Enzyme kinetics – Definition

• Study of rates of catalytic reactions involving substrates and enzymes

ENZYMATIC REACTION VARIABLES

Substrate (S)

• Substance that enzyme modifies
• Typically the controlled variable

Velocity (V)

• Rate of product formation; typically the measured variable

Maximum velocity (Vmax)

• Reached when every enzyme’s active site is bound by a substrate
• Determined experimentally (reactions do not typically reach Vmax)

Reaction constant (Km)

• Substrate concentration corresponding to 1/2 of maximum velocity
• Determined experimentally
• Determines binding affinity of enzyme to substrate

MICHAELIS-MENTEN MODEL

• Examines reaction of single substrate w/ single enzyme to create product.

Assumptions

• No intermediates
• No product inhibition
• No allostericity or cooperativity
• Total enzyme concentration is constant (and [S] >>> [E])
• Pseudo-steady-state hypothesis: rate of [ES] formation = rate of [ES] breakdown
• Initial velocity (rate measured as soon as substrate/enzyme are mixed)

First-order kinetics

• Change in [S] changes velocity of rxn

Zero-order kinetics

• Change in [S] does NOT change velocity of rxn

Vmax

• Asymptotic: rxn rate approaches Vmax, never actually reaches it

Km

• Estimates enzyme binding affinity
• High affinity = requires a low [S] to reach 1/2 Vmax

LINEWEAVER-BURK MODELS

• Uses inverse of variables in Michaelis-Menten model to represent graph as straight line

1/Vmax

• Y-intercept: x = zero.

1/Km

• X-intercept: y=0

FACTORS THAT AFFECT REACTION VELOCITY

• Increasing temperature: increases reaction velocity until denaturation
• Change in pH: can denature enzymes –> loss of function –> ionization of amino acids (changes active site conformation
• [E] and [S] substrate affect reaction velocity

ACTIVE TRANSPORT

• Movement of solutes against their electrochemical gradients
• Extracellular space is positively charged
• Intracellular space is negatively charged
• Requires energy to overcome solute’s gradient
• Facilitated by transporters NOT channel proteins

ATP DRIVEN PUMPS

Primary Active Transport

ATP hydrolysis fuels transport

Sodium-potassium pump

• Na+ electrochemical gradient: large and directed into cell
• K+ electrochemical gradient: small (chemical and electrical gradients oppose each other) and directed out of the cell
• Pumps K+ and Na+ against their gradients
• Hydrolyzes ATP (account for 30% of animal cell’s ATP consumption)

Coupled transporters

Couple movement of one solute against its gradient with movement of another solute down its gradient

Light-driven pumps

Occur in bacteria and couple active transport with light energy

COUPLED TRANSPORT

Secondary Active Transport

(Does not directly require ATP)

Glucose-sodium symport protein

• Apical surface of intestinal epithelial cell
• [Glucose] greater in cytosol
• [Na+] greater in extracellular space
• Transports glucose and sodium into cell
• Electrochemical gradient of sodium drives transport of glucose against its own gradient
• Cell can absorb glucose from the intestines even when intracellular glucose is high

Sodium-calcium antiporter

• Surface of a cardiac muscle cell
• [Ca2+] greater in extracellular space
• Couples movement of Na+ down an electrochemical gradient with the movement of Ca2+ against its gradient and out of the cell
• Influx of Ca2+ triggers a contraction and antiporter restores gradient for next contraction

CLINICAL CORRELATION
Digoxin: disrupts Ca2+ gradient to increase force of cardiac cell contraction

• Inhibits sodium-potassium pump, which increases intracellular Na+
• Sodium-calcium antiporter cannot function: intracellular Ca2+ increases and produces stronger contractions

PASSIVE TRANSPORT

• Requires no energy input because all molecules still move down their concentration gradient
• All channels and many transporters work via passive transport

CHANNELS

• Somewhat specific, only allowing a molecule through if it is the right size and charge
• Allow for faster transport than transporters or diffusion
• Some channels require a signal before solutes can travel through
• Aquaporins are an example of channels – increase the rate of water travel

TRANSPORTERS

• Also called carrier proteins
• Very specific for the molecules that they transport
• Transporters can reverse direction if the concentration gradient flips
• Glucose transporter is an example

ELECTROCHEMICAL GRADIENT

• Concentration gradient is important for movement of molecules, but voltage difference between the two sides of the membrane can also play a role

Electrochemical gradient

Combined force due to the membrane voltage and concentration gradient

Electrochemical gradient when molecules are non-charged

• Movement based on concentration gradient ONLY, voltage difference plays no role

Electrochemical gradient when molecules are charged and voltage and concentration gradient work together

• Larger electrochemical gradient when voltage and concentration gradient work in the same direction

Electrochemical gradient when molecules are charged and voltage and concentration gradient oppose one another

• Smaller electrochemical gradient when voltage and concentration work in opposite directions

Osmosis:

The diffusion of water across a semi-permeable membrane due to differences in solute concentrations

A way to think about it…

Let’s imagine a way to think about the direction of water movement. You have two glasses filled with marbles but one is filled with a lot more marbles than the other. If you added water to both glasses to reach a certain height, then the glass with more marbles would require less water to reach the height. There is a lower concentration of water in this glass than the other glass.

However, if the two glasses were connected by a semi-permeable membrane, osmosis would cause water to flow from the glass of high water concentration to the glass with low water concentration. It is important to note that this is not the actual mechanism of osmosis, just an easy way to think about it.

OSMOLARITY

Osmolarity (osmotic concentration)

• Measure of solute concentration (osmoles of solute per liter)

Ionic compounds

• Often dissociate in solution (NaCl becomes Na+ and Cl-)
• 2 moles of NaCl therefore become 4 osmoles of solute (2 Na+ and 2 Cl-)

Nonionic compounds

• Don’t dissociate in solution
• 2 moles of glucose therefore become 2 osmoles of solute

SEMI-PERMEABLE NATURE OF CELLULAR MEMBRANES

Isotonic solution

• Solution has same solute concentration as the inside of the cell

Hypertonic solution

• Solution has greater solute concentration than the inside of the cell

Hypotonic solution

• Solution has less solute concentration than the inside of the cell

If a red blood cell is placed in a:

• Isotonic solution – water freely diffuses in and out of the cell at equilibrium
• Hypertonic solution – water diffuses out of the cell and the cell shrivels up
• Hypotonic solution – water diffuses into the cell and the cell lyses

This concept, along with the concept of osmosis and osmolarity is important when discussing movement of molecules across a cell membrane.

• Diffusion is the tendency of a substance to spread out evenly in the available space: from an area of high concentration to an area of low concentration.
• A solution has one or more substances (solutes) dissolved in another substance (solvent).

Diffusion in Action

To visualize diffusion, imagine a glass of water to which a drop of food coloring is added. Notice how the color spreads out from the point the drop hits the water. This is diffusion of the food coloring molecules.

Diffusion Experiment, # 1

• We will start with the diffusion of one solute.
• We draw three boxes and indicate that they are filled with water.
• In each box, we draw a membrane with pores vertically down the middle.
• In the leftmost box, we draw small solute molecules entirely on the left side of the membrane.
• They move randomly: some of them make it through the pores and some bounce back.
• The net movement of solute molecules is toward the right side of the box (i.e. to the area of low concentration).
• In the middle box, we draw a couple solute molecules on the right and the majority on the left.
• Random movement continues, with some molecules on each side making it through the pores and others bouncing back.
• The net movement of solute molecules is still towards the right.
• In the final box, we draw equal amounts of solute on both sides.
• Random movement continues, but note that anytime a solute molecule passes through a pore, a molecule from the other side also passes through: this situation is equilibrium; here, there is no net movement of molecules from one side to the other.

Diffusion Experiment, # 2

• The rate of diffusion of two or more solutes is independent of each other.
• Now, we explore diffusion when two or more solutes are present in a solution.
• We draw three boxes filled with water.
• We draw a membrane with pores vertically down the middle of each box.
• In the leftmost box, we draw a few of one type of solute molecule (Solute A) on the left side and more of another type of solute molecule (Solute B) on the right side.
• We indicate the random motion of these molecules with some able to make it through the pores in both directions and others bouncing back.
• We indicate that the net movement of Solute A is to the right and the net movement of Solute B is to the left.
• In the middle box, we draw equal numbers of Solute A molecules on either side of the membrane and draw a few Solute B molecules on the left side of the membrane.
• Random movement continues, though now equal numbers of Solute A molecules pass back and forth across the membrane while more Solute B molecules are passing to the left than are passing to the right.
• Solute A has reached equilibrium while the net movement of Solute B is still toward the left.
• In the final box, we draw equal amounts of Solute A on both sides of the membrane and equal amounts of Solute B on both sides of the membrane: both solutes have now reached equilibrium.

The rate at which Solute A reaches equilibrium is the same no matter if Solute B is present or not, thus…

• The rate of diffusion of two or more solutes is independent of each other.

CELL MEMBRANE

• Separates intracellular and extracellular environments
• Regulates import and export of molecules
• Lipid bilayer

SIMPLE DIFFUSION
Molecules diffuse across the cell membrane

Rate of diffusion is determined by:

• Size: smaller molecules diffuse across faster than large ones
• Polarity: the less polar, the faster it diffuses across the membrane
• Charged molecules: do not diffuse across hydrophobic interior

Types of molecules

• Nonpolar molecules: hydrophobic, diffuse rapidly
  i.e. oxygen, carbon dioxide, nitrogen and steroid hormones
• Small, uncharged polar molecules: diffuse across
  i.e. water, glycerol and ethanol
• Large, uncharged polar molecules: do NOT diffuse across
  i.e. amino acids, glucose and nucleosides
• ions (charged molecules): cannot diffuse across
  ie. Hydrogen, sodium, potassium, calcium and chloride ions

MEMBRANE TRANSPORT PROTEINS
Allow molecules to cross the membrane faster and more efficiently than simple diffusion
i. Channels: form open pores in the membrane
ii. Transporters: undergo conformational changes during transport

• Solute binds solute binding site
• Binding produces conformational change in protein
• Solute leaves transporter (release facilitated by conformational change)

TWO TYPES OF TRANSPORT ACROSS MEMBRANES

Passive transport

• Molecules move down their electrochemical gradient
• No energy is required

Active transport

• Molecules move against their concentration gradient
• Energy is required

ELECTROCHEMICAL GRADIENT
Accounts for voltage across the membrane (electro-) and concentration gradient (chemical)

MEMBRANE LIPID MOVEMENT

• Rotate
• Drift laterally
• Do NOT flip

MEMBRANE FLUIDITY DETERMINANTS

1. Lipid structure

• Degree of overlap
• Tail length
• Double bonds

2. Temperature

• Transition temperature (Tm) determined by membrane composition
• Membrane phase changes as physiologic temp. fluctuate about Tm

3. Cholesterol

• Temperature buffer that resists changed in fluidity

MEMBRANE PHASES

1. Gel-like

• Little overlap of phospholipid tails
• Longer/saturated tails
• Higher Tm
• No cholesterol

2. Liquid ordered

• Physiologic temperature ~ membrane Tm
• Cholesterol present
• An intermediate phase and most common physiologically

3. Liquid disordered

• Tails overlap
• Shorter/unsaturated tails
• Lower Tm
• No cholesterol

FREEZE-FRACTURE METHOD

• Freeze cell and fracture it along cell membrane’s hydrophobic interior
• Proteins associate with either layer after fracturing
• More proteins associate with cytosolic layer

INTEGRAL PROTEINS

• Embedded in the bilayer

Transmembrane proteins: amphipathic, pass through both membrane layers

• Single pass or multi-pass
• Alpha helices: hydrophobic side chains
• Beta barrel: multi stranded beta sheet (i.e. porin proteins)

Monolayer associated

• Alpha helix
• Lipid-linked

PERIPHERAL PROTEINS

• Do not extend into the bilayer
• Protein-attached: non-covalently bound to transmembrane protein
• Oligosaccharide-attached: bound to carbohydrate head group of glycolipid

Glycocalyx

• Oligosaccharide side chains and glycolipids form carbohydrate coat on external surface of cell

MEMBRANE PROTEIN FLUIDITY

1. Fuse mouse and human cells with surface marker proteins
2. Marker proteins mix on hybrid cell surface

• Conclusion: membrane proteins are fluid

MEMBRANE PROTEIN FUNCTIONS

• Transport ions, nutrients and other substances across membrane
• Anchor cells to each other, to extracellular matrix or basement membrane
• Transduce external signals to inside of cell
• Mediate cell-cell recognition of glycoproteins on adjacent cell surfaces
• Enzymatically catalyze metabolic pathways

• Transduce chemical signals into electrical signals
• Allow for rapid response
• Important for electrically excitable cells such as nerves or muscles

Function

1. Channel protein in closed conformation so ions cannot pass
2. Ligand binds to ligand binding site
3. Channel protein changes to open conformation so ions can now pass and cause a cellular response
4. Ligand leaves
5. Channel changes back to closed conformation and ions can no longer pass

Role of Ligand-gated Ion Channel in Synaptic Transmission

1. Action potential travels down presynaptic axon
2. Cargo vesicle fuses with presynaptic plasma membrane and releases neurotransmitters
3. Neurotransmitters (ligands) bind to ligand-gated ion channel in postsynaptic cell membrane opening the channel
4. When enough ions pass into the postsynaptic cell, voltage-gated ion channels open
5. More ions pass through these channels, further changing the membrane voltage and opening voltage-gated channels further along the membrane
6. This depolarization (action potential) travels along the membrane to the next synapse continuing the signal transmission

Types of Ligand-gated Ion Channels

Excitatory

• Na+ channels – allow positive ions into the cell depolarizing the membrane and driving it closer to firing an action potential

Inhibitory

• Cl- channels – allow negative ions into the cell making it harder for the membrane to depolarize
• K+ channels – allow positive ions out of the cell making it harder for the membrane to depolarize

• Transduce signals into electrical signals
• Allow for rapid response

3 TYPES

1) Ligand-gated Ion Channels

• Specific ligand is required for each channel
• Ligand binds to ligand binding site on channel
• Channel opens allowing ions to pass through
• When ligand dissociates, channel closes

2) Mechanically-gated Ion Channels

• Physical (i.e., stretching) forces on the membrane or channels are what open the channels and allow the ions to traverse the membrane

3) Voltage-gated Ion Channels

Sodium & Potassium Channels

a) Sodium Channel

• Change in membrane potential opens the channel – activation gates change to the open conformation and sodium can traverse the membrane
• Channel becomes inactivated – Inactivation gate “plugs” the channel and sodium cannot travel through the membrane
• Channel eventually resets back to closed conformation

b) Potassium channel

• Change in membrane potential opens the channel – activation gates change to the open conformation and potassium can traverse the membrane
• Channel eventually resets back to closed conformation