Quantum Mechanical Basis of Vision

The two striking components of retina, i.e., the light sensitive neural layer in the eye, by which it responds to light are (the three types of) color sensitive Cones and color insensitive Rods (which outnumber the cones 20:1). The interaction between electromagnetic radiation and these photoreceptors (causing transitions between cisand transstates of rhodopsin molecules in the latter) offers a prime example of physical processes at the nano-bio interface. After a brief review of the basic facts about vision, we propose a quantum mechanical model (paralleling the JaynesCummings model (JCM) of interaction of light with matter) of early vision describing the interaction of light with the two states of rhodopsin mentioned above. Here we model the early essential steps in vision incorporating, separately, the two well-known features of retinal transduction (converting light to neural signals): small numbers of cones respond to bright light (large number of photons) and large numbers of rods respond to faint light (small number of photons) with an amplification scheme. An outline of the method of solution of these respective models based on quantum density matrix is also indicated. This includes a brief overview of the theory, based on JCM, of signal amplification required for the perception of faint light. We envision this methodology, which brings a novel quantum approach to modeling neural activity, to be a useful paradigm in developing a better understanding of key visual processes than is possible with currently available models that completely ignore quantum effects at the relevant neural level. Introduction: The biological features of the eye and the associated processes of vision [1] offer a unique opportunity to explore the relevance of quantum mechanical principles in understanding this remarkable system. One of the primary functions of the retina (light sensitive layer in the eye) is transduction – converting light into neural signals, which are then processed further by the brain enabling visual perception. Although, traditionally, transduction has been understood in classical terms, a plausible case can be made for a quantum mechanical explanation. The process involves a basic interaction of light (photons) with the quantum levels of the key molecules – the photopigments (such as rhodopsin) residing in the transducers of the eye, namely, rods and cones which further modulate the concentrations of various intracellular molecules (e.g.,cyclic Guanosine Monophosphate (cGMP)) and ions (Na+ and K+) thus determining the electrical state of the receptors. It is well known that rods detect dim light (small number of photons) but are insensitive to color. Several rods act together to amplify the light into a useful neural signal. At high intensities, they are saturated and do not provide any useful interpretable neural signal. On the other hand, cones detect bright light (tens of hundreds of photons) but cannot react to dim light. Furthermore, there are three types of cones sensitive to, respectively, three different wavelength ranges within the visible light spectrum with different peak sensitivities. The interaction between the outputs of these three kinds of cones forms the basis of color vision. We have here a composite system of interacting photons and at least two types of matter systems – that of rods and cones, respectively. The excitations caused by the interactions are somehow statistically correlated (and processed later) to lead to the formation of a coherent visual image. Thus, it seems clear that one can approach visual perception phenomena from a quantum mechanical point of view. The tools of quantum mechanics of composite systems [2] involve setting up a suitable, tractable model Hamiltonian describing the basic interactions in the system and express the density matrix of the system in terms of the eigensolutions of the Schrodinger equation. In our case, the density matrix would describe the system of rods or cones, given the initial specification of the transduction process. The effects of interactions and intraand inter-correlations among the rods or cones are then contained in this density matrix. There are various mathematical principles and techniques to extract the physical information of interest from this density matrix. Possible predictions arising out of such an inquiry may lead to experimental investigations as to the relevance of quantum features in this system. We will now outline the suggested models and procedures in some detail. Models of interaction of light with rods and cones: We first give a brief outline of an exactly soluble Jaynes-Cummings model (JCM) [3] of interaction of a one-mode of photon (quantized electromagnetic field) with a two-level atom (molecule). Suitable modifications of this model are then suggested for describing the interaction of light with rod and cone systems. The JCM Hamiltonian is H = ω a + a + 1 2 ( ) + ω a 2 σ z + g σ +a + σ − a + ( ) (1) The first term in this expression represents the photons with photon (light) frequency ω . The second term represents the two-levels of the atom (molecule) with ωa , the energy separation between the two levels. The last term is the interaction of light with the two-level system with g, the coupling strength. Here a,a represent the destruction and creation operators of the photon, with a a the operator representing the number of photons, a a n = n n , n = 0,1,2, . Also, a n = n +1 n +1 , a n = n n −1 . The atom (molecule) is conveniently represented by the Pauli