Cells and Cancer in Python



















import matplotlib.pyplot as plt

import numpy as np


# Plot 1: Order Parameter vs Time (S vs t)

t = np.linspace(0, 10, 500)

S = 1 / (1 + np.exp(-2 * (t - 5)))  # sigmoid rise

plt.figure()

plt.plot(t, S)

plt.title("Order Parameter S vs Time")

plt.xlabel("Time (t)")

plt.ylabel("Order Parameter (S)")

plt.grid(True)

plt.show()


# Plot 2: Energy Collapse

E = np.maximum(0, 1 - 0.1 * t**1.5)

plt.figure()

plt.plot(t, E, color='red')

plt.title("Cellular Energy (E) Collapse Over Time")

plt.xlabel("Time (t)")

plt.ylabel("Energy (E)")

plt.grid(True)

plt.show()


# Plot 3: Standing Wave Stability

x = np.linspace(0, 2*np.pi, 500)

standing_wave = np.sin(x) * np.cos(5 * x)

plt.figure()

plt.plot(x, standing_wave)

plt.title("Standing Wave Pattern Around DNA")

plt.xlabel("Distance")

plt.ylabel("Amplitude")

plt.grid(True)

plt.show()


# Plot 4: DNA Repair Rate vs Redox State

redox = np.linspace(0, 1, 100)

repair_rate = redox**2

plt.figure()

plt.plot(redox, repair_rate)

plt.title("DNA Repair Rate vs Redox State")

plt.xlabel("Redox State (R)")

plt.ylabel("Repair Rate")

plt.grid(True)

plt.show()


# Plot 5: Phase Space of Cell State

H, E = np.meshgrid(np.linspace(0, 1, 100), np.linspace(0, 1, 100))

S = H * E

plt.figure()

plt.contourf(H, E, S, levels=20, cmap='viridis')

plt.title("Phase Space of Order Parameter S(H, E)")

plt.xlabel("Hydration (H)")

plt.ylabel("Energy (E)")

plt.colorbar(label="Order Parameter S")

plt.show()


# Plot 6: Cell Collapse Threshold

M = np.linspace(0, 10, 100)

S_threshold = np.exp(-0.5 * M)

plt.figure()

plt.plot(M, S_threshold)

plt.title("Order Parameter S Collapse vs Mutation Load")

plt.xlabel("Mutation Load (M)")

plt.ylabel("Order Parameter S")

plt.grid(True)

plt.show()












 import matplotlib.pyplot as plt

import numpy as np


# Plot 7: Epigenetic Noise vs Environmental Stability

env_stability = np.linspace(0, 1, 100)

epigenetic_noise = 1 / (env_stability + 0.01)


plt.figure(figsize=(6, 4))

plt.plot(env_stability, epigenetic_noise, color='darkred')

plt.title("Epigenetic Noise vs Environmental Stability")

plt.xlabel("Environmental Stability (normalized)")

plt.ylabel("Epigenetic Noise (arbitrary units)")

plt.grid(True)

plt.tight_layout()

plt.show()


# Plot 8: Impedance Spectra of Cellular Order (mock frequency vs phase)

freq = np.logspace(0, 3, 100)

impedance = 1 / np.sqrt(1 + (freq / 10)**2)

phase_shift = -np.arctan(freq / 10)


plt.figure(figsize=(6, 4))

plt.semilogx(freq, phase_shift, label='Phase Shift', color='purple')

plt.title("Cellular Impedance Phase vs Frequency")

plt.xlabel("Frequency (Hz)")

plt.ylabel("Phase Shift (radians)")

plt.grid(True, which='both')

plt.tight_layout()

plt.show()


# Plot 9: Coupled DNA Wave Function Interference

x = np.linspace(0, 10, 500)

wave1 = np.sin(2 * np.pi * 0.5 * x)

wave2 = np.sin(2 * np.pi * 0.5 * x + np.pi / 3)

combined = wave1 + wave2


plt.figure(figsize=(6, 4))

plt.plot(x, wave1, '--', label='Wave 1')

plt.plot(x, wave2, '--', label='Wave 2')

plt.plot(x, combined, label='Constructive Interference', color='black')

plt.title("Coupled DNA Oscillations")

plt.xlabel("x (nm)")

plt.ylabel("Amplitude")

plt.legend()

plt.grid(True)

plt.tight_layout()

plt.show()


# Plot 10: Phase Transition Triggered by Temperature Rise

T = np.linspace(36, 42, 100)

S = 1 / (1 + np.exp(5 * (T - 39)))


plt.figure(figsize=(6, 4))

plt.plot(T, S, color='green')

plt.title("Order Parameter Collapse via Temperature")

plt.xlabel("Temperature (°C)")

plt.ylabel("Cellular Order Parameter (S)")

plt.grid(True)

plt.tight_layout()

plt.show()






import matplotlib.pyplot as plt

import numpy as np

import seaborn as sns

import pandas as pd

import random

from sklearn.decomposition import PCA

from sklearn.preprocessing import StandardScaler

from sklearn.datasets import make_blobs

from mpl_toolkits.mplot3d import Axes3D

import ace_tools as tools


# Simulate cell type data with 6 environmental/biophysical features: 

# Hydration (H), Ion gradient (I), Energy availability (E), Redox potential (R), Chromatin order (C), Thermal stress (T)

cell_types = [

    "Neuron", "Cardiomyocyte", "Hepatocyte", "Beta Cell",

    "Skin Epithelial", "Hematopoietic Stem Cell", "Macrophage",

    "Fibroblast", "Adipocyte", "Osteocyte", "T-cell", "B-cell"

]


n_cells = len(cell_types)

features = ["Hydration", "Ion Gradient", "Energy", "Redox", "Chromatin Order", "Thermal Stress"]

n_features = len(features)


# Random but reasonable synthetic data for each cell type

np.random.seed(42)

data = np.clip(np.random.normal(loc=0.5, scale=0.15, size=(n_cells, n_features)), 0, 1)

df = pd.DataFrame(data, columns=features)

df["Cell Type"] = cell_types


# 3D PCA projection

scaler = StandardScaler()

scaled_data = scaler.fit_transform(df[features])

pca = PCA(n_components=3)

pca_result = pca.fit_transform(scaled_data)


fig = plt.figure(figsize=(10, 7))

ax = fig.add_subplot(111, projection='3d')

colors = sns.color_palette("hsv", n_cells)


for i, cell in enumerate(cell_types):

    ax.scatter(pca_result[i, 0], pca_result[i, 1], pca_result[i, 2], color=colors[i], label=cell, s=60)


ax.set_title("3D PCA of Biophysical Profiles of Human Cell Types")

ax.set_xlabel("PC1")

ax.set_ylabel("PC2")

ax.set_zlabel("PC3")

ax.legend(bbox_to_anchor=(1.05, 1), loc='upper left')

plt.tight_layout()


tools.display_dataframe_to_user(name="Cell Biophysical Profiles", dataframe=df)


plt.show()














import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

from sklearn.decomposition import PCA


# Manually recreate the DataFrame for modeling cell types

data = {

    "Cell_Type": ["Neuron", "Hepatocyte", "Cardiomyocyte", "Pancreatic Beta Cell", "Epithelial Cell", "Hematopoietic Stem Cell"],

    "Hydration_H": [0.9, 0.7, 0.8, 0.85, 0.75, 0.88],

    "Ion_Concentration_I": [0.8, 0.75, 0.7, 0.85, 0.8, 0.9],

    "Energy_E": [0.9, 0.8, 0.85, 0.95, 0.7, 0.92],

    "Redox_R": [0.85, 0.8, 0.75, 0.9, 0.65, 0.9],

    "Crowding_C": [0.75, 0.9, 0.85, 0.7, 0.8, 0.78]

}


df = pd.DataFrame(data)


# Plot each cell type individually using raw features

import seaborn as sns

import matplotlib.pyplot as plt

import ace_tools as tools


for index, row in df.iterrows():

    values = row[1:].values.astype(float)

    labels = row.index[1:]

    

    plt.figure(figsize=(8, 5))

    sns.barplot(x=labels, y=values, palette="viridis")

    plt.ylim(0, 1)

    plt.title(f"{row['Cell_Type']} Biophysical Profile")

    plt.ylabel("Normalized Feature Value")

    plt.xlabel("Biophysical Features")

    plt.grid(True)

    plt.tight_layout()

    plt.show()















import matplotlib.pyplot as plt

import numpy as np

import pandas as pd

import seaborn as sns

from IPython.display import display


# Define cell types and biophysical parameters

cell_types = [

    "Hematopoietic Stem Cell", "Pancreatic Beta Cell", "Neuron",

    "Epithelial Cell", "Hepatocyte", "Cardiomyocyte"

]


# Normal state values (H, I, E, R, C)

normal_values = np.array([

    [0.8, 0.85, 0.9, 0.88, 0.75],  # HSC

    [0.7, 0.75, 0.95, 0.85, 0.7],   # Beta

    [0.9, 0.9, 0.85, 0.95, 0.6],    # Neuron

    [0.65, 0.7, 0.75, 0.7, 0.9],    # Epithelial

    [0.85, 0.8, 0.8, 0.7, 0.75],    # Hepatocyte

    [0.88, 0.9, 0.9, 0.85, 0.65]    # Cardiomyocyte

])


# Cancer state as a collapse in hydration, energy, and redox

cancer_values = normal_values.copy()

cancer_values[:, [0, 2, 3]] *= 0.4  # Reduce H, E, R


# Plotting

params = ['Hydration', 'Ion Conc.', 'Energy', 'Redox', 'Crowding']

x = np.arange(len(params))

width = 0.35


for i, cell in enumerate(cell_types):

    fig, ax = plt.subplots(figsize=(8, 5))

    ax.bar(x - width/2, normal_values[i], width, label='Normal')

    ax.bar(x + width/2, cancer_values[i], width, label='Cancer')

    ax.set_ylabel('Normalized Value')

    ax.set_title(f'Biophysical Profile: {cell}')

    ax.set_xticks(x)

    ax.set_xticklabels(params)

    ax.set_ylim(0, 1.1)

    ax.legend()

    plt.tight_layout()

    plt.show()




import matplotlib.pyplot as plt

import numpy as np


# Parameters representing normal neuronal state

labels = ['Hydration (H)', 'Ionic Stability (I)', 'Energy (E)', 'Redox Balance (R)', 'Chromatin Order (C)']

normal = np.array([0.95, 0.9, 0.9, 0.9, 0.95])


# Parameters representing Alzheimer’s-affected neurons

alzheimers = np.array([0.6, 0.5, 0.4, 0.3, 0.5])


x = np.arange(len(labels))  # Label locations

width = 0.35  # Bar width


fig, ax = plt.subplots(figsize=(10, 6))

rects1 = ax.bar(x - width/2, normal, width, label='Normal Neuron')

rects2 = ax.bar(x + width/2, alzheimers, width, label='Alzheimer\'s Neuron')


# Labels and formatting

ax.set_ylabel('Relative Stability (0 to 1)')

ax.set_title('Biophysical Profile of Neurons: Normal vs Alzheimer\'s')

ax.set_xticks(x)

ax.set_xticklabels(labels)

ax.set_ylim(0, 1.1)

ax.legend()

ax.grid(axis='y', linestyle='--', alpha=0.6)


plt.tight_layout()

plt.show()







import matplotlib.pyplot as plt

import numpy as np


# Simulated data for phase shift recovery

parameters = ["Hydration (H)", "Ionic Stability (I)", "Energy (E)", "Redox Balance (R)", "Chromatin Order (C)"]

baseline = np.array([0.3, 0.4, 0.35, 0.3, 0.4])  # Alzheimer's profile

restored = np.array([0.9, 0.85, 0.95, 0.9, 0.88])  # Post-phase-shift restored neuron


# Calculate total order parameter S as average

S_baseline = np.mean(baseline)

S_restored = np.mean(restored)


# Plot 1: Phase shift required for neuron recovery

fig1, ax1 = plt.subplots(figsize=(10, 6))

x = np.arange(len(parameters))

width = 0.35

ax1.bar(x - width/2, baseline, width, label='Alzheimer Neuron', color='darkred')

ax1.bar(x + width/2, restored, width, label='Post-Phase-Shift', color='darkgreen')

ax1.set_ylabel('Normalized Parameter Value')

ax1.set_title('Phase Shift in Biophysical Parameters for Neuronal Recovery')

ax1.set_xticks(x)

ax1.set_xticklabels(parameters)

ax1.axhline(S_baseline, color='red', linestyle='--', label=f'S (Alz) = {S_baseline:.2f}')

ax1.axhline(S_restored, color='green', linestyle='--', label=f'S (Restored) = {S_restored:.2f}')

ax1.legend()

ax1.grid(True)


# Plot 2: Energy required to induce the phase shift

# Assuming arbitrary unit energy cost per parameter increase for illustration

energy_cost = (restored - baseline) * 10  # Arbitrary 10 units per parameter delta

total_energy = np.sum(energy_cost)


fig2, ax2 = plt.subplots(figsize=(10, 6))

ax2.bar(parameters, energy_cost, color='orange')

ax2.set_ylabel('Energy Input (Arbitrary Units)')

ax2.set_title(f'Total Energy Required for Phase Shift: {total_energy:.2f} Units')

ax2.grid(True)


plt.show()


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