Tag Index

affinity-maturation

Affinity maturation is a process by which antibodies are iteratively improved in vivo. Described as “hyper-darwinian”.

affinity-maturation/somatic-hypermutation

alignment

Alignment collects notes on comparing proteins by either sequence-derived representations or structural information. The main split here is between sequence-based alignment approaches, including PLM embedding methods and homology retrieval, and structure-based alignment approaches that operate on coordinates, structural descriptors, or structure-derived embeddings.

alignment/sequence-based

alignment/structure-based

alphafold2

(OpenFold redirects here)

AlphaFold2 is a protein structure prediction method from 2020, and is the first to make extensive use of the Transformer architecture, consisting of 97 million parameters. AlphaMissense is a derivative of this method.

Architecture of AlphaFold2 from Jumper et al. (1)

Architectural and ML contributions

• Evoformer
• Invariant point attention
• Frame aligned point error
• Self-distillation for protein structures
• Predicted aligned error
• Triangular update

alphafold3

AlphaFold3 is a diffusion-based all-atom structure prediction method that is widely seen as state-of-the-art.

Architecture of AlphaFold3 from Abramson et al. (1)

Architectural and ML contributions

• PairFormer
• PDE: predicted distance error (replacing frame aligned point error)
• Non-equivariant per-atom prediction, which leads to occasional errors when predicting chirality
• Cross-distillation from AlphaFold2-Multimer v2.3 to avoid hallucination of low-pLDDT regions

ancestral-sequence-reconstruction

Ancestral sequence reconstruction refers to the process of inferring ancestral sequences using extant sequences. Figure from (1)

antibodies

Antibodies are proteins with two heavy chains and two light chains produced by B cells, central to the adaptive immune system. Their structure consists of a variable region (containing CDRs and a framework region) and three constant regions (CH1, CH2, CH3). The variable region and CH1 form the Fab, while the remainder forms the Fc region. B cell receptors are antibodies with an additional CH4 domain.

Types of antibodies

IgA is found in mucous membranes, cannot activate the complement system, and makes up roughly two-thirds of antibodies in healthy adults. It is notable for being double-sided.

IgE has only one binding site, mainly protects against large organisms like parasites, and is responsible for allergic reactions.

IgG is the standard antibody class used in therapeutic design. Cannot activate the complement system and can pass through the placenta.

• IgG1 makes up 67% of all antibodies in the human body, is capable of antibody-dependent cellular phagocytosis, and has the longest hinge region. IgG1 immune repertoires consist mostly of just a few dozen dominant clones and are unique to each individual, remaining largely stable over time.
• IgG2 — mice have IgG2a and IgG2b instead; some strains have IgG2c instead of IgG2a.
• IgG3 makes up ~7% of IgGs and has a notably shorter half-life due to poor binding to FcRn, attributed to an H435R mutation.
• IgG4 is the rarest IgG and undergoes Fab-arm exchange, dissociating into half-bodies and forming novel combinations via R409 in the hinge. Therapeutic IgG4 antibodies use the S228P substitution to stabilize the hinge and prevent this.

IgM is far less subject to affinity maturation than IgG, responds to lipids and polysaccharides, and activates the complement system.

Datasets

SAbDab is a database of all antibody and nanobody structures in the PDB. The full list can be downloaded with:

curl -s https://opig.stats.ox.ac.uk/webapps/sabdab-sabpred/sabdab/summary/all/

antibodies/engineering-and-design

antibodies/function

antibodies/nanobodies

antibody-antigen-interactions

antibody-antigen-interactions/binding-affinity

antibody-antigen-interactions/complex-prediction

antibody-antigen-interactions/misc

antibody-developability

Antibody developability refers to a series of properties linked to the development of antibodies as therapeutics. These arise because natural antibodies do not possess them to begin with, or because they arise during optimization as a consequence of affinity maturation via techniques such as Yeast display.

General observations

• Raybould et al. (1) outlined five criteria (in a parallel to Lepinski’s rule of five):
• Length of CDRs, specifically CDRH3
• Hydrophobic patches
• Negative patches
• Positive patches
• Viscosity

Thermostability

See Stability and thermostability

Immunogenicity

• Glycine residues doesn’t cause immunogenicity as much as other residues (2). This makes them used for including during design of cyclic peptides or peptide therapeutics.
• Antibody humanization can lead to immunogenic reactions.

antibody-developability/expression

antibody-developability/general

antibody-developability/humanization

antibody-developability/hydrophobicity

antibody-developability/immunogenicity

antibody-developability/polyspecificity

antibody-developability/self-association

antibody-developability/solubility

antibody-drug-conjugates

antibody-framework

antibody-structure-prediction

The antibody structure prediction problem is a subclass of the protein structure prediction problem that is mostly focused on predicting the CDRs, specifically the CDRH3 loop that mediates antigen binding. It also sometimes includes the antibody-antigen docking problem.

Models

• AbFold: a method that concatenates information from IgFold and AlphaFold2 Multimer when modeling antibodies, which usually predict different conformations, leading to improved prediction quality (1)
• IgFold: a method that uses embeddings from the antibody-specific PLM AntiBERTy
• ImmuneBuilder: Consists of ABodyBuilder2 (for Antibodies), NanoBodyBuilder2 (for Nanobodies), and TCRBuilder2 (for T-cell receptors).

antibody-structure-prediction/cdr

antibody-structure-prediction/complex-prediction

b-cells

B cells are a type of lymphocyte that synthesizes and secretes antibodies as well as B-cell receptors. Each cell synthesizes a single antibody sequence throughout its life cycle (a phenomenon termed allelic exclusion). Can be categorized as either naive B cells or memory B cells. Activation by antigen presentation causes them to proliferate into effector cells that secrete antibodies.

blosum62

The BLOSUM62 matrix quantifies the similarity of amino acids to one another when computing evolutionary distance sequences (1). Interestingly, it has math errors in its computation that make it a more effective matrix for substitution calculation (2). A custom version for TCRs has also been presented (3).

cdrh3

citation-fix

citation-needed

confidence-metrics

conformational-dynamics

conformational-dynamics/allostery

conformational-dynamics/evolution

conformational-dynamics/experimental-ensembles

conformational-dynamics/kinetics

conformational-dynamics/modeling

conformational-dynamics/molecular-dynamics

contrastive-learning

Contrastive learning is a supervised method for driving the latent representations of data points towards or away from each other by adding custom losses.

Implementations

• The triplet margin loss used by Yu et al. (1): $$L^{TM}=||z_a-z_p|{|}^2-||z_a-z_n|{|}^2+\alpha$$ $z_a$: Enzyme embedding $z_p$: Positive case $z_n$: Negative case, selected to have EC numbers close in Euclidean space to the positive case $\alpha$: Margin; set to 1
• The supercon hard loss used by Yu et al. (1): $$L^{sup}=\sum _{e\in E}\frac{-1}{|P(E)|}\sum _{z_p\in P(e)}log\frac{\exp (z_e{z}_p/\tau )}{{\sum }_{z_a\in A(e)}\exp (z_i{z}_a/\tau )}$$ $\tau$: temperature, set to 0.1 in the paper
• Noise contrastive estimation (variant 1): $$L_B(\theta ,\gamma )=\log \sigma (s(x_i,a_{i,0}^{+};\theta ),\gamma )+\sum _{k=1}^K\log (1-\sigma (s(x_i,a_{i,k}^{-};\theta ),\gamma )$$ $x_i$: Input text $a_{i,\circ }$: Another example (either positive or negative) $s(x_i,a_{i,\circ };\theta )$ : Scoring function, usually cosine similarity, dot product, or logit “produced by input-sample matcher sub-network” (from Rethmeier and Augenstein 2021) $\sigma (z,\gamma )$: Scaling function, usually sigmoid
• Noise contrastive estimation (variant 2, ranks a single positive pair over $K$ negative pairs): Variant 2 ranks a single positive pair over $K$ negative pairs $$L_R=\log \frac{\exp (\bar{s}\ast (x_I,a_{i,0}^{+};{\theta }_{)})}{\exp (\bar{s}\ast (x_I,a_{i,0}^{+};{\theta }_{)})+{\sum }_{k=1}^K\exp (\bar{s}\ast (x_I,a_{i,k}^{-};\theta ))}$$

diffusion-guidance

Diffusion guidance refers to inference-time methods that steer a diffusion process toward desired properties, constraints, or observations. It is a general concept that applies to both protein design, structure prediction, and sequence-based protein design, of which all-atom diffusion is just one application.

Details

Xie et al (1) outline three broad types of guidance used by diffusion models:

1. Score guidance, in which gradients from classifiers, constraints, or rewards are used to nudge the diffusion path.
2. Path-integral reweighting, such as Feynman-Kac potentials, which use importance weights to update trajectories.
3. Invariant correctors, such as Metropolis-adjusted Langevin methods, which mix within a biased marginal without changing the trajectory weights.

However, other search algorithms such as Beam search and Monte Carlo Tree Search have been used in conjunction with diffusion models (2).

diffusion-guidance/protein-design

diffusion-guidance/structure-prediction

diffusion-models

Diffusion models are generative models whose outputs are generated by iteratively denoising Gaussian noise. During inference, the reverse process is executed, whereas during training, the forward process is carried out (converting data to noise). This process can be guided at inference time to respect specific geometric constraints.

Details

Diffusion models try to recover samples ${\mathbf{X}}_0$ drawn from $p_{data}$ from Gaussian noise ${\mathbf{X}}_T$ by iteratively denoising across $T$ time steps. The forward process is defined as

$B_t$: Standard Weiner process (by which noise is added)

Typically these drift and diffusion functions are used:

The reverse process:

The scoring function is approximated by a neural network, $s_{\theta }(x,t)$.

Diffusion models can also be zero-shot classifiers (1).

Diffusion models have been combined with Replica-exchange molecular dynamics (2).

Types of sequence-based diffusion

For protein sequences, which are fundamentally discrete, Yang et al (3) describe three approaches to generation using diffusion models:

• Diffusion in pre-trained latent space (e.g., continuous diffusion)
• Diffusion in discrete space with uniform noise matrices
• Diffusion in discrete space via absorbing matrices, e.g., one-at-a-time masking/unmasking of individual tokens

diffusion-models/implementation

diffusion-models/protein-design

diffusion-models/structure-prediction

diffusion-models/training

epistasis

Epistasis refers to the non-additivity of fitness effects arising from specific combinations of mutations. (1) outline three types of epistasis: magnitude epistasis (“same direction as expected but are not perfectly additive”), sign epistasis (“effect of one of the substitutions changes direction in the context of the other”), and reciprocal epistasis (“effects of both substitutions change direction when they are made together”).

Figure from (1)

Figure from (2)

Notes

• Negative epistasis is approximately 100x more common than positive epistasis (3).
• Rates of magnitude, sign, and reciprocal epistasis are constant across positions (1). These differed from a null additive-only model with noise, which had 74% magnitude, 22% sign, and 4% reciprocal sign epistasis. Figure from (1)

Examples

• The S373P mutation in the Spike protein is disadvantageous in pre-Omicron-variant versions of SARS-CoV-2 but advantageous in Omicron. Mentioned by Bloom and Neher (4).
• The combination of N501Y and Q498R in the Spike protein of SARS-CoV-2 increases the binding affinity to ACE2 by 387-fold. This is believed to have led to the immune-evasive mutations in the Omicron-variant and was observed in vitro by Zahradník et al. (5) prior to the emergence of Omicron:
• One example of third-order epistasis is the J-domain, where strong non-additivity is observed among a triad, but disappears if any of the three are mutated to alanine (2). Figure from (2)

Measuring epistasis

Figure from (6)

• Graph Fourier Transform: A decomposition that breaks down the signal (here, fitness) into distinct “epistatic orders”
• Dirichlet energy: quantifies how variable (i.e., rugged) the landscape is, with high energy corresponding to high ruggedness $$DE={\mathbf{f}}^{\mathbf{T}}\mathbf{Lf}=\frac{1}{2}\sum _{u\sim v}(f_u-fv{)}^2$$
• NK model: A linear model where $N$ is the number of sites and $K$ is the number of interacting sites; when $K=0$, effect of all mutations is linear, whereas larger $K$ indicates more interactions and therefore more epistasis

epitope-prediction

evolution-and-natural-selection

Protein evolution is the process and result of gradual sequence changes resulting in functional and/or structural changes. See Epistasis for examples on why evolutionary trajectories are difficult to predict. This note excludes any discussion of somatic hypermutation.

Notes

Paradigms and preliminaries

• Neutral theory: most observed amino acid changes are neutral (i.e., silent in fitness effects). This leads to genetic drift. Developed by Kimura (1).
• Nearly neutral theory: deleterious mutations are retained and subsequently compensated for by advantageous mutations (which is consistent with the observation that most missense mutations are destabilizing). Developed by Ohta (2) to explain why the rate of protein evolution was independent of generation time, which is in turn inversely proportional to population size. Figure from (2)
• The theory of punctuated equilibrium suggests that phenotypes change very little for long stretches of time, followed by abrupt rapid changes (3).
• Statistical physics approach: population size is equated with inverse temperature (such that infinite population is analogous to zero degrees Kelvin), and log-fitness with energy (4). Advantageous and deleterious mutations are predicted to occur with equal frequency. This framing ignores the imbalance in sequence data (5,6).
• Fisher’s geometric model: The overall fitness of a phenotype can be quantified along $N$ dimensions; Fisher postulated that phenotypes in a population were distributed as a hypersphere centered on a local maximum.
• Protein evolvability refers to the ability of a protein to 1) evolve new functions in relatively few mutations and 2) be robust to mutations that lead to loss-of-function (7). These are described as contradictory statements by Tokuriki & Tawfik (8) but are described as complementary at the structural level.
• “The principle of minimal frustration suggests that naturally evolved proteins with the same structure should have similar folding rates and that modulation of thermodynamic stability should occur via unfolding rates” (quoted from (9)). This has been supported by the observation that thioredoxins fold at similar rates but unfold at rates that correlate with their thermostability values.

Observations

• Protein folds with high sequence diversity also have high functional diversity (7).
• The sequence capacity of a protein exceeds $10^{23}$ for even small proteins (35-40 AAs), but the fraction of stable states is extremely small and inversely correlated with protein size. These values were estimated using Potts models (10). Figure from (10)

evolution-and-natural-selection/structure

fine-tuning

immune-repertoires

Immune repertoires are the full breadth of B-cell and T-cell receptors being expressed by a human that are available for potential antigen binding. Rees (1) provides estimates suggesting that humans have naive repertoires of about $10^9$ sequences.

Related:

• Affinity maturation
• Antibodies

inverse-folding

Inverse folding describes the problem of designing a sequence for a structure. Typically these are limited to the twenty canonical amino acids.

Methods

See Hybrid sequence-structure models for a list of methods that incorporate PLMs

• ProteinMPNN and its derivatives
• ESM-IF
• GearNet
• Frame2seq
• GVP-GNN

Notes

Training

• Training inverse folding models with backbone dihedral angles as features usually improved sequence recovery (1). Figure from (1)

Execution

• Forward-folding is a stronger predictor of inverse folding success than sequence recovery ((2), citing Watson et al. (3,4)).

Datasets

• PDBench is a dataset of 595 protein structures with diverse, evenly divided topologies for benchmarking of Inverse folding methods (5). Figure 2 from Castorina et al. (5)

inverse-folding/evaluation

inverse-folding/misc

inverse-folding/training

ligand-docking

light-chains

The light chain of an antibody makes up part of its variable region and Fab, and therefore is involved in antigen binding. In humans, the Kappa and Lambda subtypes are found and split about 60:40, whereas in mice it is closer to 90:10.

Kappa and lambda subtype

• The ratio of kappa to lambda in circulating antibodies is about 60:40; when this falls out of balance, that can be a symptom of B cell lymphoma.
• Lambda light chains are more flexible than kappa light chains due to an extra glycine in the switch region (_Articles that need citations).

low-rank-adaptation

pae

Predicted aligned error (PAE) is a measurement calculated by protein structure prediction neural networks to capture positional errors between two amino acids in a computational model. It was introduced by AlphaFold2. A derivative metric, ipSAE, has been shown to be more robust at identifying potential binders.

Figure from (1)

plddt

(LDDT redirects here) pLDDT (predicted local distance difference test) is a confidence metric used by neural networks for protein structure prediction. It captures the per-residue accuracy, both in terms of neighborhood and side chain rotamer. It was first directly integrated into structure prediction by AlphaFold2 at the per-residue level and has been widely adopted since. AlphaFold3 adopted per-atom pLDDT.

Figure from (1)

Notes

• When clustering predicted protein structures, sparse clusters tend to have lower pLDDT (2). This was found to be independent of MSA depth.
• pLDDT correlates poorly with GDT-TS among AlphaFold2 models in CASP15. This was observed in a repeat that used deeper MSAs (3).
• De novo sequences designed by inversion with high pLDDT were found by ESM to have high perplexity (4).
• While the default pLDDT is not continuously differentiable and thus unsuitable for training, (5) use a modified version that can be used as a loss function.
• pLDDT can be used as spatial restraints in biomolecular simulations: $$E_{pLDDT}=\sum {\left(\frac{d_i}{1.5\ast \exp \left(4\ast \left(0.7-pLDD{T}_i\right)\right)}\right)}^2$$ The equation was originally presented by Hiranuma et al. (6) and was used by del Alamo et al. (7) as coordinate constraints in Rosetta when refining AlphaFold2 models.

protein-backbone-design

Protein backbone design is the generation of protein backbones in three-dimensional space. This section also covers generation and design of entire protein structures in Cartesian space, but most methods uncouple design of the backbone and design of the sequence given the backbone (inverse folding). As of May 2024, the current state of the art uses diffusion.

Methods

• Chroma (1)
• RF-diffusion (2) and RFam (3)
• Hallucination using AlphaFold2 and RosettaFold
• Inpainting using RosettaFold (4)

Datasets

• Verkuil et al. (5) use a test set of 39 PDBs for their validation, although they cite someone else:
• 1QYS
• 2KL8
• 2KPO
• 2LN3
• 2LTA
• 2LVB
• 2N2T
• 2N2U
• 2N3Z
• 2N76
• 4KY3
• 4KYZ
• 5CW9
• 5KPE
• 5KPH
• 5L33
• 5TPJ
• 5TRV
• 6CZG
• 6CZH
• 6CZI
• 6CZJ
• 6D0T
• 6DG6
• 6DKM A
• 6DKM B
• 6DLM A
• 6DLM B
• 6E5C
• 6LLQ
• 6MRR
• 6MRS
• 6MSP
• 6NUK
• 6W3F
• 6W3W
• 6WI5
• 6WVS
• 7MCD

protein-backbone-design/designability

protein-design

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