Craven Flashcards
What is the equation for a unimolecular irreversible reaction?
k
A —–> B
In a unimolecular irreversible system, why do molecules last in state A for diff amounts of time?
- undergo diff collisions
- stochastic process
In a unimolecular irreversible system, what is the average amount of time spent in A?
- DIAG*
- 1 / k
In a unimolecular irreversible system what is the rate of change of no. molecules in state A?
- -kNA
- where NA = no. molecules in state A
In a unimolecular irreversible system what is the rate of change of [A]?
- -k[A]
What order is the rate constant in a unimolecular irreversible system?
- 1st order
What is the numerical solution of rate equation, for unimolecular irreversible systems?
- set of values of [A] at set of times for particular values (discrete)
Why is the numerical solution always slightly approx compared to analytical solution, and how can it be made more accurate?
- assumes ROC of [A] constant during whole timestep
- use smaller timestep
What is the analytical solution of the rate equation for unimolecular irreversible systems, and how is it calc?
- works out equation for [A] as function of time
- [A] = [A]0e^-kt
What are the advantages of the analytical solution of the rate equation, for unimolecular irreversible systems?
- works for any [A]0, k and t
- exact
What are the disadvantages of the analytical solution of the rate equation, for unimolecular irreversible systems?
- need to know lots of maths
- only poss to find in simple cases
What are the advantages of the numerical solution of the rate equation, for unimolecular irreversible systems?
- maths easy
- totally general, can apply to v complex biological models
What is the disadvantage of the numerical solution, for unimolecular irreversible systems?
- slightly approx
What is the [A] at t=0, and why?
- [A] = [A]0e^kx0
- ∴ [A] = [A]0
What is the [A] if let t become v big?
- kt v big
- e^kt v big
- so e^-kt = 0
- [A] = 0 (all A used up)
How is half life calc?
- 0.693/k
How can [B] be calc in terms of [A]?
- [B] = [A]0 - [A]0e^-kt
- [B] = [A]0 (1-e^-kt)
What is the equation for a biomolecular irreversible reaction?
k
- A + B —–> C
What order is the rate constant in a biomolecular irreversible system?
- 2nd order
In a biomolecular irreversible system, what is the average time spent in A?
- 1 / k[B]
In a biomolecular irreversible system, how does [A] relate to [B]?
- from perspective of A, rate of making collisions w/ B is dep on [B]
- in ideal solution rate directly proportional to to [B]
In a biomolecular irreversible system, how is the rate of change of [C] calc?
- k[A][B]
What is the diffusion controlled limit in biomolecular irreversible systems?
- typically most collisions unsuccessful, but collision can occur straight away
- if [B] = 1mM, time for collision ≈1μs
- av time = 1 / k[B]
- so 1μs = 1 / k x 1m
10^-6s = 1 / k x 10^3M
k = 10^9M^-1s^-1 - approx largest value of 2nd order rate constant, so reaction can’t go faster than this
- but k generally a lot smaller
Why are calcs of reaction time courses much more complex for biomolecular irreversible system than unimolecular?
- likelihood of A reacting (in next moment of time) changes as B used up
- or opp true
When and why can biomolecular irreversible systems have a pseudo 1st order rate constant?
- when [B]0»_space; [A]0
- eg. [A]0 = 1μm and [B]0 = 1000μm
- after long time A –> 0 and B –> 999μm
- conc of B only drops small fraction, so can be treat as constant
- k[B] = k’
- so rate of change of A = -k’[A]
- [A] = [A]0e^-k’t
What is the equation for a unimolecular reversible reaction?
k1
- A ⇌ B
k-1
In a unimolecular reversible system, what is the average time a molecule spends in state A and B?
- A = 1 / k1
- B = 1 / k-1
What is a single molecule time course for a unimolecular reversible system?
- DIAG*
- stochastic process
How is the eq constant, K calc for a unimolecular reversible system?
- K = time spent in B / time spent in A
= k1 / k-1
- at any 1 moment in time
K = no. molecules in B / no. molecules in A
= k1 / k-1
= [B]eq / [A]eqIn a unimolecular reversible system, how are the rates of A–>B and B–>A calc?
- A –> B = k1 x NA
- B –> A = k-1 x NB
How does K allow us to calc [A] and [B] at eq as a ratio and a fraction?
- [A]eq : [B]eq
1 : K
1 / 1+K : K / 1+K - [A]eq = (1 / 1+K) x total conc A
- [B]eq = (K / 1+K) x total conc B
Which way up is K defined in A ⇌ B?
- conventionally K = [RHS]eq / [LHS]eq = [B]eq / [A]eq
- but poss to define K as [A]eq / [B]eq and get reciprocal value
- so always define which way up you calc K as
What is the equation for a biomolecular reversible reaction?
k1
- A + B ⇌ AB
k-1
How are biomolecular reversible systems v important to mol bio?
- drug based medicine
- receptors
- TFs
- enz + substrate/inhibitor
- protein 1 + protein 2 ⇌ complex
How can biomolecular reversible systems be quantified?
- assess how strong interaction is –> mutate residue and see how strength of interaction changes or mod drug molecules
- predict whether 2 molecules will bind significantly under conditions of known total concs of basic constituents
What order are the rate constants in a biomolecular reversible system?
- k1 (kon) is 2nd order
- k-1 (koff) is 1st order
What is KD and what kind of units does it have?
- dissoc constant
- units of conc
What can be defined as an alt to KD, and how is it calc?
- KA (assoc constant) = reciprocal of KD
- KA = [AB]eq / [A]eq[B]eq
= k1 / k-1
How is rate of AB formation in a biomolecular reversible system calc?
- k1[A][B]
How rate of loss of AB in a biomolecular reversible system calc?
- k-1[AB]
How is KD calc?
- at eq k1[A]eq[B]eq = k-1[AB]eq
- ∴ KD = [A]eq[B]eq / [AB]eq
= k-1 / k1
How does [B] affect behaviour of a single molecule in a biomolecular reversible system?
- DIAG*
- low [B] means spends more time in A than AB
- higher [B] means time in A shorter, but time in AB same on av
- at saturated level of B, time in A only visible as vertical lines
For higher affinity (favour binding), what value should KD and its components have?
- small KD
- small k-1 (koff) / big k1 (kon)
How can KD be measured simply?
- measure when all A in free state, fluorescence = 250
- measure when all A bound as AB, fluorescence = 100 (A bound to B doesn’t fluoresce as well)
- then measure amount of B need to add to get to fluorescence of 175 (50 + 125) –> when half A free and half bound as AB
How can it be useful to rearrange [AB]eq / [A]eq[B]eq = 1 / KD?
- [AB]eq / [A]eq = [B]eq / KD
What is the rate equation for P + L ⇌ PL?
- [PL]eq / [P]eq = [L[eq / KD
How can it be shown that if conc of free ligand is equal to KD, then half receptor molecules will be bound?
- if [L]eq = KD, then [PL]eq / [P]eq = 1
∴ [PL]eq = [P]eq
∴ 50% bound
In a biomolecular reversible system, if [P]tot «_space;KD, then how can the fraction of ligand bound be calc?
- then [L] ≈ [L]tot
- fraction bound = [L]tot / [L]tot + KD
In a biomolecular reversible system, if we assume [P]tot «_space;KD and know [P] ≤ [P]tot, what can we calc about KD?
- ∴ [P] «_space;KD
- ∴ [PL] / [L] = [P] / KD = <
In a biomolecular reversible system, how can you generalise formula for fraction of P bound, given values of [L]tot and KD - as ratios and fractions?
- as ratios –> [PL] : [P]
[L] : KD - as fractions –> [L] / [L] + KD
–> KD / [L] + KD
What is the equation for a simple enzyme reaction?
k1 k2
- E + S ⇌ ES —-> E + P
k-1
What order are the rate constants in a simple enzyme system?
- k1 is 2nd order
- k-1 and k2 are 1st order
Why can’t you talk about 1st and 2nd order rate constants together?
- completely diff units
For a simple enzyme system what would the time course of a single molecule look like if k-1»_space; k2, and what would be the times spent in E and ES?
- DIAG*
- av time in E = 1 / k1 [S]
- av sum of time in ES = 1 / k2
For a simple enzyme system, how does the time course of a single molecule change if [S] is increased?
- DIAG*
- av time in E less
- so product released after shorter time periods
For a simple enzyme system, how does the time course for a single molecule change if [S] is v v high, so never waiting for S?
- DIAG*
- product released after v short periods of time
- ≈ 1 / k2
What does the Michaelis-Menten equation tell us?
- how rapidly product will be formed for given substrate conc
In a simple enzyme system, if Stot»_space; Etot and k2 = 0, then how can [ES] be calc?
- no ES –> E + P occurring
- so at eq KD = k-1/k1 = [E]eq[S]eq / [ES]eq
- ∴ [ES] = Etot x [S] / [S] + KD
How will [ES] change if k2 «_space;k-1 (instead of k2 = 0)?
- barely alters [ES}
- ES –> E + P is 1st order unimolecular so ROF of product = k2[ES]
= k2 (Etot[S] / [S] + KD)
What is the Michaelis-Menten equation, and how is this derived from the case when k2 «_space;k-1?
- rate of P formation = kcat x Etot x [S] / [S] + Km
- if k2 «_space;k-1, then k2 = kcat and KD = Km
What is kcat?
- max rate enzyme can form product if never waiting for substrate
What is Vmax?
- in a particular case (cell, experiment) the total rate of reaction = kcat x Etot
- this is often called Vmax, ie. fastest rate of production of P
How do kcat and Vmax differ?
- kcat is a fundamental property of particular enzyme
- Vmax is specific to particular case or experiment
What does Km tell us?
- parameter that tells us how high [S] needs to be to get supply of substrate to each enzyme molecule sufficiently high
What does it mean if [S] = Km?
- enzyme molecules “idle” half the time
What does it mean if [S]»_space; Km?
- enzyme molecules able to be loaded w/ substrate all the time
What is the effect on [ES] if k2 NOT «_space;k-1?
- S in principle changing v slowly = steady state
- ie. if pu in more S to maintain its value, then stays constant, so ES stays constant
At steady state what is the rate of ES formation?
- k1[E][S]
At steady state what is the rate of ES loss?
- k-1[ES] + k2[ES]
= (k-1 + k2) [ES]
At steady state how do rate of ES formation and loss relate, and what does this mean for KD?
- they are equal
- ie. k1[E][S] = (k-1 + k2) [ES]
- ∴ [E][S] / [ES] = k-1 + k2 / k1 = Km
- [E][S] / [ES] also = k-1 / k1 = KD
∴ Km equivalent to KD
How does [S], [E], [ES] and [P] change over a reaction?
- DIAG*
- when rof of P = 0, is pre steady state
- initial drop in [S] as ES formed, then decreases at same rate as [P] increases
- after steady state, as S used up, ES will drop and E will rise
In a metabolic pathway, how are ideas of flux and steady state transfer important?
- allow calc of formation/loss of compounds
- ie. values coming in must equal those going out
- eg. 10 5
W ⇌ X ⇌ Y
7 ?
? = (7+5) - 10 = 2
What is the problem w/ representing a simple enzyme as E + S ⇌ ES –> E + P, and how can it be imporved?
- implies P falls off immediately after reaction occurs, but P likely to be close chemical derivative of S, so likely to bind E fairly well
∴ E + S ⇌ ES –> EP –> E + P - but P –> S also cat by active site, so EP –> ES may be signif
∴ E + S ⇌ ES ⇌ EP –> E + P - if [P] becomes too high have to inc rebinding of P
∴ k1 k2 k3
E + S ⇌ ES ⇌ EP ⇌ E + P
k-1 k-2 k-3
Is it easy to look at steady state kinetics?
- at steady state all systems obey Michaelis-Menten
- but kcat and Km will be complicated combo of rate constants
What is pre steady state kinetics?
- looking at early stages after mixing to try to unpick diff systems
In what instances can binding alter behaviour of molecules?
- how strongly can bind another molecule
- how effective they are as enzymes
- how open they are as enzymes
- how open they are as ion channels
- how strong signal they relay is as receptors
When might enzymes bind more than 1 molecule?
- inhibition
- enz that binds 2 substates (eg. kinase binds ATP and protein substrate)
- Hb (binds 4xO)
- ligand gated ion channels can be, eg. pentameric and bind 5 ligands
What concepts does binding of more than 1 diff ligand bring in?
- independence
- cooperativity (+ve or -ve)
- competition
- mutually exclusive binding (eg. comp inhibitor)
- allostery
- orthostery
What concepts does binding of more than 1 of same ligand bring in?
- cooperativity
- hill coefficient (Hb)
- “sharp switching” (eg. ion channels)
- allostery (as mechanism for cooperativity
What kind of direct ligand interaction takes place if 2 sites distant and binding 1 ligand doesn’t affect other site?
- DIAG*
- independent
What kind of direct ligand interactions can take place if 2 sites close and binding 1 ligand doesn’t affect other site?
- DIAG*
- if no particular clash between ligands = independent
- if favourable interaction, eg. charge-charge interaction = +vely cooperative
- if unfavourable interaction, eg. charge-charge repulsion = -vely cooperative
What kind of direct ligand interaction takes place if both ligands bind site and no poss of simultaneous occupation of site?
- DIAG*
- mutually exclusive (=competitive)
What is the problem w/ representing proteins as solid when looking at binding of ligands?
- they are dynamic and flex
- binding 1 site may affect other site even w/o direct interaction between ligands –> allosteric conformational change
What are orthosteric and allosteric sites?
- orthosteric = where substrate or main receptor ligand binds
- allosteric = where some 2nd ligand binds
- not fixed terms, like in P + L, ligand could be protein (not always clear distinction)
How does +ve cooperativity happen via allosteric conformational change of protein?
- DIAG*
- when one ligand bound, changes in both binding sites occur and that ligands binding site it drawn “closer to optimal” and other site “looks better”
- when both bind, further improvements in binding sites occur
How does value of KD change if 2 ligands are +vely cooperative?
- KD lower when binding site of other ligand occupied, as can bind to protein better
How does the value of KD change if 2 ligands bind protein independently?
- same as if only 1 ligand present
How does value of KD change if 2 ligands are -vely cooperative?
- KD higher when binding site of other ligand occupied, as can’t bind protein as well
How does value of KD change if 2 ligands are competitive, and how could this be overcome?
- v v high KD
- if put enough of other ligand in
If binding of 1 ligand improves binding of other, is the opp true?
- yes, symmetrical
- must alt KD by same factor
- also true of -ve cooperativity
What is the binding curve for Hb and Mb?
- DIAG*
- Mb like normal binding curve
- Hb curve is a sigmoid
What is the role of Hb and Mb?
- Hb is oxygen carrier in blood
- Mb is oxgen carrier in muscles
What is the mol reason for the behaviour of Hb (sigmoidal shape)?
- “unit” of Hb can bind 4 molecules of O
- binding not indep
- binding +vely cooperative
How can binding of molecules affect each other in a system where protein can bind 2 molecules of same ligand, and what are the effects on KD?
- DIAG*
- independent = binding as good whether or not site occupied, same KD applies whether or not other site occupied
- +ve cooperativity = binding stronger if other site occupied (allosteric effect), KD smaller for binding when 2nd site full
Why does +ve cooperativity make the binding curve sigmoidal?
- DIAG*
- at low conc of 1 ligand, other site likely empty
- at high conc of 1 ligand, other site likely full
- curve between those for if 2nd site always empty and if 2nd site always full
In Hb how does binding of molecules affect strength of other molecules binding, and what is the effect on KD?
- binds 4 molecules much better than 1/2/3
- KD only decreased when all 4 bind
What is the Hill equation, and when does it apply?
- for systems capable of binding Nsites molecules of ligand
- av no. sites bound = Nsites x ( [L] / [L]^nh x [KD]^nh
What is the value of nh when there is indep binding and for v extreme +ve cooperativity?
- indep = 1
- +ve cooperativity = Nsites (data exactly follows Hill equation)
What curve do real systems w/ +ve cooperativity typically have for the Hill equation?
- approx Hill form, w/ nh somewhere between 1 and Nsites
What is the Hill equation useful for?
- good way to approx characterise binding curve showing sign s of +ve cooperativity
- as full analysis would need consideration of all indiv KDs, but most data wouldn’t be precise enough to trust this detailed analysis
How does binding curve vary for diff values of Hill coefficient?
- higher = sharper switching
* DIAG*
How can binding curve for Hb and Mb be explained in muscle capillaries?
- Hb has low affinity for O at low concs of external O
- so O dissociates easily at low ambient O
- does not happen in case of Mb, so Mb will bind O released from Hb
How can binding curve for Hb and Mb be explained in the lungs?
- Hb has high affinity for O at high concs of external O
- so O will bind easily at high ambient O
How can competitive inhibition be overcome?
- if make conc of substrate high enough, can have virtually all sites full at any 1 moment
- so regain full maximal rate
What is Ki (inhibition constant), and when does it apply?
- dissoc constant for binding of inhibitor in absence of substrate
- applies in competitive an allosteric case
How does competitive inhibition affect Km and kcat?
- Km increases
- kcat unchanged
In an enzyme catalysed reaction how does response (rate of observed reaction) relate to the fraction of E sites which are filled at any 1 time?
- directly prop (linear)
How can allosteric inhibition cause an inhibitory response in enzyme?
- DIAG*
- S binding site diff when I site occupied
- enz may hold onto sub worse when I occupied
- enz may take longer to achieve chem reaction when I site occupied
How can allosteric inhibition cause an activatory response in enzyme?
- DIAG*
- debatable whether this should be labelled as inhibitor
- S binding site diff when I site occupied
- enz may hold onto sub better when I occupied
- enz may take less time to achieve chem reaction when I site occupied
What ligands can a receptor bind?
- binds ligand that nature intended to set off signal (orthosteric/endogenous agonist)
- another ligand can compete for same binding site or bind at diff site (enhance/inhibit activity)
In a receptor what is ligand conc related to?
- signalling related to ligand conc
- fractional occupancy at receptor related to ligand conc
In what way is the response in a cell complex for receptor-ligand interactions?
- cellular response may or may not be directly prop to fraction of receptor sites filled
- for some responses, as long as few filled then signalling will occur, and after certain point increasing no. won’t make any diff to signalling strength
- alt if binding has to stop a signal firing, then need virtually all filled
What parallels can be drawn between receptor binding and enzyme cat reactions?
- strongest parallel is for concepts of occupancy
- for concept of response, receptors in cellular contexts lead to more complex ideas –> still somewhat loosely relate response to occupancy
How can antagonists affect agonists in receptor binding?
- may alt binding of endogenous agonist
- may alt signalling ability of endogenous agonist
- might compete for same site as endogenous agonist
