Part II

• Proteins as Processing units:

  Cells continually make decisions that affect how they respond to their environment. The decision-making circuits in cells typically consist of proteins that process “inputs” and generate “outputs"
• Binding isotherm

  A) hyperbolic

  B) L

  C) fractional occupancy

  
• Ultrasensitivity yuh

  A) reduces

  B) 100

  
• Graded response:

  An output function that depends on the input in a hyperbolic fashion, as in a simple binding equilibrium, is known as a graded, or linear, response. In such a response, the output switches from ~10% to ~90% of the maximum response over a 100 fold change in input strength (i.e. concentration of the ligand)
• Ultrasensitivity:

  An ultrasensitive system is one in which the response to an input is sharper than expected from a simple binding equilibrium. For example, when the output switches from ~10% to ~90% of the maximum response over a less than ~100-fold concentration range of the ligand, the system is said to be ultrasensitive
• Graded response:

  A monomeric protein with a single binding site cannot display ultrasensitivity, thus the output will be graded

  
• Ultrasensitivity:

  A dimeric protein with two binding sites can display ultrasensitivity if the

  conformations of the two binding sites are coupled. Ligand binding to one site causes an allosteric change in the other site, thereby altering the unoccupied sites affinity for the ligand. Ligand binding to such a system is said to be cooperative

  Allostery (“allo” is greek for “different” or “other”):

  An allosteric protein is one in which the activity of the protein is modulated by interactions that occur at a distance from the active site

  
• Cooperative binding can occur without allostery. In this example, a transcription factor has two closely spaced and inverted binding sites on DNA. If two molecules of the transcription factor interact with each other when bound to DNA, then cooperative binding results without necessitating a conformational change. This kind of cooperativity is quite rare, and the cooperativity that we will focus on involves allostery and coupled binding sites

  
• Ultrasensitivity can also arise through mechanisms other than cooperative binding to multiple subunits. Many different kinds of feedback mechanisms are utilized in cells, and these can increase the sharpness of the response. Above the conversion of substrate to product by a monomeric enzyme generates an allosteric activator

  of the enzyme. The activator binds to an allosteric site on the enzyme and causes a conformational change that opens up the active site of the enzyme, thereby speeding up the rate of catalysis (positive feedback)

  
• Bacteria exhibit chemotaxis, which is directed movement towards sources of food and away from toxins. This is a consequence of the correlated movement of the bacterial flagella, which all rotate in a counterclockwise direction and propel the bacterium forward in a whip-like fashion. If there is a chemical repellant present, then the flagella start to rotate in a clockwise fashion and disengage from each other. The uncorrelated rotations of the disengaged flagella cause the bacteria to tumble and move away from the repellant

  
• • Chemotaxis is controlled by the “Che” family of proteins
  • When CheY is bound to the motor protein, the flagellum rotates in a clockwise fashion and tumbling results
  • In order for CheY to bind to the motor protein, it has to be phosphorylated, and this phosphorylation is brought about as a consequence of a repellant molecule binding to a receptor on the surface of the cell
  • When CheY is dis-engaged (unphosphorylated), the rotation is in a counterclockwise fashion, and multiple flagella rotate in a coordinated fashion propelling the bacterium forward

  
• • The observed relationship between the concentration of phosphorylated CheY and the extent of clockwise rotation of the flagella shows that the extent of clockwise rotation changes over an extremely narrow phosphorylated CheY concentration range (2-4 μM)
  • Because the extent of clockwise rotation is governed by the binding of phosphorylated CheY to the flagellar motor, the response can be interpreted in terms of a binding isotherm, where KD is 3 μM (blue rectangular hyperbola above).

  
• The behaviour of the flagellar motor when the concentration of CheY-P changes resembles a sharp, switch-like response and is obviously ultrasensitive. The motor does not turn on until the concentration of CheY-P has reached a certain level, but the motor turns on decisively, over a narrow concentration range. Decisive molecular switches are very important in biology because they are less sensitive to noise (small

  amounts of the input signal do not evoke the response) and are efficient (once a threshold concentration is reached, the system switches on the desired process)

  
• When two or more ligands bind to a protein in such a way that they mutually reinforce each of their binding affinities, the phenomenon is called positive cooperativity, which is another way of achieving an

  ultrasensitive response.

  Binding of ligand B (LB) increases the protein’s affinity for ligand A (LA)

  
• Hemoglobin greatly increases the oxygen carrying

  capacity of the blood. Oxygen is not very soluble, and the dissolved oxygen concentration in blood is 0.1mM.

  The hemoglobin concentration in human blood is ~2mM, and because each tetramer has four oxygen binding sites, the effective concentration

  of oxygen binding sites in hemoglobin is ~8 mM. This is ~80X greater than the dissolved oxygen concentration
• Hemoglobin efficiently transports oxygen from the

  lungs to peripheral tissues

  • The oxygen concentration of venous blood is ~30 torr (tissues), whereas it is ~100 torr in arterial blood (lungs). The difference in dissolved oxygen concentration means that hemoglobin must exhibit an ultrasensitive response to oxygen in order to to be an effective oxygen transporter
  • The binding isotherm for hemoglobin (left, red) resembles a sigmoid binding curve; a characteristic of an allosteric system with positive cooperativity and is essential for the proper delivery of oxygen

  
• The first oxygen to bind to hemoglobin does so with difficulty, but this

  initial binding event triggers a conformational change such that the three remaining binding sites are switched to a conformation that has much higher affinity for oxygen. This conformation is called the “relaxed” or R state of the system (circles). It is this switch in binding affinity that allows hemoglobin to pick up oxygen with high affinity in the lungs, but

  then release it with ease in the tissues

  
• Positive cooperativity in a dimeric protein

  A) T

  B) R

  C) low

  D) high

  
• Hill coefficient

  The Hill coefficient (nH) reflects the steepness of the log-log binding isotherm at the point when the protein is half saturated with ligand. A non-cooperative system has a Hill coefficient of one (i.e. nH = 1). Systems exhibiting positive and negative cooperativity have Hill coefficients that are greater than one, and less than one, respectively

  
• The Hill coefficient (nH) for a simple dimeric protein is defined by:

  A) 2

  B) 1

  C) KD2

  D) KD1

  E) tense

  F) relaxed

  G) binding sites

  
• The reaction order is the number of molecules that must “collide” with one another to make the reaction occur
• Where “k” is a kinetic rate constant which reflects how likely the particular chemical reaction will occur, regardless of the concentration of reactants. The overall rate of a reaction always has units of concentration per unit time (i.e. M·s-1 or the number of moles of product produced per liter, per second)

  A) 1

  B) 2

  C) 3
• Reaction rate

  A) s-1

  B) m-1s-1

  C) m-2s-1

  
• All reactions are bidirectional

  1. The order of the forward and reverse reactions, and their associated rate constants (“k+3” and “k-3”), can be different (as above)
  2. For both the forward and reverse reactions the overall reaction Rate is directly proportional to the rate constant for the reaction, irrespective of the order
  3. At equilibrium, the Rate of the forward (“Rate f”) and reverse (“Rate r”) reactions is the same (i.e. equal). This is useful to remember, because these rate equations can be used to derive expressions for the equilibrium constant (“Keq”) for the reaction (see next slide)

  
• All reactions are bidirectional

  A) f

  B) r

  C) +

  D) -

  E) Keq

  
• All chemical reactions go through a “transition state” (X‡), the highest energy species in the path between reactants and products. The transition state is...

  • ...unstable - it exists only transiently (i.e. for a very short time!).
  • ...the “activation energy” (or “EA”) barrier between reactants and products, and the height of this energy barrier dictates how fast a reaction will occur (i.e. relates to the rate constant, k, of the reaction)

  Enzymes can enhance reaction rates by lowering this “activation energy” barrier(known as “Transition State Stabilization”).

  
• A Reaction Coordinate diagram is a plot of the Gibbs free energy (G) vs. the “reaction coordinate” or reaction path. The energy between the reactants and products is referred to as “∆Grxn”. The activation energy (EA) is the energy between reactants (or products) and the transition state (X‡), and is referred to as “EA forward (EAf)” (or “EA reverse (EAr)”).

  
• ∆G rxn = −RT ln (Keq)
• Kinetics refers to the rates at which a reaction approaches equilibrium. The forward rate constant, k for (or k+3 in our example), is related to EA forward (EAf), which is the energy difference between the reactants and transition state. The larger the activation energy (EA), the slower the reaction. The rate constant, krev (or k-3 in our example) is related to EA

  reverse (EAr).

  
• Arrhenius equation

  A) f

  B) r

  
• Catalysts can increase the rate of a reaction by...

  1. decreasing EA (activation energy)
  2. increasing “A”, the “preexponential factor”
  3. fundamentally altering the reaction mechanism
• The “preexponential factor”, A, reflects a combination of the rates of collisions (kcollision) and the fraction of these that are productive (i.e. “fp”; in the correct orientation to actually react). A catalyst can increase the rate of collisions, or can cause more collisions to occur in a productive orientation by interacting with the reactants

  
• Enzyme catalyzed reactions have three phases

  1. Phase 1: Time approximates zero (“initial phase”). There is a high [Substrate] and no product. The initial rate of the reaction depends only on the [Enzyme] and [Substrate]
  2. Phase 2: At a later time, there is less substrate (as it has been consumed) and now some product, so we start to see the reverse reaction occurring, and thus the overall rate of formation of product slows down
  3. Phase 3: At infinity (∞), the rates of the forward and reverse reactions are equivalent. The overall reaction rate is zero and the reaction is at equilibrium

  
• When studying enzymatic mechanisms we focus on only the first of the three phases (i.e. Phase 1). The initial rate of product formation, or “initial velocity” (ν0), describes the reaction rate in the absence of product (i.e. no reverse reaction), so it is directly related to kfor, and thus the catalytic ability of the enzyme
• Adrian Brown assumed that the enzyme binds the substrate

  -> Brown proposed that for catalysis to occur, the enzyme (E) rapidly binds the substrate (S) to form what we now call a “Michaelis complex”, or “ES”, and then the ES goes through a transition state, ES‡, before decomposing to free enzyme and product (P)
• Both assumptions lead to similar equations. The pioneering work of Michaelis & Menten led to both derivations - this is why the steady-state assumption leads to an equation typically referred to as the Michaelis-Menten equation - even though it was not derived by Michaelis & Menten

  
• Serine proteases:

  • Cleave / hydrolyze peptide bonds
  • Impart specificity to where in a polypeptide sequence the cleavage occurs
  • All have a conserved set of three residues (Ser - His - Asp), which form a motif known as the catalytic triad
• In a catalytic triad, a charge relay system depresses the pKa of the serine hydroxyl, making it more acidic, and thus the oxygen a better nucleophile
• In serine proteases, the bond we want to break is the scissile bond
• Serine proteases: mechanism of peptide bond cleavage STEP 1

  • The side chain oxygen of Ser195 performs a nphilic attack on the amide carbonyl of the scissile bond
  • Leads to an unstable tetrahedral intermediate (trans state 1), where the config of the carbonyl of the peptide bond switches from sp2 to sp3, leaving a neg charge on an oxygen (now an oxyanion)
  • Acyl-enzyme intermediate: The proton associated with the serine hydroxyl moves to the amide and break our scissile bond, releasing the C-term segment of the peptide substrate, leaving the N-term segment covalently bonded to the enzyme