Math gives us a language for patterns. Physics describes the constraints on matter and energy. Biology asks how living systems maintain themselves, pass on information, evolve and interact—within those constraints, with a history that matters.
12connected branchesDifferent scales of the living world
10chaptersA path with room to explore
3interactive modelsDiffusion, inheritance and growth
THE LIVING WORLD / A CONNECTED ATLAS
One living world. Many ways to study it.
Select a star to explore an idea, its study connections and its applications. The rings suggest approximate study levels; advanced topics are not all unsolved, and every branch contains open research.
This is a curated atlas. The routes are suggested learning paths, and the dependency links are useful connections rather than a complete account of biology.
A useful explanation identifies what is being explained and at what scale. Knowing a molecule's structure, a cell's response and a population's history answers different questions.
Molecule
An enzyme catalyzes a reaction.
How do structure, chemistry and the environment affect what it does?
Cell
A membrane separates an internal environment from its surroundings.
How are energy, materials and signals exchanged?
Organism
Organs coordinate transport, movement and regulation.
How do parts maintain a functioning whole?
Population
Individuals reproduce, compete and vary.
How do abundance and inherited traits change across generations?
Ecosystem
Organisms interact with one another and their physical environment.
How do energy, matter and disturbances move through the system?
Mechanism
How does a process occur? Channels, chemical reactions and feedback can explain a cell's response.
History
How did a feature arise and change? Inheritance, common ancestry and environments constrain the answer.
Evidence
What observation would distinguish explanations? Measurement, controls and independent replication make the claim testable.
Organisms use energy, regulate internal conditions and participate in lineages that reproduce and evolve. No single checklist resolves every boundary case: viruses, for example, depend on host cells for reproduction. Biology investigates these cases rather than defining them away.
CHAPTER 02
Chemistry supplies the parts. Energy constrains the process.
Water, carbon chemistry and molecular interactions make cells possible. Biology also requires a continuing account of where energy and matter enter, move and leave.
Proteins
Amino-acid sequences form molecules with structural, catalytic and signaling roles. Function depends on conformation, dynamics, partners and environment; some regions remain disordered.
Nucleic acids
DNA stores inherited sequence information in cellular organisms. RNA has coding, regulatory, structural and catalytic roles.
Carbohydrates and lipids
Carbohydrates contribute to energy storage, structure and recognition. Lipids include membrane components, stores of energy and signaling molecules.
ATP couples reactions
Enzymes lower activation barriers and change reaction rates; they do not change the equilibrium free-energy difference. Coupling a favorable reaction, such as ATP hydrolysis under cellular conditions, to an unfavorable one can make the combined process proceed.
Membranes separate compartments while allowing regulated exchange. A lipid bilayer, embedded proteins and concentration gradients create different routes for different substances.
Passive transport proceeds down an appropriate concentration or electrochemical gradient. Active transport couples movement to an energy source and can maintain a gradient. Osmosis concerns water movement; it should not be confused with every kind of solute diffusion.
CHANGE A PARAMETER. EXPLAIN THE RESULT.
A boundary can slow exchange without stopping it.
Two equal, fixed-volume compartments exchange a dissolved substance. Their initial concentrations sum to 20. This simplified model assumes passive transport proportional to the concentration difference, with no reaction, pumping or volume change.
Solid: A. Dashed: B. Time runs horizontally; concentration vertically. The equal-volume total is conserved.
Concentration A11.083
Concentration B8.917
A + B20.000
What happens when k = 0?
Exchange stops: both compartments retain their initial concentrations. When k is positive, they approach equal concentrations. Molecules can still move in both directions at equilibrium; the net flux is zero.
Compartments change what can happen together
Eukaryotic cells use organelles to organize processes. Prokaryotic cells have a different organization, and not every cellular structure is membrane-bound. Cells also use cytoskeletal structures, signaling networks and regulated division to coordinate their activity.
CHAPTER 04
Information is copied, expressed and regulated.
Separate the sequence stored in a genome from when and where its products are made. A sequence alone does not specify the full state of a cell.
DNA→Transcription → RNA→Translation → protein
DNA replication copies DNA; transcription produces RNA from a template; translation uses an RNA message to assemble an amino-acid sequence. This familiar pathway is not a claim that every RNA encodes a protein. Reverse transcription also transfers sequence information from RNA to DNA.
Regulation acts at multiple stages, including access to DNA, transcription, RNA processing, translation and degradation. Many cell types share most of their genome but express different combinations of genes. Alternative splicing can generate different products from one gene.
Inheritance is more than a dominant/recessive table
An allele is a sequence variant at a locus. Genotype describes the variants carried; phenotype describes an observed trait. Dominance is a relationship between alleles for a specified phenotype, not a measure of strength, frequency or evolutionary value. Many traits depend on multiple loci and the environment.
Evolution describes changes in inherited population characteristics across generations. Natural selection is one mechanism; it is not the entire process.
Mutation and recombination
Mutation changes sequence; recombination rearranges existing variation. Effects depend on context and are not directed toward an organism's future needs.
Selection and drift
Selection involves differences in reproductive success associated with heritable variation. Drift changes frequencies through finite-population sampling.
Gene flow and ancestry
Migration and reproduction move alleles between populations. Shared ancestry explains similarities while different histories explain divergence.
CHANGE A PARAMETER. EXPLAIN THE RESULT.
Allele frequency and genotype frequency are different.
At a diploid locus with alleles A and a, let p be the frequency of A and q = 1 − p. Random pairing of gametes gives the Hardy–Weinberg proportions p², 2pq and q². The equilibrium model also assumes a large population with no selection, mutation or migration.
AA · p²0.250
Aa · 2pq0.500
aa · q²0.250
Total frequency1.000
Green: AA. Lime: Aa. Blue: aa. These are expected proportions, not exact counts in a finite population. Dominance describes a heterozygote's phenotype; it does not determine which allele is common or favored by selection.
Why is the heterozygote term 2pq?
The A allele can come from either parent: A then a contributes pq, and a then A contributes qp. Their sum is 2pq, maximized at p = q = 0.5.
Fitness refers to reproductive contribution in a specified setting. It does not imply progress toward a universal best organism. A trait can be advantageous in one environment, costly in another, or carried along with another selected trait.
CHAPTER 06
Bodies coordinate through signals and feedback.
Development builds organized tissues from cells. Physiology studies how those tissues function together, while neuroscience asks how nervous systems sense, act and change with experience.
Homeostasis
Negative feedback can resist disturbances to temperature, concentration or other regulated quantities. Real biological control has delays, changing targets and limits.
Nervous systems
Membrane potentials, action potentials and synapses support signaling. Network behavior depends on cell properties, connections and ongoing activity.
Immune systems
Innate defenses and adaptive responses contribute differently to protection. Immune memory involves biological cell populations and molecular recognition.
A neural network is a model, not a miniature brain
Artificial neurons use simplified mathematical operations. Biological neurons have spatial structure, biochemical states and multiple timescales. Similar vocabulary can inspire a question, but it does not establish that the two systems learn or represent information in the same way.
Ecology connects organisms to one another and to resources, climate and habitat. Energy flows through food webs, while matter cycles through living and nonliving components.
CHANGE A PARAMETER. EXPLAIN THE RESULT.
A growth model needs an account of its limits.
Start with N₀ = 20 and model continuous population growth as dN/dt = rN(1 − N/K). The per-capita growth rate falls as N approaches carrying capacity K. Here r and K stay fixed; this is a teaching model, not a forecast for a species.
Solid: modeled population. Dashed: fixed carrying capacity. This continuous model does not produce chaos.
Population N(t)171.697
Growth dN/dt12.149
Fraction of capacity0.858
Why does exponential growth work only as an approximation here?
When N is small relative to K, the factor 1 − N/K is close to one, so dN/dt ≈ rN. Near K that approximation fails. Real populations may also face delays, seasonal resources, migration and stochastic events absent from this model.
Predator–prey interactions, competition and cooperation can create feedback at population scales. Simple models isolate a mechanism; field observations determine whether that mechanism is sufficient in a particular setting.
A useful prediction still needs a biological test.
Computation helps organize measurements, estimate relationships and propose explanations. The experimental design determines which conclusions the data can support.
Task
Data
Computational approach
What to check
Protein structure prediction
Amino-acid sequences, evolutionary information and known structures
Learn spatial relationships and predict a structure
Assess confidence and compare against independent experimental measurements. Structure prediction is not a complete account of folding dynamics or function.
Sequence analysis
DNA, RNA or protein sequences
Alignment, statistical models and learned sequence representations
Separate related sequences between training and testing when evaluating generalization; random splits can hide similarity leakage.
Cell imaging
Microscopy images and annotations
Detect, segment and track cells
Check performance across instruments, preparation methods and biological conditions, not only images from the same batch.
Single-cell measurements
Many molecular measurements per cell
Model variation, cluster observations and estimate cell states
Account for donors, batch effects and measurement noise. Nearby points on a 2D embedding do not prove a developmental or causal relationship.
Ecological monitoring
Camera, acoustic and field observations
Classify species and estimate occupancy or abundance
Account for imperfect detection and changes in habitat, season and sampling effort.
AlphaFold's 2021 study demonstrated major improvements in protein structure prediction on the CASP14 benchmark. That result supports a specific prediction task; it does not mean that sequence alone answers every question about a protein's function, dynamics or behavior inside a cell.
For intervention claims, distinguish correlation from causation and include appropriate controls. Biological and clinical outcomes require their own evidence; success on a computational benchmark is a different kind of result.
CHAPTER 09
Keep the unresolved questions visible.
A field can have strong explanations for particular mechanisms while still lacking a complete account across scales.
QUESTION 01
How did the first evolving systems arise?
Origin-of-life research connects chemistry, compartments, energy and heredity. Experiments demonstrate individual mechanisms, but a complete historical sequence remains unresolved.
QUESTION 02
How does a genome build a body?
Development combines regulation, signaling, mechanics and environment. Predicting a whole organism from sequence alone leaves many levels of organization unspecified.
QUESTION 03
How does neural activity support behavior and experience?
Neural recordings and interventions reveal mechanisms at many scales. A connectome describes wiring; it does not by itself specify dynamics, learning or subjective experience.
QUESTION 04
When can we predict an ecosystem's response?
Feedback, adaptation, migration and environmental change can alter responses to the same disturbance. Useful models need a stated scale and tests against new observations.
CHAPTER 10
Build an explanation you can test.
Use the chapters as a starting path and the atlas to explore connections. Return to Math for the model and Physics for its physical assumptions.
STEP 01Start with chemistry and cells
Sketch a membrane, identify the main molecular families, and explain why maintaining a gradient requires an energy account.
STEP 02Follow genetic information
Distinguish replication, transcription and translation. Explain why changing a DNA sequence does not necessarily change a trait.
STEP 03Think in populations
Separate mutation, selection, drift and gene flow. Read genotype proportions without assuming that dominant means common.
STEP 04Connect mechanisms across scales
Trace a signal through molecules, cells, tissues and behavior, stating which parts you measured and which you inferred.
STEP 05Design an experiment before a model
Name the experimental unit, control, response and potential confounder. Keep independent biological replication separate from repeated measurements.
STEP 06Use computation to test a claim
Write a simple model, inspect its assumptions, and compare its predictions with observations it was not fitted to.