Scientific Writing

Creates publication-quality markdown documents with mathematical rigor and visual clarity.

Core Principles

1. •Concision: Every sentence must earn its place
2. •Structure: Logical flow with clear hierarchies
3. •Precision: Technical accuracy over verbosity
4. •Integration: Seamlessly embed figures and equations
5. •Clarity: Complex ideas expressed simply

Document Structure

Standard Template

# [Descriptive Title]

## Summary
[2-3 sentences: what was done, key finding, significance]

## Methods
[Essential details only - enough to reproduce]

## Results
[Observations → Data → Interpretation]

### [Subsection 1]
[Finding with supporting figure/equation]

### [Subsection 2]
[Finding with supporting figure/equation]

## Discussion
[Implications, limitations, future directions - 1 paragraph max]

Section Guidelines

Summary (3-5 lines)

• •First sentence: what you investigated
• •Second sentence: how you investigated it
• •Third sentence: what you found
• •NO background or motivation

Methods (minimal)

• •Only non-standard procedures
• •Reference standard protocols by name
• •Use lists for clarity

Results (core content)

• •Lead with observation, follow with data
• •One finding per subsection
• •Figure/equation immediately after relevant text
• •NO speculation (save for Discussion)

Discussion (1 paragraph)

• •Interpret in broader context
• •State limitations explicitly
• •Suggest next steps

Writing Style Rules

Concision Tactics

Before (wordy):

The results that we obtained from the experiment clearly demonstrate that there is a significant increase in the fluorescence intensity.

After (concise):

Fluorescence intensity increased 3.2-fold (p < 0.001).

Common eliminations:

• •❌ "It is important to note that..."
• •❌ "The results clearly demonstrate..."
• •❌ "As can be seen from the figure..."
• •❌ "In order to..." → ✅ "To..."
• •❌ "Due to the fact that..." → ✅ "Because..."

Active Voice

• •✅ "We measured force using AFM"
• •❌ "Force was measured using AFM"
• •✅ "Cells exhibited biphasic dynamics"
• •❌ "Biphasic dynamics were exhibited by cells"

Precision

Vague: "The protein concentration was high" Precise: "Protein concentration was 2.5 mg/mL"

Vague: "Cells responded quickly" Precise: "Cells responded within 30 s"

LaTeX Equations

Inline Math

Use $...$ for inline equations:

The diffusion coefficient $D = 0.43 \pm 0.05 \, \mu\text{m}^2/\text{s}$ indicates...

Display Math

Use $$ with \begin{} and \end{} for block equations:

The force balance is described by:

$$
\begin{equation}
F_{\text{total}} = F_{\text{spring}} + F_{\text{drag}} = kx + \gamma \frac{dx}{dt}
\end{equation}
$$

where $k$ is the spring constant and $\gamma$ is the drag coefficient.

Equation Environments

Common environments:

• •equation - Single numbered equation
• •align - Multiple aligned equations
• •split - Split long equations across lines

Examples:

$$
\begin{align}
\sigma_{xx} &= E \epsilon_{xx} \\
\sigma_{yy} &= E \epsilon_{yy}
\end{align}
$$

Equation Style

Good practices:

• •Define all variables immediately after equation
• •Use \text{} for words in equations: $F_{\text{max}}$
• •Use proper spacing: \, for thin space (units)
• •Use equation environment for automatic numbering

Example:

The relationship between stress $\sigma$ and strain $\epsilon$ follows:

$$
\begin{equation}
\sigma = E \epsilon
\end{equation}
$$

where $E = 5 \pm 0.3$ kPa is the Young's modulus.

Figure Integration

Workflow

1. •Generate figure during analysis (follow python-coding-standards)
2. •Save as SVG in figures/ folder
3. •Reference immediately after relevant text
4. •Caption format: statement of finding, not description

Figure Template

Force increased linearly with deformation up to 20% strain, then plateaued (Figure 1).

![Force-deformation relationship](figures/force_vs_strain.svg)
**Figure 1.** Linear stress-strain response transitions to plateau regime at ε > 0.2.

Caption Guidelines

Bad (descriptive):

Figure 1. A plot showing force on the y-axis and deformation on the x-axis.

Good (interpretive):

Figure 1. Force increases linearly with deformation until strain exceeds 0.2.

Best (finding):

Figure 1. Biphasic mechanical response reveals strain-stiffening at ε > 0.2.

Multiple Panels

For multi-panel figures:

![Analysis overview](figures/analysis_overview.svg)
**Figure 2.** Cell morphology changes with substrate stiffness. **(A)** Representative images on soft (1 kPa), medium (10 kPa), and stiff (100 kPa) substrates. **(B)** Quantification shows area increases 2.5-fold from soft to stiff. **(C)** Aspect ratio decreases with stiffness (p < 0.001, n = 150 cells per condition).

Data Presentation

Tables (use sparingly)

Only when comparing multiple conditions across multiple metrics:

| Condition | Spring Constant (pN/nm) | Relaxation Time (s) | n |
|-----------|------------------------|---------------------|---|
| Control   | 12.3 ± 1.2            | 45 ± 8             | 23 |
| Drug A    | 8.7 ± 0.9*            | 67 ± 12*           | 21 |
| Drug B    | 15.1 ± 1.8            | 38 ± 6             | 19 |

*p < 0.05 vs. control

Table caption: Place above table, descriptive

Inline Data

For single comparisons, embed in text:

Treatment increased velocity from 0.23 ± 0.03 to 0.41 ± 0.05 μm/s (p < 0.001, n = 45).

Common Patterns

Introducing Analysis

Pattern: Goal → Approach → Key result

To determine whether force depends on loading rate, we performed constant-velocity indentation at speeds from 0.1 to 10 μm/s. Peak force scaled linearly with velocity (Figure 3A), consistent with viscoelastic behavior.

Quantitative Results

Pattern: Observation → Measurement → Statistics

Cells on stiff substrates adopted elongated morphologies. Aspect ratio increased from 1.8 ± 0.2 (soft) to 3.4 ± 0.4 (stiff), a 1.9-fold change (p < 0.001, n = 120 cells, Figure 2B).

Model Validation

Pattern: Model → Prediction → Test → Result

If force transmission is primarily via focal adhesions, disrupting integrin binding should reduce traction forces. We treated cells with RGD peptide and measured a 73% reduction in traction stress (Figure 4), confirming integrin-mediated adhesion.

Checklist

Before finalizing document:

• • Summary states finding in 3 sentences
• • No sentence exceeds 25 words
• • All equations defined immediately after appearance
• • Figures referenced in text before appearing
• • Figure captions state findings, not descriptions
• • NO phrases: "clearly", "obviously", "it is important to note"
• • NO repetition between sections
• • Methods include only non-standard details
• • Discussion is ≤ 1 paragraph
• • All data includes uncertainty and sample size
• • Active voice used throughout

Quick Reference

Numbers and Units

• •Use ± for uncertainty: 5.2 ± 0.3 kPa
• •Thin space before units: 10 \, \mu\text{m}
• •Scientific notation for extremes: $3.2 \times 10^{-6}$
• •Significant figures match precision

Common Abbreviations

First use: full term (abbreviation)

Atomic force microscopy (AFM) measurements revealed...

Subsequent: abbreviation only

AFM images showed...

References

Inline citation:

Previous studies^[1,2]^ demonstrated...

End of document:

## References

1. Smith et al. (2023) Nature 612: 123-130
2. Jones et al. (2022) Science 378: 456-460

Anti-Patterns

Avoid Redundancy

Bad:

Figure 1 shows the force-distance curve. As can be seen in Figure 1, force increases with distance. The figure clearly demonstrates that...

Good:

Force increased linearly with distance (Figure 1).

Avoid Throat-Clearing

Bad:

It is important to note that our results suggest that it may be possible that cells potentially exhibit...

Good:

Cells exhibit viscoelastic behavior.

Avoid Over-Qualification

Bad:

The data appear to suggest that there might be a possible trend toward increased stiffness.

Good:

Stiffness increased 1.8-fold (p = 0.03).