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  • Single-Neuron Models Allow Study of the Integration of Synaptic Inputs and Intrinsic Conductances

    • Neurons Show Sharp Threshold Sensitivity to the Number and Synchrony of Synaptic Inputs in Quiet Conditions Resembling In Vitro

    • Neurons Show Graded Sensitivity to the Number and Synchrony of Synaptic Inputs in Noisy Conditions Resembling In Vivo

    • Neuronal Messages Depend on Intrinsic Activity and Extrinsic Signals

  • Network Models Provide Insight into the Collective Dynamics of Neurons

    • Balanced Networks of Active Neurons Can Generate the Ongoing Noisy Activity Seen In Vivo

    • Feed-forward and Recurrent Networks Can Amplify or Integrate Inputs with Distinct Dynamics

    • Balanced Recurrent Networks Can Behave Like Feed-forward Networks

    • Paradoxical Effects in Balanced Recurrent Networks May Underlie Surround Suppression in the Visual Cortex

    • Recurrent Networks Can Model Decision-Making

In one way or another all scientific researchers construct models. The role of theory is to develop, refine, and investigate these models to uncover new insights and to make new predictions. Theoretical (or computational) neuroscience explores the application of mathematical and computational methods to the study of neural systems.

Defining models of neural systems in mathematical terms assures that the models are self-consistent, with clearly revealed assumptions and limitations. Formulating models mathematically also allows the powerful techniques of mathematics and physics and the extraordinary capacity of modern computers to be used to understand model behavior. This power allows the implications of the models to be worked out fully, revealing features that are surprising and nonintuitive.

What makes a model good? Clearly it must be based on biological reality, but modeling necessarily involves an abstraction of that reality. It is important to appreciate that a more detailed model is not necessarily a better model. A simple model that allows us to think about a phenomenon more clearly is more powerful than a model with underlying assumptions and mechanisms that are obscured by complexity. The purpose of modeling is to illuminate, and the ultimate test of a model is not simply that it makes predictions that can be tested experimentally, but whether it leads to better understanding. No matter how detailed, no model can capture all aspects of the phenomenon being studied. As theoretical neuroscientist Idan Segev has said, borrowing from Picasso's description of art, modeling is the lie that reveals the truth.

Appendix E introduced two ideas that are central in theoretical neuroscience: the perceptron and the attractor. In this appendix we extend the discussion of theoretical neuroscience by considering the effect of synaptic input on neuron models that produce action potentials, by showing how inhibition and excitation can interact in network models to produce interesting and nonintuitive effects, and by presenting a model of decision-making. These examples convey a sense of how theoretical neuroscience research is done, and how it can shed light on the types of computations that neurons and networks of neurons can perform.

Single-Neuron Models Allow Study of the Integration ...

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