that is required for the protein's biological activity. These proteins are commonly enzymes, and cofactors can be considered "helper molecules" that assist in biochemical transformations Enzyme function is often assisted by additional chemical components known as cofactors. For example, the active sites of many enzymes contain metal ions that help draw electrons away from substrate molecules. The enzyme carboxypeptidase digests proteins by employing a zinc ion (Zn++) in its active site to remove electrons from the bonds joining amino acids. Other elements, such as molybdenum and manganese, are also used as cofactors. Like zinc, these substances are required in the diet in small amounts. When the cofactor is a nonprotein organic molecule, it is called a coenzyme. Many vitamins are parts of coenzymes. In numerous oxidation-reduction reactions that are catalyzed by enzymes, the electrons pass in pairs from the active site of the enzyme to a coenzyme that serves as the electron acceptor. The coenzyme then transfers the electrons to a different enzyme, which releases them (and the energy they bear) to the substrates in another reaction. Often, the electrons pair with protons (H+) as hydrogen atoms. In this way, coenzymes shuttle energy in the form of hydrogen atoms from one enzyme to another in a cell. Some enzymes or enzyme complexes require several cofactors. For example, the multienzyme complex pyruvate dehydrogenase at the junction of glycolysis and the citric acid cycle requires five organic cofactors and one metal ion: loosely bound thiamine pyrophosphate (TPP), covalently bound lipoamide and flavin adenine dinucleotide (FAD), and the cosubstrates nicotinamide adenine dinucleotide (NAD+) and coenzyme A (CoA), and a metal ion (Mg2+). Organic cofactors are often vitamins or are made from vitamins. Many contain the nucleotideadenosine monophosphate (AMP) as part of their structures, such as ATP, coenzyme A, FAD, and NAD+. This common structure may reflect a common evolutionary origin as part of ribozymes in an ancient RNA world.
It has been suggested that the AMP part of the molecule can be
considered a kind of "handle" by which the enzyme can "grasp" the
coenzyme to switch it between different catalytic centers. One of the most important coenzymes is the hydrogen acceptor nicotinamide adenine dinucleotide (NAD+)as shown in the figure below. The NAD+ molecule is composed of two nucleotides bound together.A nucleotide is a five-carbon sugar with one or more phosphate groups attached to one end and an organic base attached to the other end. The two nucleotides that make up NAD+, nicotinamide monophosphate (NMP) and adenine monophosphate (AMP), are joined head-to-head by their phosphate groups. The two nucleotides serve different functions in the NAD+ molecule: AMP acts as the core, providing a shape recognized by many enzymes; NMP is the active part of the molecule, contributing a site that is readily reduced (that is, easily accepts electrons). When NAD+ acquires an electron and a hydrogen atom (actually, two electrons and a proton) from the active site of an enzyme, it is reduced to NADH. The NADH molecule now carries the two energetic electrons and the proton. The oxidation of energy-containing molecules, which provides energy to cells, involves stripping electrons from those molecules and donating them to NAD+. As we’ll see, much of the energy of NADH is transferred to another molecule. Enzymes have an optimum temperature and pH, at which the enzyme functions most effectively. Inhibitors decrease enzyme activity, while activators increase it. The activity of enzymes is often facilitated by cofactors, which can be metal ions or other substances. Cofactors that are non-protein organic molecules are called coenzymes.
How enzymes can be inhibited. (a) In competitive inhibition, theinhibitor interferes with the active site of the enzyme. (b) Innoncompetitive inhibition, the inhibitor binds to the enzyme at aplace away from the active site, effecting a conformational change in the enzyme so that it can no longer bind to its substrate.
The chemical structure of nicotinamide adenine dinucleotide (NAD+). This key cofactor is composed of two nucleotides, NMP and AMP, attached head-to-head. Thus Enzymes and Inhibitors can play major role in effectiveness of any drug and and its action on the target .Thus drug manufacturers always consider about the element mainly transition elements like molybdenum,cobalt,iron,zinc,titanium,copper ..as active site of enzymes and their fit to the substrate for its effective action.
It takes energy to break the chemical bonds that hold the atoms in a molecule together. Heat energy, because it increases atomic motion, makes it easier for the atoms to pull apart. Both chemical bonding and heat have a significant influence on a molecule, the former reducing disorder and the latter increasing it. The net effect, the amount of energy actually available to break and subsequently form other chemical bonds, is called the free energy of that molecule. In a more general sense, free energy is defined as the energy available to do work in any system. In a molecule within a cell, where pressure and volume usually do not change, the free energy is denoted by the symbol G (for “Gibbs’ free energy,” which limits the system being considered to the cell). G is equal to the energy contained in a molecule’s chemical bonds (called enthalpy and designated H) minus the energy unavailable because of disorder (called entropy and given the symbol S) times the absolute temperature, T, in degrees Kelvin (K = °C + 273): G = H – TS reactions break some bonds in the reactants and form new bonds in the products. Consequently, reactions can produce changes in free energy. When a chemical reaction occurs under conditions of constant temperature, pressure, and volume—as do most biological reactions— the change in free energy (ΔG) is simply: ΔG = ΔH – T ΔS <0 for any spontaneous reaction Driving factor behind any Biological reaction is to make overall del(G)<0.In the previous paper i defined why del(G) is required to be negative.Mathematically it is related to Thermodynamics and second law of thermodynamics which says about the direction of chemical reaction which depends upon both Enthalpy change for a chemical reaction and Entropy change of a chemical reaction. I will mathematically talk about these factor in Bio-chemistry as i am a mathematician but today i wanted to give you its overall picture. Lets depict it in terms of graph
Energy in chemical reactions. (a) In an endergonic reaction, the products of the reaction contain more energy than the reactants, and the extra energy must be supplied for the reaction to proceed. (b) In an exergonic reaction, the products contain less energy than the reactants, and the excess energy is released. Free energy is the energy available to do work. Within cells, the change in free energy (ΔG) is the difference in bond energies between reactants and products (ΔH), minus any change in the degree of disorder of the system (T ΔS). Any reaction whose products contain less free energy than the reactants (ΔG is negative) will tend to proceed spontaneously. Activation Energy: The rate of an exergonic reaction depends on the activation energy required for the reaction to begin. Reactions with larger activation energies tend to proceed more slowly because fewer molecules succeed in overcoming the initial energy hurdle. Activation energies are not constant, however. Stressing particular chemical bonds can make them easier to break. The process of influencing chemical bonds in a way that lowers the activation energy needed to initiate a reaction is called catalysis, and substances that accomplish this are known as catalysts. The rate of a reaction depends on the activation energy necessary to initiate it. Catalysts reduce the activation energy and so increase the rates of reactions, although they do not change the final proportions of reactants and products.\\
Activation energy and catalysis. (a) Exergonic reactions do not necessarily proceed rapidly because energy must be supplied to destabilize existing chemical bonds. This extra energy is the activation energy for the reaction. (b) Catalysts accelerate particular reactions by lowering the amount of activation energy required to initiate the reaction. ATP : Adenosine TriPhosphate. Each ATP molecule is a nucleotide composed of three smaller components as given below The first component is a five-carbon sugar, ribose, which serves as the backbone to which the other two subunits are attached. The second component is adenine, an organic molecule composed of two carbon-nitrogen rings. Each of the nitrogen atoms in the ring has an unshared pair of electrons and weakly attracts hydrogen ions. Adenine, therefore, acts chemically as a base and is usually referred to as a nitrogenous base (it is one of the four nitrogenous bases found in DNA and RNA). The third component of ATP is a triphosphate group (a chain of three phosphates).
The ATP molecule. (a) The model and (b) structural diagram both show that like NAD+, ATP has a core of AMP. In ATP the reactive group added to the end of the AMP phosphate group is not another nucleotide but rather a chain of two additional phosphate groups. The bonds connecting these two phosphate groups to each other and to AMP are energy-storing bonds.
How ATP Stores Energy The key to how ATP stores energy lies in its triphosphate group. Phosphate groups are highly negatively charged, somthey repel one another strongly. Because of the electrostatic repulsion between the charged phosphate groups, the two covalent bonds joining the phosphates are unstable. The ATP molecule is often referred to as a “coiled spring,” the phosphates straining away from one another. The unstable bonds holding the phosphates together in the ATP molecule have a low activation energy and are easily broken. When they break, they can transfer a considerable amount of energy. In most reactions involving ATP, only the outermost high-energy phosphate bond is hydrolyzed, cleaving off the phosphate group on the end. When this happens, ATP becomes adenosine diphosphate (ADP), and energy equal to 7.3 kcal/mole is released under standard conditions. The liberated phosphate group usually attaches temporarily to some intermediate molecule. When that molecule is dephosphorylated, the phosphate group is released as inorganic phosphate (Pi).
1.Energy and Metabolism 2.Free-Energy Changes in Biological Systems. 3.Thermodynamics I. Free energy of formation II. Effect of temperature on spontaneity III. Thermodynamics in biological systems. A. ATP-coupled reactions B. Hydrogen bonding
The laws of thermodynamics describe how energy changes. The Flow of Energy in Living Things. Potential energy is present in the valance electrons of atoms, and so can be transferred from one molecule to another. The Laws of Thermodynamics. Energy is never lost but as it is transferred, more and more of it dissipates as heat, a disordered form of energy. Free Energy. In a chemical reaction, the energy released or supplied is the difference in bond energies between reactants and products, corrected for disorder. Activation Energy. To start a chemical reaction, an input of energy is required to destabilize existing chemical bonds Enzymes are biological catalysts and lowers the activation energy required by any reactant to convert to product by passing through the transition state called Activated state. Thus it helps lowering activation energy of any reactant and thus increase the rate constant as supported by following figure and formula.
Thus the activation energy has been lowered by using Bio catalyst called catalyst .Other than enzyme the rate constant depends upon temperature It has been found that for a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled.The temperature dependence of the rate of a chemical reaction can be accurately explained by Arrhenius equation It was first proposed by Dutch chemist, J.H. van’t Hoff but Swedish chemist, Arrhenius provided its physical justification and interpretation.
k = A e -Ea /RT (Arrhenius formula)
where A is the Arrhenius factor or the frequency factor. It is also called pre-exponential factor. It is a constant specific to a particular reaction. R is gas constant and Ea is activation energy measured in joules/mole (J mol –1).
It can be understood clearly using the following simple reaction
H2(g) + I2( g) → 2HI(g).
According to Arrhenius, this reaction can take place only when a molecule of hydrogen and a molecule of iodine collide to form an unstable intermediate.The energy required to form this intermediate, called activated complex (C), is known as activation energy (Ea).
Taking natural logarithm of both sides of Arrhenius equation we get
ln k = – Ea/ RT + ln A
Applying this equation at two different temperatures T1 and T2 such that T2>T1.
At T1
ln k1 = –E/RT1 + ln A
At T2
ln k2 = –Ea/RT2 + ln A
(since A is constant for a given reaction) k1 and k2 are the values of rate constants at temperatures T1 and T2 respectively.
ln k2 – ln k1 =Ea/RT1 –Ea/ RT2.
ln(K2/K1)=-Ea/R[1/T2-1/T1].
Plot is as following.
To deal with energetics in bio-chemistry we have to deal with thermodynamics and thermodynamics associated with Redox reaction. ENERGIES AND ENTHALPIES OF CHEMICAL REACTIONS
BOND ENERGY/ BOND ENTHALPY
change in H, bond dissociation Enthalpy , is the change in heat accompanying the dissociation of a bond (measured at constant pressure P).
Enthalpy is a “STATE” FUNCTION, which means H is independent of path. Hess's Law: If two or more chemical equations are added to give another chemical equation, corresponding Enthalpies or Gibb's free energy or Entropy must be added ie Hess's law is true for Enthalpy,Gibb's free energy and Entropy of any reaction. Equavalently it says the following
And this is the decomposition theory of energetics.
Another example is
We will come to the point and see how thermodynamics is responsible for double helical structure of DNA and will see that it makes it's Gibb's energy negative ie product side that is double helix more stable than the plain sheetby maximizing the hydrogen bondingthus providing the necessary energy release as hydrogen bonding is Exogenous.
Lets come to enzymes and its energetics and see how it lowers the activation energy by binding the substrate to the activesite.All these concepts are associated with energetics i will come to energetics in terms of oxidation and reduction reaction in Bio molecules. You will be amazed to know that the energetics also coming into picture in all biological reaction whether it would be the process of reduction of NAD+ to NADH+P or any biological reaction Enzymes come into picture to lower the Ea=Activation Energy which we have already discussed. Let's illustrate it by picture.
An oxidation-reduction reaction. Cells use a chemical called NAD+ to carry out oxidation-reduction reactions. Energetic electrons are often paired with a proton as a hydrogen atom. Molecules that gain energetic electrons are said to be reduced, while ones that lose energetic electrons are said to be oxidized. NAD+ oxidizes energy-rich molecules by acquiring their hydrogens (in the figure, this proceeds 1→2→3) and then reduces other molecules by giving the hydrogens to them (in the figure, this proceeds 3→2→1).
Diagrammatically this can be represented as
Where mechanism of this oxidation and reduction reaction can be explained by this following equation 1)Arrhenius equation The Arrhenius equation
gives the quantitative basis of the relationship between the activation
energy and the rate at which a reaction proceeds. From the Arrhenius
equation, the activation energy can be found through the relation
where A is the frequency factor for the reaction, R is the universal gas constant, T is the temperature (in kelvin), and k is the reaction rate coefficient. Ea
can be evaluated from the variation in reaction rate coefficients as a
function of temperature (within the validity of the Arrhenius equation). 2)Gibb's free energy Equation or entropy Equation total Entropt change>0 Entropy change(System)+Entropy Change(Surrounding)>0. And if you solve it To derive the Gibbs free energy equation for an isolated system, let Stot be the total entropy of the isolated system, that is, a system that cannot exchange heat or mass with its surroundings. According to the second law of thermodynamics:
and if ΔStot = 0 then the process is reversible. The heat transfer Q vanishes for an adiabatic system. Any adiabatic process that is also reversible is called an isentropic process. Now consider a system having internal entropy Sint. Such a system is thermally connected to its surroundings, which have entropy Sext.
The entropy form of the second law applies only to the closed system
formed by both the system and its surroundings. Therefore a process is
possible only if
.
If Q is the heat transferred to the system from the surroundings, then −Q is the heat lost by the surroundings, so that corresponds to the entropy change of the surroundings. We now have:
Multiplying both sides by T:
Q is the heat transferred to the system; if the process is now assumed to be then Qp = ΔH:
ΔH is the enthalpy change of reaction (for a chemical reaction at constant pressure). Then:
for any chemical reaction to be spontaneous
for a possible process. Let the change ΔG in Gibbs free energy be defined as
Notice that it is not defined in terms of any external state functions, such as ΔSext or ΔStot. Then the second law, which also tells us about the spontaneity of the reaction, becomes:
Neither the forward nor the reverse reaction prevails (Equilibrium)
disfavoured reaction (Nonspontaneous)
Gibbs free energy G itself is defined as
Enzymes typically catalyze only one or a few similar chemical reactions because they are specific in their choice of substrates. This specificity is due to the active site of the enzyme, which is shaped so that only a certain substrate molecule will fit into it.
The catalytic cycle of an enzyme. Enzymes increase the speed with which chemical reactions occur, but they are not altered themselves as they do so. In the reaction illustrated here, the enzyme sucrase is splitting the sugar sucrose (present in most candy) into two simpler sugars: glucose and fructose. (1) First, the sucrose substrate binds to the active site of the enzyme, fitting into a depression in the enzyme surface. (2) The binding of sucrose to the active site forms an enzyme-substrate complex and induces the sucrase molecule to alter its shape, fitting more tightly around the sucrose. (3) Amino acid residues in the active site, now in close proximity to the bond between the glucose and fructose components of sucrose, break the bond. (4) The enzyme releases the resulting glucose and fructose fragments, the products of the reaction, and is then ready to bind another molecule of sucrose and run through the catalytic cycle once again. This cycle is often summarized by the equation: E + S ↔ [ES] ↔ E + P, where E = enzyme, S = substrate, ES = enzyme-substrate complex, and P = products. How Enzymes Work Most enzymes are globular proteins with one or more pockets or clefts on their surface called active sites as shown above figure Substrates bind to the enzyme at these active sites, forming an enzyme-substrate complex. For catalysis to occur within the complex, a substrate molecule must fit precisely into an active site. When that happens, amino acid side groups of the enzyme end up in close proximity to certain bonds of the substrate. These side groups interact chemically with the substrate, usually stressing or distorting a particular bond and consequently lowering the activation energy needed to break the bond. The substrate, now a product, then dissociates from the enzyme. Proteins are not rigid. The binding of a substrate induces the enzyme to adjust its shape slightly, leading to a better induced fit between enzyme and substrate refer figure above .This interaction may also facilitate the binding of othersubstrates; in such cases, the substrate itself “activates” the enzyme to receive other substrates. So for most of the Biological and chemical reaction Gibb's energy change is paramount in driving a reaction forward or backward because Gibb's Energy change considers both Enthalpy change del(H) and Entropy change del(S) thus it is the complete relation for predicting the spontaneity of any chemical or biological process.The motivation of any event or process in Biological system is governed by to make del(G)<0.
THERMODYNAMICS IN BIOLOGICAL SYSTEMS A) ATP-COUPLED REACTIONS Many biological reactions are non-spontaneous, meaning they require energy to proceed in the forward direction. The hydrolysis of ATP (ATP → ADP), a spontaneous process, can be Coupled to a non-spontaneous reaction to drive the reaction forward. The resulting ΔGº of the coupled reaction is the sum of the individual ΔGº values. First, let’s calculate the ΔGº for ATP hydrolysis at 310 K (body temperature). ΔH° = -24 kJ/mol, ΔS° = +22 J/K•mol
Example of an ATP-coupled reaction: the conversion of glucose to glucose-6-P. Adding a phosphate (P) group to glucose gives the glucose a negative charge, which prevents the glucose molecule from diffusing back out of the cell through the“greasy” cell membrane.
An enzyme couples the glucose-to-glucose-6-P reaction to ATP hydrolysis. The net change in free energy = If ATP hydrolysis is spontaneous, why is it not occurring unregulated in the cell? KINETICS! A reaction can be thermodynamically spontaneous, but kinetically very very slow.
HYDROGEN BONDING A hydrogen bond is an electrostatic interaction between a hydrogen atom in a polar bond (typically a H-F, H-O or H-N bond) and a “hydrogen-bond donor”, a strongly electronegative atom.
The H-bond donor (Y) atom must be small, highly electronegative atom with a a Lone pair of electrons available for bonding. For example, hydrogen bonds form between water molecules:
H-bonding can be intermolecular (as in the water molecules above) or intramolecular.Intramolecular H-bonds in proteins are required for a protein’s 3-dimensional shape.
In next blog i will come with some unique examples of Energetics in Bio-molecules and their process of synthesis inside the cell and you will come to know that it is the negative Gibb's energy of a Redox reaction del(G)= nFE(Reduction) which is stored during Photosynthesis in the plant in the form of Glucose ,ATP ,NADPH etc..
To see my lectures on the related topic click and Subscribe to my channel at the following address.