Theoretical Neuroscience: State of the Art

Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems by Peter Dayan and L.F. Abbott Cambridge, MA: The MIT Press (2001), 576 pp. $50.00Once upon a time, an experimental neurobiologist was asked whether he thought there was a role for theory in neurobiology. He answered with a resounding “No.” Then he explained his reasoning for giving this answer. The irony of this story is that the experimentalist had a theory of why there was no role for theory. On a serious note, any experimental research activity, from planning an experiment to interpreting the data, requires having in mind an abstract representation of the studied phenomenon. This representation, no matter how simplistic or complex, is a theory, and is indispensable for any coordinated research effort. Then, undoubtedly, there is a role for theory in neurobiology; the real question facing neurobiology today is whether there is a role for theorists. Although as a theorist I obviously think that the answer is yes, this may not be evident to everyone. The argument in favor of having theorists is based on the division of labor concept. Just as having professional millers and bakers results in better and cheaper bread, having professional theorists and experimentalists is likely to result in higher quality papers and more efficient research.A theorist's role in science is to create an abstract representation of the studied phenomenon. To be valid, this representation must be logically self-consistent. To be relevant, this representation must explain experimental observations and make experimentally testable predictions. These are often very challenging requirements that demand a full-time effort from a scientist, thus supporting the division of labor argument. However, the division of labor may not always be advantageous. Even in physics, where theorists have a well-accepted role today, the situation was different just two hundred years ago when each scientist was the source of theoretical and experimental skills in his own work. What drove the division of labor in physics was the ever-increasing sophistication of both experiment and theory.Figure 1Figure 1Figure 1View Large Image | View Hi-Res Image | Download PowerPoint SlideHow can one tell whether neurobiology has reached the level of sophistication requiring professional theorists? The sophistication of theory is reflected mainly in its extensive use of mathematics. In natural sciences, mathematics is incredibly useful for precisely formulating and communicating ideas and, therefore, building theories. But to take advantage of mathematical theories, two conditions must be met. Construction of a mathematical theory requires the existence of fundamental principles. Testing of a mathematical theory requires quantitative experimental measurements. In some subfields of neurobiology, these conditions are beginning to be met. Moreover, the immense complexity of the brain guarantees that the sophistication of neurobiology will keep growing, thus driving up the demand for theorists. This makes the future of theoretical neuroscience rather bright.How can someone learn the craft of theoretical neurobiology? The first generation of theoretical neuroscientists came mostly from a physics background. In physics, where a theoretical culture exists, the craft is learned by students through courses and textbooks. To become a self-perpetuating field, neuroscience has to develop its own theoretical culture and fundamental texts. There are already several excellent books covering various specialized topics in theoretical neurobiology such as, for example, Spikes: Exploring the Neural Code by F. Rieke et al. (MIT Press; 1996) on representation of sensory signals in neural spike trains using information theory, or Biophysics of Computation: Information Processing in Single Neurons by C. Koch (Oxford University Press; 1998) combining biophysical and computational approaches to neuronal function. A recently published book by Peter Dayan and L.F. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, attempts to accomplish more than cover one specialized topic; it attempts to cover the whole field of theoretical neuroscience. I think that the authors have mostly succeeded in this Herculean task. Not only does the book set a high standard for theoretical neuroscience, it defines the field.The book has three parts loosely corresponding to the three levels of description of brain function, as defined in relation to the action potential spikes. Part I addresses the information encoded in the neuronal spike trains and how it can be decoded. This theoretical framework grew out of the experiments with extracellular recordings of single neurons, relating those recordings to the sensory input and motor output. It represents the “mid-level” description of brain function. Part II is devoted to the modeling of biophysical properties of neurons and synapses. This theory is closely related to the experiments with intracellular recordings. It describes the physical processes going into spike generation and represents the “low-level” description. Also, it discusses modeling of networks of spiking neurons. Part III discusses the field of machine learning and its application to neurobiology. It relates to experiments on behavioral and representational learning. This is the “high-level” description of brain function, which does not necessarily rely on the existence of action potentials.As Peter Dayan and Larry Abbott are both exceptionally strong and productive theoretical neuroscientists, the book has a certain “first-hand” quality to it: the authors have clearly thought through all the subjects and personally contributed to many of them. This manifests in elegant and concise presentations such as, for example, in sections on information theory and neuroelectronics. The presentation of many neuroscience topics combines deep intuition with mathematical rigor. The balance between the two is generally well maintained. The reader is assumed to have a mathematical background, some of which can be supplemented by mathematical appendices. Importantly, the book demonstrates most of the tools that can be found in the toolbox of a theoretical neurobiologist today.The great thing about this book is that most of the knowledge accumulated in theoretical neuroscience is collected under one cover, using uniform notation and style of presentation. One does not have to search for original articles and try to translate different notation systems. Some of the topics that particularly benefited from this systematic approach are visual receptive fields, synaptic plasticity rules, and classical conditioning. Although the ordering of the topics is not as deductive as may be expected from a theoretical physics textbook, this is probably characteristic of the state of theoretical neuroscience: we are yet to discover unifying principles that would make a deductive presentation possible.The authors took the unusual step of making the book freely available on the Internet before publication. I think that was the right thing to do; the reduction in sales caused by free availability must have been offset by the positive effect of the generated publicity. Most importantly, this step eliminated (if only temporarily) a financial barrier for access to scientific information that often penalizes scientists from economically disadvantaged countries.Theoretical Neuroscience should do well as a textbook for advanced undergraduate or graduate courses. It covers a wide range of topics, and offers pedagogical presentation, Internet-based exercises, and guidance for further reading. The necessary mathematical background is presented in the appendices throughout the book and in the end. Most of the chapters are self-contained, allowing their reshuffling by the instructor. Although the book gives some neurobiology background, the authors recommend that readers new to the field refer to a general neuroscience textbook.Although the book does an excellent job in covering most aspects of theoretical neuroscience, it touches perhaps too lightly on the anatomy of neuronal circuits and, most importantly, on physical and biological constraints shaping them. For example, the widespread use of learning rules in developmental models often ignores the fact that the neuronal circuits must be wired in the physical world and thus are subject to constraints on valuable resources such as space, time, and energy. If an electrical engineer designing modern computers has to be aware of these constraints, wouldn't nature have to deal with them, too? I believe that we need to study and understand these constraints.The need for understanding constraints is emphasized by the shortcomings of many computational models of brain function. All too often, the existing computational models focus on a single feature of a studied system, ignoring the fact that the system performs a great variety of tasks. This makes the problem of building a model under-constrained thus allowing multiple solutions, such as, for example, the many different developmental models of cortical map formation. To overcome this, it would be helpful to understand constraints imposed by the biological hardware. Studies of biophysical constraints are likely to lead to the discovery of “engineering” principles, which, like the laws of conservation in physics, will rule out many incorrect candidate solutions. This will allow theoretical neuroscientists to narrow down the set of possible solutions and better focus their efforts.Overall, Theoretical Neuroscience is an excellent book. I strongly recommend it to anyone who is seriously interested in learning about the field. This book should be a top choice for anyone teaching a course in theoretical neuroscience.