In Defense of Minimal Models

At first glance, defending minimal models in biology seems silly. Biology is famously messy. It is rife with noise, variability, and overlapping mechanisms that allow one system to compensate when another fails. Complexity isn't a bug of biological systems; it's a defining feature.

And yet minimal models remain one of the most powerful tools available to biologists. By stripping away the noise, they distill a system down to its essential mathematical structure, revealing the core logic underlying a given function. One of the most influential minimal models in neuroscience is the perceptron, which is arguably the simplest possible model of a neuron. It takes a set of inputs, multiplies each by a weight, sums them, and passes the result through a sigmoidal nonlinearity before sending the output downstream. Despite omitting nearly all biophysical detail, this model captures the essential roles of the dendrites, soma, and axon. Perceptron’s eventually gave rise to artificial and deep neural networks, and from there to the large language models we use today.

A biologist might reasonably balk at this level of simplification; there's no action potential to be found. How could something so reduced be useful beyond the classroom or a machine learning textbook? The skepticism is fair; a perceptron genuinely lacks biophysical detail. But the counterargument is just as strong: you don't need quantum mechanics to explain the function of a table. This is the principle of emergence, the idea that simple units, combined at scale, can produce complex behavior no single unit could achieve alone. Perceptron-style neurons, simple as they are, proved sufficient to power modern computer vision from the early 2000s till today. That dominance is only just now starting to be contested by transformer-based architectures starting around 2023.

There's a flip side to this emergence, though. Sometimes the units composing the "table" are too simple to produce the property you're after. This is where minimal models earn their keep a second time. You can add a single new property to the model and directly compare the emergent behavior of the two versions side by side.

To give an example, the Morris-Lecar model is a clear example of this approach applied to a single neuron. Developed in 1981 by Catherine Morris and Harold Lecar, the model was built from voltage-clamp recordings of the barnacle giant muscle fiber. While this is not a neuron, it is a highly excitable cell whose conductance dynamics turned out to generalize well to neuron’s action potentials. What makes the model elegant is its minimalism: a single excitatory current (an instantaneous calcium current) paired with a delayed-rectifier potassium current. At its core, it's just a two-dimensional system of ordinary differential equations, yet that's enough to reproduce action potentials.

Comparing networks of Morris-Lecar neurons to networks of perceptrons (or transformers) yields a striking observation. The added biophysical complexity doesn't reliably translate into better performance, at least not yet. That strikingly suggests action potentials may not be necessary for intelligence as we currently understand it. There is, however, a promising case for spiking models on the grounds of efficiency: spiking neurons activate only when needed, computing in response to discrete events rather than continuously. Event-based cameras, which transmit signals only when a pixel's value changes, are a working example of this principle. The approach isn't yet competitive with LLM-scale systems, but it remains an active and promising area of research.

Minimal models aren't just useful for AI; they're equally valuable for neuroscientists and biologists working to understand how the brain and body function, with direct implications for medicine. The Morris-Lecar model, for instance, has been essential to understanding how populations of neurons synchronize. Action potentials in neighboring neurons can fire together (synchrony) or alternate in a regular pattern (anti-synchrony); highly synchronized states with elevated firing rates closely resemble seizure activity. Studying networks of Morris-Lecar neurons has given researchers a mathematical account of the conditions that drive hypersynchronization, such as, excessive excitation, overly strong connections, or excessive connectivity. From there, researchers can build progressively more detailed, electrophysiologically accurate models to test drug mechanisms. The minimal model supplies the intuition first: if excessive excitation drives synchronization, which biological lever in the more detailed model might correct it? As is often the case in biology, there's more than one valid answer. You could block excitation (AMPA/NMDA antagonists), boost inhibitory tone to act as a brake (GABA agonists such as ativan), or raise the neuron's own firing threshold (sodium channel antagonists or potassium channel agonists). The minimal model hands you a small set of interpretable knobs to experiment with, so that when you return to the messier biological system, you already know roughly what to expect.

There are countless other examples of minimal models advancing biological understanding, and specifically the Morris-Lecar model alone has many applications beyond what's covered here. The throughline is simple: minimal models build intuition. They isolate what's essential to producing a given emergent behavior, and they offer a working hypothesis for what the corresponding biological mechanism is likely doing in the real system. If you're building artificial systems, that intuition tells you which details actually matter. If you're working toward medicine, it gives you a fast, interpretable foundation to guide more complex models that may take days to run, while the minimal model itself runs in minutes. Either way, a minimal model isn't a toy — it's a genuine working tool.

Author: Alexander White