Odorants are mixtures of many different molecules. The complexity of the human sense of smell can be represented visually as a grid of 100 cells (10 x 10 grid) with each cell associated with a unique molecule-receptor pair. An odorant is detected when the brain integrates the signals generated by each molecule in the mixture.

Four olfactory sensors, each innervated by a nerve that transmits information to the brain as an action potential, are shown in the diagram at the right. Three of the sensors each respond to one of the three odor molecules in the geometric representation of the odorant mixture.

Figure 27.23

1. In the diagram the odorant-receptor pairing is imagined geometrically; a round peg fits in a round hold and a square peg does not. The receptors are located in the epidermal cell surface, shown in the drawing as a light gray line. Create a geometric representation by drawing receptors on the surfaces of the sensors that are activated by one of the molecules in the mixture. Draw a geometric representation of a fourth receptor surface that is not activated by a molecule in the odorant mixture.
   
    
    
   In the receptor cell labeled A, two signaling molecules S1M and S2M are shown as are two types of gated ion channels; one that transports Ca⁺² in response to S1M while generating S2M, and three that transport Na⁺ in response to S2M.
2. Construct an explanation of the mechanism for transmission of information when the odorant molecule is detected at receptor A using this signaling cascade. In your explanation include the role of positive feedback and the mechanism of the generation of an action potential.
   
    
   
    
   Signal integration allows the brain to discriminate this particular odorant mixture from others using the time dependence in each signal. The sensitivity of an olfactory system increases as the number of unique receptors increases.
3. Complete the following table to construct a mathematical representation of sensitivity to the chemical landscape assuming that there are 100 unique odorant molecules. Use the following mathematic routine to determine the number of odors caused by groups of molecules selected from the 100 odorant molecules:
   
    

   Number, r, of odor-producing molecules in the odorant	Number of different odorants
   3	100•99•98/(3•2)=161,700
   4
   5
   6
   7

   
    
   $\text{number of groups}=\frac{100!}{r!(100–r)!}$ where $n!=n\text{g}(n–1)\text{g}(n–2)\text{g}(n–3)...$ and $0!=1$
   
    
   Bushdid et al (Science, 343, 2014) extended this model and then used human subjects to experimentally determine the number of unique odorant molecules that they could discriminate to obtain an estimate of 1.72 trillion different detectible smells.
   
    
   
    
   Olfactory receptor proteins that recognize chemicals as odors are expressed in humans by approximately 400 different genes. This is the largest number of genes coding for a single function in the human genome (Nimura, Human Genetics, 4, 2009). Other mammals have an even greater diversity of olfactory receptors: roughly 800 and 1200 genes in dogs and rats, respectively. Some olfactory receptors are adapted for odorants in an aqueous environment and some are adapted for an air environment.
   
    

   

   Figure 27.24
4. Use the representation above, showing classes of genes within groups of organisms to construct a representation of the phylogenetic relationships among these groups. Annotate your representation to show gene additions and deletions. To your representation also add annotation that connects the phenotype to the environment.

When you get cold you may shiver. The shivering response is a reflex in which the hypothalamus in the brain integrates sensory input, comparing input against a temperature set point. When a threshold signal is detected, nerves of the somatic nervous system that innervate skeletal muscle are stimulated. The extension and contraction of muscle cells releases heat energy that elevates the body temperature.

1. Construct a representation of the information flow for the shivering response. Annotate your representation to include
   
    
   • the sensory input
   • signal transmission to the hypothalamus
   • signal transmission from the hypothalamus to the somatic nervous system
   • transmission to muscle tissue
   • and output response.
   
    
   Include in your annotation the negative feedback loop that is established.
2. Shivering occurs when you have a fever even though your body temperature has not fallen. Identify the component of the information flow represented above that can cause this effect and describe how the brain has integrated the immune system and nervous system to maintain homeostasis.
   
    
   
    
   Thermogenesis from accelerated metabolism in adipose (fat) tissue is a non-shivering response to a cold stimulus. Using a neurotropic virus, investigators are able to trace the paths of nerves in animals.
   
    
   
    
   Neurons infected by virus can then be visualized by exposing the tissue to antibodies that can be stained or using dyes that fluoresce. Ryu and co-workers (Journal of Neuroscience, 35, 2015) used this technique to demonstrate communication between nerves of the sympathetic nervous system and nerves of the sensory nervous system innervating thermoreceptors that are sensitive to hot and cold.
3. Construct a representation of information flow and annotate the representation with labels for
   
    
   • signal input caused by low temperature
   • signal transmission through nerves of the sensory system
   • transmission of signal from the sensory system to the sympathetic system
   • transmission to adipose cells
   • output response of cells
   
    
   Include in your annotation the negative feedback loop that is established.