Fit polyclonal model

Here we fit polyclonal models to the data.

First, import Python modules:

import pickle

import altair as alt

import pandas as pd

import polyclonal

import yaml

# allow more rows for Altair
_ = alt.data_transformers.disable_max_rows()

Read input data

Get parameterized variable from papermill

# papermill parameters cell (tagged as `parameters`)
prob_escape_csv = None
n_threads = None
pickle_file = None
antibody = None

# Parameters
prob_escape_csv = "results/prob_escape/B_2022-09-27_rescue-3_IDF033_1_prob_escape.csv"
pickle_file = "results/polyclonal_fits/B_2022-09-27_rescue-3_IDF033_1.pickle"
n_threads = 2

Read the probabilities of escape, and filter for those with sufficient no-antibody counts:

print(f"\nReading probabilities of escape from {prob_escape_csv}")

prob_escape = pd.read_csv(
    prob_escape_csv, keep_default_na=False, na_values="nan"
).query("`no-antibody_count` >= no_antibody_count_threshold")
assert prob_escape.notnull().all().all()

Reading probabilities of escape from results/prob_escape/B_2022-09-27_rescue-3_IDF033_1_prob_escape.csv

Read the rest of the configuration and input data:

# get information from config
with open("config.yaml") as f:
    config = yaml.safe_load(f)

antibody = prob_escape["antibody"].unique()
assert len(antibody) == 1, antibody
antibody = antibody[0]

# get site numbering map and the reference sites in order
site_numbering_map = pd.read_csv(config["site_numbering_map"])
reference_sites = site_numbering_map.sort_values("sequential_site")[
    "reference_site"
].tolist()

# get the polyclonal configuration for this antibody
with open(config["polyclonal_config"]) as f:
    polyclonal_config = yaml.safe_load(f)
if antibody not in polyclonal_config:
    raise ValueError(f"`polyclonal_config` lacks configuration for {antibody=}")
antibody_config = polyclonal_config[antibody]

# print names of variables and settings
print(f"{antibody=}")
print(f"{n_threads=}")
print(f"{pickle_file=}")
print(f"{antibody_config=}")

antibody='IDF033'
n_threads=2
pickle_file='results/polyclonal_fits/B_2022-09-27_rescue-3_IDF033_1.pickle'
antibody_config={'max_epitopes': 2, 'n_bootstrap_samples': 50, 'min_epitope_activity_to_include': 0.25, 'fit_kwargs': {'fix_hill_coefficient': True, 'fix_non_neutralized_frac': True, 'reg_escape_weight': 0.1, 'reg_uniqueness_weight': 0, 'reg_uniqueness2_weight': 2, 'reg_spatial_weight': 0.0, 'reg_spatial2_weight': 0.001}, 'plot_kwargs': {'addtl_slider_stats': {'times_seen': 3, 'functional effect': -1.5}, 'heatmap_max_at_least': 2, 'heatmap_min_at_least': -2, 'slider_binding_range_kwargs': {'n_models': {'step': 1}, 'times_seen': {'step': 1, 'min': 1, 'max': 25}}, 'sites_to_show': {'include_range': [30, 702]}}}

Read spatial distances if relevant:

if ("spatial_distances" in config) and (config["spatial_distances"] is not None):
    print(f"Reading spatial distances from {config['spatial_distances']}")
    spatial_distances = pd.read_csv(config["spatial_distances"])
    print(f"Read spatial distances for {len(spatial_distances)} residue pairs")
else:
    print("No spatial distances")
    spatial_distances = None

Reading spatial distances from results/spatial_distances/spatial_distances.csv
Read spatial distances for 159895 residue pairs

Some summary statistics

Note that these statistics are only for the variants that passed upstream filtering in the pipeline.

Number of variants per concentration:

display(
    prob_escape.groupby("antibody_concentration").aggregate(
        n_variants=pd.NamedAgg("barcode", "nunique")
    )
)

	n_variants
antibody_concentration
1.0	15476
2.0	15476
3.0	15476

Plot mean probability of escape across all variants with the indicated number of mutations. Note that this plot weights each variant the same in the means regardless of how many barcode counts it has. We plot means for both censored (set to between 0 and 1) and uncensored probabilities of escape. Also, note it uses a symlog scale for the y-axis. Mouseover points for values:

max_aa_subs = 4  # group if >= this many substitutions

mean_prob_escape = (
    prob_escape.assign(
        n_subs=lambda x: (
            x["aa_substitutions_reference"]
            .str.split()
            .map(len)
            .clip(upper=max_aa_subs)
            .map(lambda n: str(n) if n < max_aa_subs else f">{max_aa_subs - 1}")
        )
    )
    .groupby(["antibody_concentration", "n_subs"], as_index=False)
    .aggregate({"prob_escape": "mean", "prob_escape_uncensored": "mean"})
    .rename(
        columns={
            "prob_escape": "censored to [0, 1]",
            "prob_escape_uncensored": "not censored",
        }
    )
    .melt(
        id_vars=["antibody_concentration", "n_subs"],
        var_name="censored",
        value_name="probability escape",
    )
)

mean_prob_escape_chart = (
    alt.Chart(mean_prob_escape)
    .encode(
        x=alt.X("antibody_concentration"),
        y=alt.Y(
            "probability escape",
            scale=alt.Scale(type="symlog", constant=0.05),
        ),
        column=alt.Column("censored", title=None),
        color=alt.Color("n_subs", title="n substitutions"),
        tooltip=[
            alt.Tooltip(c, format=".3g") if mean_prob_escape[c].dtype == float else c
            for c in mean_prob_escape.columns
        ],
    )
    .mark_line(point=True, size=0.5)
    .properties(width=200, height=125)
    .configure_axis(grid=False)
)

mean_prob_escape_chart

Fit polyclonal model

First, get the fitting related keyword arguments from the configuration passed by snakemake:

max_epitopes = antibody_config["max_epitopes"]
print(f"{max_epitopes=}")

fit_kwargs = antibody_config["fit_kwargs"]
print(f"{fit_kwargs=}")

min_epitope_activity_to_include = antibody_config["min_epitope_activity_to_include"]
print(f"{min_epitope_activity_to_include=}")

max_epitopes=2
fit_kwargs={'fix_hill_coefficient': True, 'fix_non_neutralized_frac': True, 'reg_escape_weight': 0.1, 'reg_uniqueness_weight': 0, 'reg_uniqueness2_weight': 2, 'reg_spatial_weight': 0.0, 'reg_spatial2_weight': 0.001}
min_epitope_activity_to_include=0.25

Fit a model to all the data, and keep adding epitopes until we either reach the maximum specified or the new epitope has negative activity. Note that that we fit using the reference based-site-numbering scheme, so results are shown with those numbers:Z

models = []

for n_epitopes in range(1, max_epitopes + 1):
    print(f"\nFitting model with {n_epitopes=}")

    # create model
    model = polyclonal.Polyclonal(
        n_epitopes=n_epitopes,
        data_to_fit=prob_escape.rename(
            columns={
                "antibody_concentration": "concentration",
                "aa_substitutions_reference": "aa_substitutions",
            }
        ),
        alphabet=polyclonal.AAS_WITHSTOP_WITHGAP,
        sites=reference_sites,
        spatial_distances=spatial_distances,
    )

    # fit model
    opt_res = model.fit(logfreq=200, **fit_kwargs)

    # display activities
    print("Activities of epitopes:")
    display(model.activity_wt_df.round(1))
    print("Max and mean absolute-value escape at each epitope:")
    display(
        model.mut_escape_df.groupby("epitope")
        .aggregate(
            max_escape=pd.NamedAgg("escape", "max"),
            mean_abs_escape=pd.NamedAgg("escape", lambda s: s.abs().mean()),
        )
        .round(1)
    )

    # stop if activity below threshold for any epitope and fit at least one epitope
    if len(models) and any(
        model.activity_wt_df["activity"] <= min_epitope_activity_to_include
    ):
        print(f"Stop fitting, epitope has activity <={min_epitope_activity_to_include}")
        model = models[-1]  # get previous model
        break
    else:
        models.append(model)

print(f"\nThe selected model has {len(model.epitopes)} epitopes")

Fitting model with n_epitopes=1
# First fitting site-level model.
# Starting optimization of 842 parameters at Sat Feb 25 15:01:09 2023.
        step    time_sec        loss    fit_loss  reg_escape  reg_spread reg_spatial reg_uniqueness reg_uniqueness2 reg_activity reg_hill_coefficient reg_non_neutralized_frac
           0    0.050611      2633.7      2632.2           0           0           0              0               0       1.5004                    0                        0
         110       6.213      627.24      616.52      2.9763           0      5.2614              0               0        2.481                    0                        0
# Successfully finished at Sat Feb 25 15:01:15 2023.
# Starting optimization of 6144 parameters at Sat Feb 25 15:01:15 2023.
        step    time_sec        loss    fit_loss  reg_escape  reg_spread reg_spatial reg_uniqueness reg_uniqueness2 reg_activity reg_hill_coefficient reg_non_neutralized_frac
           0     0.10035      743.33      712.95      22.636   2.419e-32      5.2614              0               0        2.481                    0                        0
         129      14.713      682.84      647.35      22.904      1.3389      8.7262              0               0       2.5272                    0                        0
# Successfully finished at Sat Feb 25 15:01:30 2023.
Activities of epitopes:

	epitope	activity
0	1	2.0

Max and mean absolute-value escape at each epitope:

	max_escape	mean_abs_escape
epitope
1	3.9	0.1

Fitting model with n_epitopes=2
# First fitting site-level model.
# Starting optimization of 1684 parameters at Sat Feb 25 15:01:33 2023.
        step    time_sec        loss    fit_loss  reg_escape  reg_spread reg_spatial reg_uniqueness reg_uniqueness2 reg_activity reg_hill_coefficient reg_non_neutralized_frac
           0    0.073132      563.25      561.24           0           0           0              0               0       2.0059                    0                        0
         196      14.959       455.4      437.11      5.5692           0       7.547              0           3.261       1.9218                    0                        0
# Successfully finished at Sat Feb 25 15:01:48 2023.
# Starting optimization of 12288 parameters at Sat Feb 25 15:01:48 2023.
        step    time_sec        loss    fit_loss  reg_escape  reg_spread reg_spatial reg_uniqueness reg_uniqueness2 reg_activity reg_hill_coefficient reg_non_neutralized_frac
           0     0.15515      1164.3      543.83      50.271  4.4061e-31       7.547              0          560.69       1.9218                    0                        0
         200      32.935      539.02      493.39      31.268      1.3905      9.9211              0           1.097       1.9511                    0                        0
         360      59.901       537.9      492.75      30.759      1.4443      9.8983              0          1.0988       1.9498                    0                        0
# Successfully finished at Sat Feb 25 15:02:48 2023.
Activities of epitopes:

	epitope	activity
0	1	-0.1
1	2	1.0

Max and mean absolute-value escape at each epitope:

	max_escape	mean_abs_escape
epitope
1	2.4	0.0
2	5.3	0.1

Stop fitting, epitope has activity <=0.25

The selected model has 1 epitopes

Plot the neutralization curves against unmutated protein (which reflect the wildtype activities, Hill coefficients, and non-neutralizable fractions):

model.curves_plot()

Plot of escape values:

df_to_merge = site_numbering_map.rename(columns={"reference_site": "site"})

plot_kwargs = antibody_config["plot_kwargs"]
if "plot_title" not in plot_kwargs:
    plot_kwargs["plot_title"] = str(antibody)
if "region" in site_numbering_map:
    plot_kwargs["site_zoom_bar_color_col"] = "region"
if "addtl_slider_stats" not in plot_kwargs:
    plot_kwargs["addtl_slider_stats"] = {"times_seen": 1}
elif "times_seen" not in plot_kwargs["addtl_slider_stats"]:
    plot_kwargs["addtl_slider_stats"]["times_seen"] = 1
if "functional effect" in plot_kwargs["addtl_slider_stats"]:
    del plot_kwargs["addtl_slider_stats"]["functional effect"]  # only antibody averages
if any(site_numbering_map["sequential_site"] != site_numbering_map["reference_site"]):
    if "addtl_tooltip_stats" not in plot_kwargs:
        plot_kwargs["addtl_tooltip_stats"] = ["sequential_site"]
    else:
        plot_kwargs["addtl_tooltip_stats"].append("sequential_site")

model.mut_escape_plot(df_to_merge=df_to_merge, **plot_kwargs)

Pickle and save model:

print(f"Saving {len(models)} models to {pickle_file=}")
with open(pickle_file, "wb") as f:
    pickle.dump(models, f)

Saving 1 models to pickle_file='results/polyclonal_fits/B_2022-09-27_rescue-3_IDF033_1.pickle'