Sunday, July 27, 2025

Bioengineer

 Inspired by this post I went down the chatgpt rabbithole and made a ecoli-design-lab react app.

ecoli-gfp-simulator

Series Title: "E. coli Design" — DNA as an Engineering Language

Premise: Anyone can learn to program biology. DNA is code. Watch as we write it, transform cells, and literally see it change the behavior of life.


๐Ÿ“ฆ Intro Video: The Blueprint of Life (aka DNA = Code)

  • Set the vision: “You’ve seen code run on a computer. What if we could run code on a living cell?”

  • Show E. coli swimming, glowing, changing behavior — all controlled by synthetic DNA.

  • Core ideas: promoter, RBS, CDS, terminator — these are the "functions" of biological programming.


๐Ÿงช Module 1: Make E. coli Glow

"Your first genetic program: lighting up a cell."

  • Construct a simple transcription unit: constitutive promoter + GFP + terminator.

  • Use a standard vector (e.g., pSB1C3 or pET series).

  • Transform E. coli → plate → grow → view under blue light.

  • Discuss how the DNA sequence becomes mRNA → protein → observable trait.

Learning goals:

  • Plasmid design

  • Bacterial transformation

  • Why a promoter matters

  • Fluorescence basics


๐ŸŒˆ Module 2: Change GFP Color Using a Base Editor

"A few letters changed in DNA... and the color shifts. Welcome to molecular editing."

  • Use a base editor (e.g. CRISPR-Cas9 nickase fused to a cytidine or adenine deaminase).

  • Target specific codons in GFP to create YFP or BFP variants.

  • Use fluorescence imaging to compare.

Learning goals:

  • Codon changes and amino acids

  • Introduction to CRISPR base editing

  • Mutation as a design tool


๐ŸŒ€ Module 3: Make E. coli Spin

"Let's reprogram motility."

  • Express cheY mutant that biases flagellar rotation.

  • Could include chemotaxis circuit tweaks.

  • Cells "tumble" in place instead of swimming forward.

Learning goals:

  • Bacterial locomotion

  • Signaling pathways

  • Flagellar motor basics


๐Ÿ’จ Module 4: Speed, Size, and Shape

"What if cells moved faster? Or just... got big?"

  • Overexpress motA/motB to boost motility.

  • Express ftsZ mutants or inhibit division (e.g., SulA) to make long filaments.

  • Add plasmids that affect cell wall biosynthesis to tweak shape (e.g., induce bulges).

Learning goals:

  • Cell morphology

  • Cell division machinery

  • Engineering metabolic load


๐Ÿงฌ Module 5: Uneven DNA Partitioning

"Can we break symmetry in cell division?"

  • Play with Par system or delete minCDE to disrupt mid-cell division.

  • Watch daughter cells with uneven contents — some die, some thrive.

Learning goals:

  • Chromosome segregation

  • Developmental biology in microbes

  • Fitness trade-offs


⏱️ Final Module: The Repressilator – Blinking Life

"A genetic oscillator made from DNA logic."

  • Construct the classic repressilator (LacI-TetR-cI feedback loop).

  • Observe time-lapse microscopy of fluorescence oscillations.

  • Sync multiple cells via quorum sensing?

Learning goals:

  • Synthetic gene circuits

  • Feedback and control theory in biology

  • Temporal behavior from static DNA


๐Ÿ“ธ Gear Checklist

EquipmentPurpose
Basic IncubatorGrow E. coli at 37°C
Centrifuge (mini)Plasmid preps, transformations
Gel ElectrophoresisVerify PCR, plasmid digests
Blue Light Transilluminator + FilterView GFP and variants
Fluorescence-capable Microscope + CameraVisualize cell behavior
ThermocyclerPCR, Gibson Assembly
Pipettes + TipsMolecular biology basics
LB + Antibiotics + AgarMedia for growth/selection

(You can simplify with prebuilt kits for beginners, like BioBits or Amino Labs.)


๐ŸŽฏ Series Goals

  • Demystify synthetic biology

  • Empower a new generation of bioengineers

  • Show DNA as an intuitive, visual programming language

  • Encourage creativity in biology

  • Bridge DIYBio with formal education


๐Ÿš€ Bonus Ideas for Expansion

  • Let viewers submit gene designs and test them in real cells

  • Simulations before wet-lab (e.g., "predict what happens if we double promoter strength")

  • Host challenges: "Design a toggle switch", "Create an E. coli pattern", etc.

  • Feature guest modules by researchers and community labs


Would you like help developing a script, lesson plan, or materials for one of these modules? Or even mock up visuals or diagrams for the videos?

You said:
are there any simulators that can do this?
ChatGPT said:

Yes — there are several simulators and digital tools that can help you design, simulate, and predict gene expression and synthetic circuits in E. coli. Some even let you visualize expected behaviors like fluorescence intensity, circuit oscillations, or protein levels over time.

Here’s a breakdown of the most useful ones for the kind of E. coli Design series you're thinking of:


๐Ÿงช 1. iBioSim

Best for: Genetic circuits, oscillators (like the repressilator), logic gates

  • A visual synthetic biology design tool that simulates genetic networks using ODEs or stochastic models.

  • You can drag-and-drop parts (promoters, genes, repressors), and simulate time-course data (e.g., how GFP oscillates).

  • Supports SBOL (Synthetic Biology Open Language), which is an open standard for sharing biological designs.

๐ŸŒ https://github.com/MyersResearchGroup/iBioSim
๐Ÿ’ป Java-based, open-source


๐Ÿงฌ 2. CellDesigner

Best for: Modeling biochemical networks & genetic regulation

  • Not E. coli–specific, but you can build models of metabolic and gene regulatory networks, with kinetic simulation.

  • Great for visualizing pathways, feedback loops, and seeing how changing parameters affects outcomes.

๐ŸŒ http://www.celldesigner.org/
๐Ÿ’ป Free, desktop app (Windows/macOS/Linux)


๐Ÿงซ 3. Tinkercell (discontinued but usable)

Best for: Drag-and-drop circuit design for synthetic biology

  • Was designed as a visual platform for synthetic biology education.

  • Lets you model transcriptional units, simulate gene expression, and play with circuit logic.

  • Though it's no longer actively developed, it still works on many systems.

๐ŸŒ https://www.tinkercell.com/
๐Ÿ’ป Windows/Linux (may require compatibility settings)


๐Ÿ“ˆ 4. COPASI (COmplex PAthway SImulator)

Best for: Detailed biochemical + gene regulation simulations

  • Can simulate gene expression dynamics, enzyme kinetics, and reactions.

  • Has stochastic and deterministic solvers.

  • Not made for synthetic biology per se, but with effort, you can simulate things like repressilators or toggle switches.

๐ŸŒ https://copasi.org/
๐Ÿ’ป Cross-platform


๐Ÿงฌ 5. BioCRNpyler + bioscrape (for Python users)

Best for: Programmable, modular synthetic biology simulation

  • BioCRNpyler: Build CRNs (Chemical Reaction Networks) from genetic part libraries.

  • bioscrape: Fast simulation of gene circuits, with deterministic + stochastic options.

  • Great for coders who want to automate or simulate many designs programmatically.

๐ŸŒ https://github.com/BuildACell/bioscrape
๐ŸŒ https://github.com/BuildACell/BioCRNpyler
๐Ÿ’ป Python-based


๐Ÿ‘จ‍๐Ÿซ 6. Cello 2.0 (Logic Circuits to DNA)

Best for: Designing logic circuits that get compiled into real DNA sequences

  • You input a logic truth table (e.g. “IF A AND NOT B, THEN express GFP”) and Cello turns it into a genetic circuit using pre-characterized parts.

  • Simulates performance in silico and outputs GenBank-ready plasmid maps.

๐ŸŒ https://cellocad.org/
๐Ÿ’ป Web-based, cloud simulation


๐ŸŽฎ 7. Biota or Gene Game–style Apps (limited)

There are experimental or educational games (like Foldit or Eterna for RNA), but fewer aimed at bacterial gene circuit engineering. However, some tools/games are being prototyped (like “Living Computers” or “Cell Architect”) and might evolve in that direction.


๐Ÿ”„ Combine With:

  • Benchling or SnapGene for DNA design (no simulation, but integrates well)

  • SBOL Designer for standardized design diagrams

  • Google Colab + Python for building your own simulators with packages like Tellurium or PySB


✅ Recommendation for Beginners:

  • Start with iBioSim or Cello 2.0 if you want to visually build circuits and simulate how they'll behave.

  • For hands-on or coding-literate users, bioscrape + BioCRNpyler gives you real modeling power.


Would you like a starter template in one of these tools (like the repressilator or GFP construct)? I can mock one up for you or walk you through setting it up.

You said:
sure
ChatGPT said:

Great! Let’s start with a simple and visual repressilator model using iBioSim — one of the most accessible tools for beginners who want to simulate real synthetic biology circuits without needing to write code.


๐Ÿงฌ What We'll Build:

The Repressilator — a synthetic gene oscillator made of 3 genes:

  • LacI represses TetR

  • TetR represses cI

  • cI represses LacI

Each gene is transcribed and translated, and the resulting proteins repress the next gene in a loop — leading to oscillations (like blinking GFP).


๐Ÿงฐ Step-by-Step: Building the Repressilator in iBioSim

Step 1: Download iBioSim

Let me know if you hit any Java install/setup snags — I can walk you through those.


Step 2: Start a New Project

  • Click: File → New → Project

  • Name it: Repressilator

  • Click "Create"


Step 3: Add Species (Proteins)

  1. Open the project and click Model Editor

  2. Add species:

    • LacI (protein)

    • TetR (protein)

    • cI (protein)

These will each represent repressors that inhibit the next gene in the loop.


Step 4: Add Reactions

We’ll simulate simplified gene expression + repression (no full transcriptional detail for now):

  1. LacI production

    • Reaction: null → LacI

    • Rate: alpha1 / (1 + (cI/K)^n)

  2. TetR production

    • Reaction: null → TetR

    • Rate: alpha2 / (1 + (LacI/K)^n)

  3. cI production

    • Reaction: null → cI

    • Rate: alpha3 / (1 + (TetR/K)^n)

  4. Degradation for each

    • LacI → null, rate: delta * LacI

    • TetR → null, rate: delta * TetR

    • cI → null, rate: delta * cI

You’ll enter these in the Reaction View by clicking “+ Add Reaction” and specifying the kinetic laws.


Step 5: Set Parameters

Add the following global parameters:

ParameterValueDescription
alpha1, alpha2, alpha350Max production rate
K40Repression threshold
n2Hill coefficient (cooperativity)
delta1.0Degradation rate

These values are from the original repressilator paper and should produce oscillations.


Step 6: Simulate

  • Go to Simulation tab

  • Time: 0 → 500

  • Click “Simulate”

๐ŸŒ€ You should see oscillations in the levels of LacI, TetR, and cI over time — out of phase like a clock.


๐Ÿ“ธ Next Step: Add GFP as Output

To make the circuit visible under a microscope:

  • Add GFP as a species.

  • Add a reaction: null → GFP

    • Rate: alphaGFP / (1 + (cI/K)^n)

  • Add degradation: GFP → null, rate: delta * GFP

Now GFP will blink in sync with one of the repressors!


✅ Want the .xml or .sbml project file?

I can generate a working iBioSim project file for the repressilator and send it to you (or show you what the SBML looks like). If you're using Python instead (bioscrape, etc.), I can port it too.

Would you prefer:

  • A downloadable iBioSim project

  • A Python bioscrape simulation

  • Or both?

Let me know what system you’re working on (Windows/macOS/Linux) and whether you prefer GUI-based or code-based modeling.

You said:
gui based modeling that is open without requiring login
ChatGPT said:

Perfect — in that case, here are the best GUI-based, open-source, no-login-required tools for simulating genetic circuits like the repressilator visually. I'll also provide direct download links and usage notes to get you started today.


Best Option: iBioSim

๐Ÿงฌ Why it’s great:

  • Fully GUI-based — drag-and-drop genes, repressors, species

  • No login or online account required

  • Supports simulation of genetic circuits using deterministic or stochastic models

  • Can model oscillators, toggle switches, logic gates, etc.


๐Ÿ“ฆ How to Install and Launch:

  1. Install Java (if you haven’t yet):

  2. Download iBioSim:

  3. Run iBioSim:

    • Open terminal or command prompt

    • Navigate to the folder with the .jar file

    • Run:

      bash
      java -jar iBioSim-3.0.0.jar

      (Replace with actual filename)


๐Ÿงฌ Example: The Repressilator

If you'd like, I can provide you a ready-to-go project file for:

  • Repressilator (LacI →| TetR →| cI →| LacI)

  • Optional: GFP expression tied to one of the repressors for "blinking"

Would you like me to prepare and share a .gcm or .xml file you can import directly into iBioSim?


๐Ÿ‘จ‍๐Ÿซ Alternative Option: TinkerCell (Old but Educational)

⚠️ Notes:

  • Still works on some systems (mainly Windows/Linux)

  • Designed specifically for synthetic biology

  • Includes part libraries, promoter logic, repressors, etc.

  • Development stopped, but useful for offline demos and teaching

๐Ÿ”— Download: https://tinkercell.com/Downloads.html

(If you want help getting this running, I can guide you based on your OS.)


๐Ÿ“Œ Summary

ToolGUISimulates CircuitsOpen SourceOffline UseNotes
iBioSim✅ Yes (ODEs/stochastic)✅ Yes✅ YesBest maintained, powerful
TinkerCell✅ Basic logic & dynamics✅ Yes✅ YesEducational, but legacy
CellDesigner✅ Pathway-focused✅ Yes✅ YesLess synthetic-bio specific

➕ Bonus

If you confirm you'd like it, I’ll send you:

  • ๐Ÿ“ A ready-to-import iBioSim repressilator project file

  • ๐Ÿ“ธ Screenshots showing how to simulate and interpret the output

  • ๐Ÿ› ️ A guide to modifying the circuit (e.g., switch out repressors, add GFP)

Would you like that ZIP package? Also let me know what OS you're using (Windows/macOS/Linux), and I’ll tailor the files to that environment.

You said:
like phet simulations is there not a website where this whole or part of this thing could be implemented?
ChatGPT said:

Ah — now I understand exactly what you're asking. You're looking for something like PhET simulationsfully browser-based, visual, no-login, interactive simulations — but for synthetic biology or genetic circuit design, ideally with the ability to tweak DNA components and see how E. coli behavior changes.

TL;DR:

✅ Some tools kind of do this
❌ But nothing yet fully matches the PhET-level polish and simplicity for genetic circuit simulation in cells like E. coli — especially at the intersection of DNA editing → observable behavior (like swimming, glowing, or dividing).

That said, there are some close contenders — and I’ll outline those below, then explain how this could be built (which is very possible).


๐Ÿง  Closest Web-Based Simulators (Visual, No Login)

๐Ÿงฌ 1. Cello 2.0

  • Browser-based, free, no login

  • Build logic circuits using standard genetic parts (promoters, repressors, etc.)

  • Inputs: Truth tables → Outputs: DNA sequences and predicted behavior

  • Great for logic design (e.g., “IF A and NOT B, turn on GFP”)

๐ŸŸข Pros:

  • Realistic synthetic biology model

  • Visual circuit design

๐Ÿ”ด Cons:

  • Doesn’t simulate swimming, size, or physical traits

  • Focused on logic circuits, not behavior dynamics


๐Ÿ”ฌ 2. GenoCAD

  • Visual DNA sequence design using rules and part libraries

  • Lets you design transcription units

  • Web-based and intuitive

๐ŸŸข Pros:

  • Visual DNA design tool

  • Pre-built promoters, CDS, etc.

๐Ÿ”ด Cons:

  • No dynamic simulation (e.g., no blinking GFP, motility modeling)


๐Ÿ“Š 3. Virtual Biology Lab – Genetic Circuits

  • Some very basic simulators showing gene regulation principles

  • Sliders for repression, induction, etc.

  • More educational, less custom

๐ŸŸข Pros:

  • Purely browser-based, easy to use

๐Ÿ”ด Cons:

  • Oversimplified

  • Not usable for actual synthetic circuit design


⚙️ 4. Biosimulators.org

  • Directory of simulation tools that can run in the browser

  • Uses SBML, COMBINE archives, and BioSimulations platform

  • Advanced but fragmented — needs SBML input

๐ŸŸข Pros:

  • Open, standards-based

  • Can simulate many biological models

๐Ÿ”ด Cons:

  • Not PhET-like

  • Requires technical setup or model uploads


๐Ÿง  Why Doesn’t a PhET-Style E. coli Design Lab Exist Yet?

It really comes down to this:

  • Simulating DNA → protein → behavioral phenotype is computationally complex

  • Most tools focus on gene expression, metabolic modeling, or circuit logic

  • Physical traits (like swimming, size, blinking) require agent-based modeling or biomechanics


๐Ÿ”ฎ What Would a PhET-Style E. coli Design Simulator Look Like?

Core Features:

  • Drag-and-drop: Promoters, CDSs, repressors

  • Preview of plasmid/DNA map

  • Live output graph: GFP levels, cell growth, oscillations

  • Toggle between:

    • Fluorescence view (e.g., blinking GFP)

    • Behavior view (e.g., cells spinning or growing)

  • No login, runs in browser

Powered by:

  • SBOL/GenBank parser

  • Bioscrape/iBioSim backend

  • Agent-based modeling for physical behavior

  • WebGL or HTML5 canvas for live simulation


✅ Good News

Something like this absolutely could be built, and there’s growing momentum:

  • Community labs & DIY bio are hungry for tools like this

  • SBOL and BioCRNpyler provide the foundation

  • Visualizations could be built using p5.js or three.js

If you're interested, I could:

  • Mock up a concept UI for this type of simulator

  • Create a roadmap or open-source template for building it

  • Help you launch a prototype if you're developing this as a project


๐Ÿงฉ Summary Table

ToolBrowserNo LoginCircuit DesignPhenotype Simulation
Cello 2.0✅ Logic gates❌ No physical traits
GenoCAD✅ Transcription units
Virtual Bio Lab⚠️ Very simple
iBioSim (Java)✅ Advanced✅ (Gene-level only)
TinkerCell✅ Legacy✅ (limited)
Custom simulator๐Ÿšง✅ (Possible!)

Would you like a visual mock-up or early-stage prototype concept of this PhET-style E. coli designer? I'd be thrilled to help sketch it out with you.

You said:
Sure
ChatGPT said:

Awesome. Let's sketch a concept for a PhET-style, browser-based E. coli Design Lab — a simple, intuitive simulation where users can design DNA constructs and instantly see their impact on cell behavior.


๐ŸŽจ Concept: E. coli Design Lab (Interactive Simulator)

Tagline:
“Write DNA. Watch cells glow, blink, swim, or grow.”


๐Ÿงฑ Core Interface (3-Pane Layout)

less
+--------------------------------------------+ | [DNA DESIGN PANEL] | | Drag: Promoter ▢ | RBS ▢ | CDS ▢ | Term ▢ | | | | [Your Construct:] | | [ ▢ Promoter ][ ▢ RBS ][ ▢ GFP ][ ▢ T ]| | | +--------------------------------------------+ | [SIMULATION VIEW] | [OUTPUT GRAPH] | | (E. coli cells in dish) | GFP Levels over time | | ๐Ÿฆ ๐Ÿฆ ๐Ÿฆ ๐Ÿฆ  glowing/oscillating | ๐Ÿ“ˆ๐ŸŸฉ⬆⬇ Oscillation curve | +----------------------------+--------------------------+

๐Ÿ”„ What You Can Do

ActionResult
Drag-and-drop parts into a constructDNA design is assembled
Choose a promoter strength (e.g. weak/medium/strong)Changes transcription rate
Choose a CDS (GFP, RFP, MotA, CheY, etc.)Changes what the cell expresses
Press "Simulate"Cells respond to DNA — glow, blink, swim
View Output GraphShows expression level or behavior over time
Add logic (repressor → target gene)Builds repressilators, toggle switches

๐ŸŒˆ Example Modules

✅ Module 1: Make Cells Glow

  • Drag: [Strong Promoter] — [RBS] — [GFP] — [Terminator]

  • Press simulate → E. coli on screen begin to glow!

๐Ÿ” Module 2: Blinking Cells (Repressilator)

  • Add LacI → TetR → cI → represses LacI

  • Tie GFP to one repressor

  • Output: Cells blink every ~90 seconds

๐ŸŒ€ Module 3: Spinning Cells

  • Use CDS: cheY D13K mutant

  • Simulate: Cells randomly tumble or spin in place


๐Ÿ”ง Technical Architecture (Behind the Scenes)

ComponentTech
Frontend GUIReact or Vue.js with drag-and-drop UI
DNA ParserSBOL.js or custom GenBank builder
Simulation EngineWebAssembly backend using bioscrape, tellurium, or custom CRN solver
VisualizationHTML5 Canvas or p5.js for cells, Chart.js for output
Cell BehaviorSimple agent-based model (motility, growth)

๐ŸŽฏ Goals for the Simulator

  • Zero install, no login, runs in browser

  • Ideal for high schools, intro bioengineering classes, and DIYers

  • Build intuition: DNA = behavior

  • Open-source and embeddable in educational sites


๐Ÿ“ธ Mockup Example (Text-based)

Imagine seeing this:

less
Your Construct: [Promoter (strong)][RBS][GFP][Terminator] [Simulate] ๐Ÿฆ ๐Ÿฆ ๐Ÿฆ ๐Ÿฆ ๐Ÿฆ ๐Ÿฆ ๐Ÿฆ  ← Cells begin glowing green! ๐Ÿ“ˆ Fluorescence over time: rising curve

Or this:

less
Your Construct: [Promoter][RBS][LacI] [Promoter (lac repressed)][RBS][GFP] [Simulate] ๐Ÿฆ ๐Ÿฆ ๐Ÿฆ ๐Ÿฆ  ← Cells glow only when IPTG (input) is added ๐Ÿ“ˆ Output toggles ON/OFF

๐Ÿ”ง Build This?

This simulator could be made by:

  • Using open SBML/SBOL parsers

  • Integrating bioscrape or a minimal CRN simulator in WebAssembly

  • Modeling cells as agents (like in NetLogo or p5.js)

  • Open-source, hosted on GitHub Pages


๐Ÿš€ Next Steps (If You're Interested)

  1. Prototype UI sketch (I can create a wireframe or interactive mockup)

  2. Open-source repo template (with DNA drag-and-drop + basic simulation)

  3. Collab with educators, DIYBio labs to test and iterate

Would you like me to:

  • Build a UI wireframe mockup?

  • Outline how to build a MVP (minimal viable product) version?

  • Help you start a GitHub repo or project page?

Let me know your focus — education, research, open source, etc. — and I’ll tailor the next steps.

You said:
sure github repo
ChatGPT said:

Awesome! Here's a simple plan and starter code to kick off an open-source GitHub repo for this E. coli Design Lab simulator, focused on drag-and-drop DNA design and simple dynamic visualization — all running in the browser, no login needed.


๐Ÿš€ Repo Plan: ecoli-design-lab

๐ŸŽฏ Goals

  • Browser-based (React + JavaScript)

  • Drag-and-drop DNA parts (promoter, RBS, CDS, terminator)

  • Visualize simple gene expression (e.g., GFP fluorescence over time)

  • Simulate repressilator-style oscillations (basic ODE solver in JS)

  • Modular & extensible for adding behaviors (motility, growth)


๐Ÿ› ️ Tech Stack

PartTech/Library
UI FrameworkReact.js
Drag-and-DropReact DnD or React-Beautiful-DnD
PlottingChart.js or Recharts
Simulation EngineSimple JS ODE solver or integrate WASM version of bioscrape
VisualizationHTML5 Canvas or SVG

๐Ÿ”– Repo Structure (initial)

bash
/ecoli-design-lab │ ├── public/ │ └── index.html │ ├── src/ │ ├── components/ │ │ ├── DNADesigner.jsx # Drag-and-drop DNA parts │ │ ├── CellSimulation.jsx # Canvas visualization of cells & GFP glow │ │ ├── OutputGraph.jsx # Plots expression over time │ │ └── Controls.jsx # Simulate button, parameter sliders │ │ │ ├── simulation/ │ │ └── odeSolver.js # Basic ODE solver for gene circuits │ │ │ ├── data/ │ │ └── dnaParts.js # List of parts with properties │ │ │ ├── App.jsx │ └── index.js │ ├── package.json └── README.md

๐Ÿ“ฆ Starter Code Snippet: Simple React ODE Simulator

jsx
// src/simulation/odeSolver.js export function runRepressilator(tMax, dt, params) { // Simple Euler solver for repressilator ODEs // Variables: LacI, TetR, cI concentrations let {alpha, K, n, delta} = params; let t = 0; let LacI = 0, TetR = 0, cI = 0; let results = []; while (t < tMax) { let dLacI = alpha / (1 + Math.pow(cI / K, n)) - delta * LacI; let dTetR = alpha / (1 + Math.pow(LacI / K, n)) - delta * TetR; let dCI = alpha / (1 + Math.pow(TetR / K, n)) - delta * cI; LacI += dLacI * dt; TetR += dTetR * dt; cI += dCI * dt; results.push({t, LacI, TetR, cI}); t += dt; }

No comments: