add mdr version 1

monomer_dimer_ribosome.py

@@ -0,0 +1,188 @@
+# %%
+import numpy as np
+import sympy as sp
+from scipy.optimize import root_scalar
+import ultraplot as uplt
+from smitfit.symbol import Symbols
+from smitfit.model import Model
+import polars as pl
+# %%
+
+s = Symbols("TF1, TF2, TFR, R, T_TF, T_R, kD_MD, kD_MR", positive=True)
+# %%
+mb_ribosome = s.TFR + s.R - s.T_R  # type: ignore
+mb_TF = s.TF1 + 2 * s.TF2 + s.TFR - s.T_TF  # type: ignore
+eq_MD = s.TF1**2 - s.kD_MD * s.TF2  # type: ignore
+eq_MR = (s.TF1 * s.R) - s.kD_MR * s.TFR  # type: ignore
+
+#
+knowns = ["T_TF", "T_R", "kD_MD", "kD_MR"]
+
+# solve for: TF1
+# take Monomer-dimer equillibrium, put it in mass balance TF to eliminate TF2
+sub_TF2 = (s.TF2, sp.solve(eq_MD, s.TF2)[0])
+
+# same for monomer dimer, eliminate TF_R
+sub_mb = (s.R, sp.solve(mb_ribosome, s.R)[0])
+sub_TFR = (s.TFR, sp.solve(eq_MR.subs(*sub_mb), s.TFR)[0])
+
+# we know have an expr to find free TF monomer
+eq_TF1 = mb_TF.subs([sub_TF2, sub_TFR])
+eq_TF1
+
+
+# %%
+
+d = {
+    s.TF2: sp.solve(eq_MD, s.TF2)[0],
+    s.TFR: sp.solve(mb_TF, s.TFR)[0],
+    s.R: sp.solve(mb_ribosome, s.R)[0],
+}
+m = Model(d)
+
+# %%
+
+ld = sp.lambdify([s.TF1] + [s[k] for k in knowns], eq_TF1)
+
+# %%
+
+
+def solve_system(params: dict) -> dict:
+    args = tuple(params[k] for k in knowns)
+    # root find TF1
+    sol = root_scalar(ld, bracket=(0, params["T_TF"]), args=args)
+    # calculate the others
+    ans = m(**params, TF1=sol.root)
+
+    return {"TF1": sol.root, **ans}
+
+
+def make_df(records: list[dict]) -> pl.DataFrame:
+    df = pl.DataFrame(records)
+    cols = [
+        (pl.col("TF1") + pl.col("TF2") + pl.col("TFR")).alias("total TF"),
+        (pl.col("TFR") + pl.col("R")).alias("total R"),
+    ]
+    df = df.with_columns(cols)
+    return df
+
+
+# %%
+# The concentration of TF exceeds that of ribosomes (∼50 μM and ∼30 μM, respectively)[12,13]
+# TF binds free ribosomal 50S subunits with a Kd of ∼1 μM
+# Purified TF forms dimers with a Kd of 1–2 μM (ref. 14).
+# " Real-time observation of trigger factor function on translating ribosomes", https://doi.org/10.1038/nature05225
+
+# "the cytosol contains 2.6 moles of trigger factor per mole of ribosomes. "
+# The “trigger factor cycle” includes ribosomes, presecretory proteins, and the plasma membrane
+#
+
+ecoli_params = {
+    "T_TF": 50,
+    "T_R": 30,
+    "kD_MD": 1,
+    "kD_MR": 2,
+}
+
+solve_system(ecoli_params)
+
+# %%
+
+vmin, vmax = 1e-6, 1000e-6
+total_tf_protomer = np.logspace(
+    0, 4, endpoint=True, num=100
+)  # total TF protomer from 1 uM to 1
+
+input_params = [ecoli_params | {"T_TF": v} for v in total_tf_protomer]
+input_params
+
+# %%
+output_records = [solve_system(params) for params in input_params]
+df = make_df(output_records)
+
+
+# %%
+species = ["TF1", "TF2", "TFR"]
+cycle = iter(uplt.Cycle("default"))
+fig, axes = uplt.subplots(nrows=2, aspect=2.5, axwidth="120mm")
+for s in species:
+    axes[0].plot(
+        total_tf_protomer,
+        df.select(pl.col(s) / pl.col("total TF")),
+        label=s,
+        **next(cycle),
+    )
+
+axes[0].format(title="TF")
+species = ["TFR", "R"]
+for s in species:
+    axes[1].plot(
+        total_tf_protomer,
+        df.select(pl.col(s) / pl.col("total R")),
+        label=s,
+        **next(cycle),
+    )
+axes[1].format(title="ribosome")
+
+axes.format(
+    ylim=(0, 1),
+    xscale="log",
+    xformatter="sci",
+    ylabel="Fractional population",
+    xlabel="Total protomer TF (uM)",
+)
+axes.legend(loc="r", ncols=1)
+
+# %%
+# lets repeat for ribosome titration, fixed 100 nM TF protomer concentration
+
+microscopy_params = {
+    "T_TF": 1,  # 100 nM
+    "kD_MD": 1,
+    "kD_MR": 1,
+}
+
+# %%
+
+total_ribosome = np.linspace(0, 5, endpoint=True)
+input_params = [microscopy_params | {"T_R": v} for v in total_ribosome]
+
+# %%
+output_records = [solve_system(params) for params in input_params]
+df = make_df(output_records)
+
+# %%
+species = ["TF1", "TF2", "TFR"]
+cycle = iter(uplt.Cycle("default"))
+
+fig, axes = uplt.subplots(nrows=2, aspect=2.5, axwidth="120mm")
+for s in species:
+    axes[0].plot(
+        total_ribosome,
+        df.select(pl.col(s) / pl.col("total TF")),
+        label=s,
+        **next(cycle),
+    )
+
+axes[0].format(title="TF")
+
+species = ["TFR", "R"]
+for s in species:
+    axes[1].plot(
+        total_ribosome,
+        df.select(pl.col(s) / pl.col("total R")),
+        label=s,
+        **next(cycle),
+    )
+axes[1].format(title="ribosome")
+
+axes.format(
+    ylim=(0, 1),
+    # xscale="log",
+    xformatter="sci",
+    ylabel="Fractional population",
+    xlabel="Total protomer TF (uM)",
+)
+axes.legend(loc="r", ncols=1)
+
+# %%