Tutor profile: James M.
What is a derivative?
The simplest way to explain a derivative is with an example: Let's take this function: f(x) = 2x Basically the independent variable is x and the dependent variable is f(x) (i.e. since it's a FUNCTION of x, it is DEPENDENT on x). So you can plug in any value as x (1,2,3) and you'll get value for f(x) : f(1) = 2 f(2) = 4 f(3) = 6 You notice that as you increase x, f(x) is always double whatever x is in this function. There is always a constant increase in x, in a linear fashion. Try graphing this to prove this to yourself. Essentially, every time x goes up by 1, f(x) goes up by 2. The derivative is essentially a function (f'(x)) in itself that describes the rate of change (i.e. the slope) at any point x on the original function. The derivative intuitively is 2 for this function because at ANY point, there is an instantaneous rate of change of 2. So, in this case, the derivative is always 2 regardless of where on the function f(x) you are!
Explain Le Chatelier's principle
It's simple - no chemical reaction can ever go to 100% completion and all reactions are reversible (if you've ever read a reaction is irreversible it technically is wrong but it just means that it will go to 99.99999% completion - there is always SOME reactant leftover). There is always an equilibrium that is quantified by a constant - Keq. Keq = [products]/[reactants]. What does this mean? It means that the products divided by the reactants always yields the same number, the Keq (it could be 1 it could be 100000, but it never changes for a specific reaction). Think about it - if you add more of the [product], there MUST be some sort of compensation so that Keq remains the same -> the reaction will go in the opposite direction so that more reactants get formed from the products you've added. Let's say you wanted to produce more product, if you removed the product as the reaction goes on (i.e. if the product is a gas that evaporates like in the production of chlorine gas), then the reaction will be pushed in the forward direction, favouring the formation of the product to keep the Keq constant. This is Le Chatelier's principle. It's like a seesaw. If you add reactant, more product gets produced. If you add more product the reaction reverses and produces more reactant until equilibrium is achieved. The relative proportion of reactant and product is always the same!
Describe the weak intramolecular forces that favour the formation of secondary and tertiary structure of proteins.
Proteins (such as albumin, antibodies, fibrinogen, digestive enzymes, glycolytic enzymes etc...) are essentially biomolecules that are polymers (long chains) of a single subunit: the amino acid. So, protein = chain of linked amino acids. These amino acids have unique properties because they have two important functional groups: an amine (-NH3+) and a carboxylic acid (CO2-). At physiological pH in the body, these amino acids exist in their respective charged states. The amino group is positively charged and the carboxyl group is negatively charged. On top of this, there exists 20 amino acids, each characterized by their unique amino acid side chains. We know that molecules (especially larges ones like proteins) always try to arrange themselves in a conformation that maximizes intramolecular bonding forces in a so-called low energy state (i.e. more favourable attractive forces between groups reduces the energy state). So, proteins undergo a complex process of folding whereby the once "linear" chain of amino acids become folded onto itself. This folding is mediated by intramolecular forces such as electrostatic (positive attract negative in the case of carboxyl oxygens to amino hydrogens) and hydrogen bonds (partial positive charges of hydrogens bonded to nitrogen atoms attracts the negatively-charged oxygens). It is fascinating that proteins often consistently adopt the same shape (think of enzymes that need to have a precise tertiary structure to be able to catalyze a reaction specific to discrete subset of substrates). It is these so-called "weak" intramolecular forces that guide proteins into adopting local structure (secondary structure) and overall three-dimensional structure in single subunits (tertiary structure). Proteins are so biologically important for our normal function and they, in turn, rely on these weak forces. However, the term "weak" shouldn't fool you into thinking they aren't strong (as we know they certainly are) because many of these weak interactions (there are so many in large molecules) collectively contribute a great deal of overall strength. The term weak just means that a single one of these interactions is weaker than a covalent bond between two atoms (direct sharing of electrons between atoms). On a small scale a weak force IS weak, but when there are millions of them, they are much stronger than a single covalent bond!
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