Computational Biology

(BIOSC 1540)

Oct 29, 2024

Lecture 16:
Structure-based drug design

Announcements

  • A06 is due Thursday by 11:59 pm
    • Reminder: There is a (soft) limit of 100 words for each question
  • A07 (final assignment) will be released Friday
  • No class on Nov 5 for election day
  • The next exam is on Nov 14
    • We will have a review session on Nov 12
    • Request DRS accommodations if needed
  • Project will be released Nov 21 and is due on Dec 10

After today, you should better understand

Drug development pipeline

Drug development is a complex, multi-stage process requiring significant time and resources

1. Discovery and Preclinical Research
Potential drugs are identified and tested in non-human studies

2. Clinical Trials
Testing in human subjects to assess safety and efficacy

3. Regulatory Approval
Evaluation by agencies like the FDA before the drug can be marketed

4. Post-Marketing Surveillance:
Ongoing monitoring after the drug is available to the public

Computation is most helpful with the drug discovery stage

Identifying the right protein target is crucial for developing effective and safe drugs

Proteins regulate nearly all cellular processes and drugs can inhibit or activate proteins to correct disease states

Criteria for Selecting a Protein Target

  • Disease Relevance: The protein plays a critical role in the disease mechanism.
  • Druggability: The target has a structure that allows it to bind with drug-like molecules.
  • Specificity: Targeting the protein minimizes effects on healthy cells, reducing side effects.

Example: Bruton’s tyrosine kinase (BTK) is a critical signaling enzyme that controls B-cell development, maturation, and activation by mediating B-cell receptor signal transduction

(Mohamed et al., 2009)

Now we can use ...

(Vetrie et al., 1993 & Tsukada et al., 1993)

BTK gene was implicated in X chromosome-linked agammaglobulinemia (XLA) 

Target identification is accelerated with bioinformatics

Genome-wide association studies, high-throughput screening

(Aokl et el., 1994; Weers et al., 1994; Saouaf et al., 1994)

(Singh et al., 2018)

Revealed that BTK as a central hub in B-cell receptor (BCR) signaling

Target identification is accelerated with bioinformatics

Now we can use ...

Proteomics, transcriptomics

With a protein target in hand, we can now identify potential drug candidates

After today, you should better understand

Role of structure-based drug design

Chemical space contains an astronomical number of possible compounds to explore

Effective drugs must bind to the target protein with sufficient affinity and specificity

Estimated to be between 1060 to 10200 possible small organic molecules

We need methods to navigate chemical space and identify promising leads accurately and efficiently

High-throughput screening (HTS) allows testing of thousands of compounds against the target protein

  • Library Preparation: Collection of diverse compounds
  • Assay Development: Design of biological assays to measure compound activity against the target
  • Screening: Compounds are tested in miniaturized assays
  • Data Analysis: Identification of "hits" that show desired activity

Virtual screening evaluates vast libraries to identify potential leads efficiently

Experimental assays are still expensive, and limited to commercially available compounds

Instead, we can use computational methods to predict which compounds we should experimental validate

Can screen millions to billions of compounds in silico, thereby dramatically expanding our search space

After today, you should better understand

Thermodynamics of binding

Selective binding to a protein is governed by thermodynamics (and kinetics)

Binding occurs when a compound/ligand interacts specifically with a protein

Protein

Ligand

Binding

Protein-

ligand

We can model this as a reversible protein-ligand binding

P + L \leftrightharpoons PL

Binding affinity is determined by the Gibbs free energy change

The change in free energy when a ligand binds to a protein

\Delta G_{bind} = G_{PL} - G_{P} - G_{L}

Determines binding process spontaneity

Gibbs free energy combines enthalpy and entropy

\Delta G_{bind} = \Delta H_{bind} - T\Delta S_{bind}
\Delta H_{bind}
\Delta S_{bind}

Entropy

Enthalpy

Accounts for energetic interactions

How much conformational flexibility changes

Note: Simulations capture free energy directly instead of treating enthalpy and entropy separately

After today, you should better understand

Enthalpic contributions to binding

Enthalpy accounts for noncovalent interactions

Noncovalent interactions: Electrostatics, hydrogen bonds, dipoles, π-π stacking, etc.

Ensemble differences in noncovalent interactions provide binding enthalpy

\Delta H_{bind} = \left\langle H_{PL} \right\rangle - \left\langle H_{P} \right\rangle - \left\langle H_{L} \right\rangle
\left\langle \cdots \right\rangle

Ensemble average

Chemical interactions are determined by fluctuating electron densities

Our noncovalent interactions conceptual framework:

3. Regions of increased electron density are associated with higher partial negative charges

4. Electrons are mobile and can be perturbed by external interactions

1. Coulomb's law describes the interactions between charges

Molecular interactions are governed by their electron densities (Hohenberg-Kohn theorem)

This is rather difficult, so we often use conceptual frameworks to explain trends (e.g., hybridization and resonance)

2. Molecular geometry uniquely specifies an electron density

Electrostatic forces govern interactions between charged and polar regions

Charged molecules have a net imbalance between

  • Positive charges in their nuclei
  • Negative charges from their electrons

This leads to net electrostatic attractions or repulsions between different atoms or molecules

Arginine

Glycine

~5 to 20 kcal/mol per interaction

Long-Range Interaction: Can attract ligands to the binding site from a distance

Anchor Points: Often serves as key anchoring interactions in the binding site

Role in binding

Hydrogen bonds are a type of electrostatic interactions

Attraction between a (donor) hydrogen atom covalently bonded to an electronegative atom and another (acceptor) electronegative atom with a lone pair

  • Common donors: O-H, N-H groups
  • Common acceptors: O and N atoms with lone pairs

~2 to 7 kcal/mol per hydrogen bond

Strongest when the hydrogen, donor, and acceptor atoms are colinear

Specificity​: Precise orientation of the ligand

Stabilization​: Moderately strong interactions

Role in binding

Dynamic​: Allows for adaptability of ligands

Uneven electron distribution creates partial charges and dipoles

Electronegativity differences lead to unequal distribution of electron density

Unequal distribution results in regions or partial positive or partial negative charges

Consistent electron density spatial variation results in permanent dipoles

~0.01 to 1 kcal/mol per interaction

Directional binding: Highly directional, ensuring that the ligand aligns correctly

Flexibility: Can accommodate slight conformational changes

Role in binding

Van der Waals forces are weak, non-directional interactions

Dispersion: Electrons in molecules are constantly moving, leading to temporary uneven distributions that induce dipoles in neighboring molecules

~0.4 to 4 kcal/mol per interaction

Complementary fit​: Maximizes surface contact

Flexibility: Allows small conformational changes

Role in binding

Induction: The electric field of a polar molecule distorts the electron cloud of a nonpolar molecule, creating a temporary dipole

π-π interactions involve stacking of aromatic rings

Noncovalent interactions between aromatic rings due to overlap of π-electron clouds

~1 to 15 kcal/mol per interaction

Edge-to-face

Displaced

Face-to-face

Orientation​: Proper positioning of aromatics

Selectivity: Recognition of ligands

Role in binding

Summing all of these contributions during a simulation provides our ensemble average

\left\langle H_{AB} \right\rangle

After today, you should better understand

Entropic contributions to binding

Entropy accounts for microstate diversity of a single system state

One of Alex's esoteric points: "Entropy is disorder," is a massive oversimplification that breaks down in actual practice

Entropy is formally defined as 

S = k_B \ln \Omega

is the total number of microstates available to the system without changing the system state

\Omega

Entropy is "energy dispersion"

Higher entropy implies greater microstate diversity

"System state" can be arbitrarily defined and compared as

  • Unbound ligand vs. bound ligand
  • Unfolded protein vs. folded protein
  • Liquid water at 300 K vs. 500 K

Grid-based protein-ligand binding

Suppose I have a system with

  • Protein receptor
  • Ligands positioned on a grid

My macrostate (number of particles, temperature, and pressure) remain constant

How many ways can I rearrange the ligands without binding to the receptor?

L
N

Number of ligands

Number of sites

\Omega = \frac{N!}{L! \left( N - L \right)!}

Number of ways to choose L grid sites out of N is the binomial coefficient

Grid-based protein-ligand binding

\Omega = \frac{N!}{(L-1)! \left( N - L + 1 \right)!}

What if one ligand binds to the receptor?

How does entropy change?

Increase

No change

Decrease

It depends on our ligand concentration!

How to interpret this: Pick a number of ligands and move to the right (L - 1), does entropy go up or down?

For protein-ligand binding, we need to account for how the number of accessible microstates/configurations for protein and ligand

After today, you should better understand

Alchemical free energy simulations

We can now run molecular simulations of different states

To compute the free energy of a "system state", we have to compute the state's partition function, Z

We can run simulations and directly compute the ensemble average free energy

This is theoretically valid but not practical. Why?

\Delta G_{PL} =
\left\langle G_{PL} \right\rangle
\left\langle G_{P} \right\rangle
\left\langle G_{L} \right\rangle
-
-
\left\langle G \right\rangle = -k_B T \ln Z

Exact partition functions include all microstates

To compute the partition function of protein; for example, we need to know the energy for

  • All possible conformations (folded, partially folded, unfolded)
  • All possible atomic positions (backbone and sidechains)
  • All possible velocities of the atoms
  • All possible rotational states
  • All possible vibrational states

This is impossible

Fortunately, the low-energy conformations contribute the most to the partition function

Molecular simulations can sample some low-energy conformations; however, minor errors will drastically impact absolute free energy calculation

e^{-\beta E}

What if we slowly disappear the ligand?

\Delta G_1
\Delta G_2
\Delta G_3
\Delta G_4
\lambda = 1.0
\lambda = 0.5
\lambda = 0.0

We could use an alchemical parameter,    , to scale noncovalent interactions between protein and ligand

\lambda

This allows us to sum relative free energies to estimate amount of energy to bind/unbind the ligand

\Delta G = \sum \Delta G_i

How does this help us?

Relative free energies are expressed as a partition function ratio

\Delta G = - k_B T \ln Z_B + k_B T \ln Z_A = - k_B T \ln \left( \frac{Z_B}{Z_A} \right)

The free energy change from state A to B can be computed as

Advantage: Partition function ratios are dominated by overlapping microstates common between states A and B

Maintaining phase space overlap ensures more reliable and converged free energy estimates

A
B

(This is conceptually similar to having a small integration step size.)

Thermodynamic integration provides a way to compute free energy differences

\Delta G_{A \to B} = \int_0^1 \left\langle \frac{\partial U(\lambda)}{\partial \lambda} \right\rangle_\lambda d\lambda

We can to integrate over these small free energy changes 

We can use this to reliably calculate the free energy difference between bound and unbound states

Alchemical simulations are actually very expensive

We use "docking" to more efficiently screen molecules before (if ever) doing alchemical simulations

Before the next class, you should

Lecture 16:
Structure-based drug design

Today

Thursday

Lecture 17:
Docking and virtual screening

The partition function is the sum of all energy-weighted microstates

Let's go back to our grid model with two system states: (A) unbound and (B) bound

Note: To make our lives easier, we assume each microstate has the same energy

Energy

State

L \varepsilon_{sol}
(L - 1) \varepsilon_{sol} + \varepsilon_{b}

Multiplicity

\frac{N!}{L!(N - L)!} \approx \frac{N^L}{L!}
\frac{N!}{(L-1) !(N - L + 1)!} \\ \approx \frac{N^{L - 1}}{(L - 1)!}

Weight

Z_B = \frac{N^{L - 1}}{(L - 1)!} e^{- \beta \left[ (L - 1) \varepsilon_{sol} + \varepsilon_{b} \right]}
Z_A = \frac{N^L}{L!} e^{-\beta \left[ L \varepsilon_{sol} \right]}

The Stirling approximation

Z = Z_A + Z_B

Energy

              of each microstate. (In our model, this is based on number of solvated and bound ligands)

The               of this system state in our macrostate ensemble

weight

Total partition function

Multiplicity

, or the the number microstates

So, what's the issue with computing this for each state?