Medical Biochemistry I and Elementary Mathematics I Review

Vocabulary practice flashcards covering medical biochemistry foundations (cell structure, biomolecules, buffers, enzyme kinetics) and elementary mathematics (set theory, real number systems, sequences, quadratic equations, and complex numbers).

Medical Biochemistry

The branch of general biochemistry defined as the study of biochemical processes that occur within the human body in relation to their application in the field of medicine.

Biomolecules

The organic molecules that make up cellular components—primarily proteins, carbohydrates, lipids, and nucleic acids—whose structures and functions give rise to the processes occurring within living cells.

Mitochondria

The power plants of the cell composed of an outer and an inner lipid bilayer-protein membrane, where the inner membrane encloses the mitochondrial matrix containing metabolic pathways for the oxidation of carbohydrates, lipids, and amino acids.

Lysosomes

Single-membrane vesicles with a highly acidic internal fluid environment ($pH \thickapprox 2$) containing a variety of enzymes that catalyze the breakdown of cellular macromolecules and digest large ingested particles.

Amphipathic Molecules

Molecules that possess both a hydrophilic ("water-loving") polar region and a hydrophobic ("water-hating") non-polar region, such as membrane phospholipids.

Liposome

An aqueous compartment enclosed by a phospholipid bilayer used as a clinical vehicle to deliver therapeutic drugs or DNA into target cells by fusing with the plasma membrane.

Aquaporins

Specialized protein channels embedded in the cell membrane that facilitate the rapid passive movement of water molecules at rates required for cellular activities.

Symport

A coupled transport (co-transport) mechanism across a membrane in which two different molecules or ions are moved in the same direction, such as the sodium-glucose transporter.

Antiport

A coupled transport (counter-transport) mechanism across a membrane in which two different molecules or ions are moved simultaneously in opposite directions.

Uniport, Symport, and Antiport

The three distinct modes of carrier-mediated transport across a lipid bilayer, categorized by whether a single solute is moved (uniport) or two solutes are co-transported in the same direction (symport) or opposite directions (antiport).

Primary Active Transport

A form of active transport that derives energy directly from the enzymatic hydrolysis of ATP, exemplified by the $\text{Na}^+\text{-K}^+\text{ ATPase}$ pump which exports three $\text{Na}^+$ ions for every two $\text{K}^+$ ions imported.

Mutarotation

The equilibrium change in optical rotation that occurs when an acyclic aldehyde of D-glucose equilibrates in aqueous solution into a mixture of cyclic hemiacetals containing $36\%$ of the $\alpha$-anomer, $64\%$ of the $\beta$-anomer, and trace acyclic aldehyde.

Reducing Sugar

A carbohydrate whose anomeric carbon is free (not involved in a glycosidic bond) and capable of acting as an electron donor to reduce chromogenic agents such as Benedict's reagent or Fehling's solution.

Buffer

An aqueous solution typically composed of approximately equal amounts of a weak acid and its conjugate base that resists substantial changes in $pH$ upon the addition of small amounts of strong acid or base.

Metabolic Acidosis

An acid-base disturbance characterized by a drop in blood $pH$ below $7.35$ due to excessive accumulation of metabolic acids, loss of bicarbonate, or decreased renal acid excretion.

Henderson-Hasselbalch Equation

The mathematical relationship used to calculate the $pH$ of a buffer solution: $pH = pK_a + \log\frac{[\text{conjugate base}]}{[\text{weak acid}]}$.

Zwitterion

A dipolar molecule carrying distinct positive ($\text{-NH}_3^+$) and negative ($\text{-COO}^-$) charges on the same structure while maintaining an overall net electrical charge of zero at physiological $pH$.

Isoelectric Point ($pI$)

The specific $pH$ value midway between the ionization constants ($pK$ values) on either side of the isoionic species at which a molecule possesses an overall net charge of zero.

Peptide Bond

A covalent amide bond formed between the $\alpha$-carboxyl group of one amino acid and the $\alpha$-amino group of another amino acid with the loss of a water molecule.

Sanger's Reagent

1-fluoro-2,4-dinitrobenzene (FDNB), a reagent that reacts with the free $\alpha$-amino group of the N-terminal residue in a polypeptide to form a stable dinitrophenyl (DNP) derivative.

Edman's Reagent

Phenylisothiocyanate (PITC), a chemical used to selectively label and cleave the amino-terminal residue of a peptide as a phenylthiohydantoin (PTH) derivative without hydrolyzing the rest of the peptide chain.

Primary Structure

The linear sequence of amino acids joined by peptide bonds in a polypeptide chain, including the exact locations of any disulfide cross-links.

Secondary Structure

The regular local steric conformations assumed by segments of a polypeptide chain, stabilized by hydrogen bonds between the main-chain $\text{NH}$ and $\text{CO}$ groups, such as the $\alpha$-helix and $\beta$-pleated sheet.

Tertiary Structure

The overall three-dimensional arrangement of all atoms in a single polypeptide chain, showing how secondary structures fold into compact globular domains via non-covalent interactions and disulfide bonds.

Quaternary Structure

The spatial arrangement and non-covalent association of multiple polypeptide subunits in a multimeric protein, such as the $\alpha_2\beta_2$ tetramer of hemoglobin.

Polyunsaturated Fatty Acids (PUFA)

Fatty acids containing two or more carbon-carbon double bonds typically separated by a methylene group ($\text{-CH}_2\text{-}$), including the essential dietary fatty acids linoleic acid and linolenic acid.

Triacylglycerols

Neutral lipids composed of three fatty acids esterified to a single molecule of glycerol, constituting the major anhydrous energy storage reservoir in adipose tissue.

High Density Lipoprotein (HDL)

A dense lipoprotein particle composed of approximately $50\%$ protein and $50\%$ lipid that mediates reverse cholesterol transport (RCT) by extracting cholesterol from peripheral tissues and delivering it to the liver.

Low Density Lipoproteins (LDL)

Cholesterol-rich lipoprotein particles that carry approximately $75\%$ of the total plasma cholesterol to extrahepatic tissues, associated with atherosclerosis when elevated in the bloodstream.

Nucleoside

A biomolecule composed of a nitrogenous purine or pyrimidine base covalently linked to a ribose or deoxyribose pentose sugar via a $\beta\text{-N-glycosidic}$ bond.

Nucleotide

A phosphorylated nucleoside composed of a nitrogenous base, a five-carbon pentose sugar, and one or more phosphate groups attached by ester bonds.

DNA Denaturation

The separation of the complementary hydrogen-bonded double helix of DNA into single strands, induced by elevated temperature, low salt concentration, or extreme $pH$.

Michaelis Constant ($K_m$)

The specific substrate concentration at which an enzyme-catalyzed reaction proceeds at half its maximum velocity ($\frac{V_{\max}}{2}$), representing an inverse measure of the enzyme's affinity for its substrate.

Lineweaver-Burk Plot

A double reciprocal linear transformation of the Michaelis-Menten equation ($\frac{1}{v}$ versus $\frac{1}{[S]}$) with a slope of $\frac{K_m}{V_{\max}}$, a y-intercept of $\frac{1}{V_{\max}}$, and an x-intercept of $-\frac{1}{K_m}$.

Competitive Inhibition

A reversible enzyme inhibition mechanism where the inhibitor competes directly with the normal substrate for the active site, resulting in an increased apparent $K_m$ while the $V_{\max}$ remains unchanged.

Non-competitive Inhibition

A reversible enzyme inhibition mechanism where the inhibitor binds to an alternative site on both the free enzyme and the enzyme-substrate ($ES$) complex, resulting in a decreased $V_{\max}$ while $K_m$ remains constant.

Uncompetitive Inhibition

A reversible enzyme inhibition mechanism where the inhibitor binds exclusively to the enzyme-substrate ($ES$) complex to form an inactive $ESI$ complex, decreasing both $K_m$ and $V_{\max}$.

Allosteric Enzymes

Regulatory oligomeric enzymes whose catalytic activity is modulated by the non-covalent binding of specific effector molecules at sites physically distinct from the active site, typically displaying sigmoidal (S-shaped) velocity curves.

Isozymes

Multiple distinct structural forms of an enzyme that catalyze the same chemical reaction within a single organism or cell type but differ in amino acid sequence, physical properties, electrophoretic mobility, and kinetic parameters.

Set

Any well-defined list, collection, or class of objects.

Tabular Form

A method of designating a set by explicitly listing all of its elements separated by commas and enclosed within curly braces, such as $A = \{1, 3, 7, 10\}$.

Set-Builder Form

A notation where a set is defined by stating the specific property that its arbitrary members must satisfy, written in the form $\{x \mid P(x)\}$.

Finite Set

A set consisting of a specific number of different elements such that the process of sequentially counting its elements comes to an end.

Infinite Set

A set whose elements cannot be counted to an end because the counting process continues indefinitely without termination.

Null Set

The unique set that contains no elements, denoted by $\emptyset$, which is considered a subset of every set.

Proper Subset

A set $B$ that is a subset of set $A$ ($B \subset A$) such that $B$ is not identical to $A$ ($B \neq A$).

Comparable Sets

Two sets $A$ and $B$ in which one set is a subset of the other, satisfying either $A \subset B$ or $B \subset A$.

Universal Set

The overarching, fixed reference set that contains all the elements under investigation in a given mathematical discourse, denoted by $U$.

Power Set

The family of all subsets of a given set $S$, denoted by $2^S$, which contains $2^n$ elements when set $S$ contains $n$ elements.

Disjoint Sets

Two sets $A$ and $B$ that have no elements in common, meaning that their intersection is the empty set ($A \cap B = \emptyset$).

Union of Sets

The set of all elements that belong to set $A$, to set $B$, or to both sets, defined as $A \cup B = \{x \mid x \in A \text{ or } x \in B\}$.

Intersection of Sets

The set of elements that are common to both set $A$ and set $B$, defined as $A \cap B = \{x \mid x \in A, x \in B\}$.

Difference of Sets

The set of elements that belong to set $A$ but do not belong to set $B$, denoted by $A - B = \{x \mid x \in A, x \notin B\}$.

Complement of a Set

The set of elements that do not belong to set $A$, equivalent to the difference between the universal set $U$ and set $A$, denoted by $A' = \{x \mid x \in U, x \notin A\}$.

Rational Numbers ($\mathbb{Q}$)

The set of real numbers that can be expressed as the ratio of two integers, defined by $\mathbb{Q} = \{x \mid x = \frac{p}{q} \text{ where } p \in \mathbb{Z}, q \in \mathbb{Z}, q \neq 0\}$.

Irrational Numbers ($\mathbb{Q}'$)

The set of real numbers that cannot be represented as a ratio of integers and correspond to non-terminating, non-repeating decimals, represented as the complement of $\mathbb{Q}$ in $\mathbb{R}$.

Absolute Value

The geometric distance on the real line between a number $x$ and the origin, algebraically defined as $|x| = x$ if $x \ge 0$ and $|x| = -x$ if $x < 0$.

Bounded Set

A set of real numbers $A$ that is a subset of a finite interval, meaning there exists a positive number $M$ such that $|x| < M$ for all $x \in A$.

Arithmetic Sequence (A.P.)

A sequence of numbers in which each successive term differs from the preceding term by a constant value called the common difference ($d$), with general term $U_n = a + (n - 1)d$.

Geometric Sequence (G.P.)

A sequence of numbers in which the ratio between consecutive terms is constant, known as the common ratio ($r$), with general term $U_n = ar^{n-1}$.

Discriminant

The algebraic expression $b^2 - 4ac$ derived from the quadratic equation $ax^2 + bx + c = 0$, which determines whether the roots are distinct and real ($> 0$), equal and real ($= 0$), or complex conjugates ($< 0$).

Mathematical Induction

A mathematical proof technique asserting that if a statement $P(n)$ involving natural numbers is true for $n = 1$, and its validity for $n = k$ implies its validity for $n = k + 1$, then the statement is true for all natural numbers $n \in \mathbb{N}$.

Complex Number

A number written in the form $z = a + bi$, where $a$ and $b$ are real numbers representing the real and imaginary parts respectively, and $i$ is the imaginary unit satisfying $i^2 = -1$.

Conjugate of a Complex Number

The complex number $z = a - bi$ formed by reversing the sign of the imaginary component of $z = a + bi$, such that their product is the non-negative real value $a^2 + b^2$.

De Moivre's Theorem

The algebraic formula stating that for any complex number in polar form and any integer exponent $n$, $[r(\cos(\theta) + i\sin(\theta))]^n = r^n(\cos(n\theta) + i\sin(n\theta))$.

Circle

The geometric locus of a point in a plane that moves so that its distance from a fixed point (the centre $(a, b)$) remains constant (the radius $r$), represented algebraically by $(x - a)^2 + (y - b)^2 = r^2$.