Visual System: The visual system is a good example of a "stimulus-response" system. Light (stimulus) causes electrical activity (response) in the visual cortex portion of the brain. The system is complex and contains many "subsystems" each of which can be viewed as a stimulus response system. In the picture below, the retina, the Lateral-Geniculate-Nucleus (LGN- small dark blue oval) and the visual cortex can each be viewed as stimulus response systems.
Shown directly above (in yellow background) is a blowup of the retina. Specialized cells called rods and cones (in blue) react to light causing an electrical depolarization. The electrical potential (voltage) across the cell membrane is caused by differing ionic concentrations in intracellular and extracellular spaces. This electrical depolarization excites a network of other cells ("bipolar" and "ganglion"). Ultimately, the electrical activity of the ganglial cells (white) travels down long cellular appendages (axons) toward the LGN. After processing at the LGN in a separate network of nerve cells, the activity then travels to the visual cortex.
As a subsystem, the rods (or cones) may be regarded as subsystems themselves. Rods react to light intensity whereas cones react to wavelength (color) as well. Below, photons activate a chemical called rhodopsin which binds to G-proteins. A subsequent cascade of chemical events causes protein channels (proteins) in the cell membrane to open (and close) allowing ions (sodium, potassium and calcium) to flow through the membrane. Ultimately, the differing intracellular and extracellular ionic concentrations induce an electrical potential across the cell membrane. Again, the stimulus here is light and the response is an electrical depolarization.
As a subsystem, the LGN has an electrical stimulus (from the retinal ganglia) and an electrical response (from the axons which leave the LGN).
The general physiological structure and function is interesting but there are a few general facts which should be observed:
- Subsystems are networked into larger subsystems, i.e., the space scale is very relevant.
- Complexity arises from how the subsystems are networked.
- Stimuli and responses are measureable quantities.
- Mathematical models exist for each of the subsystems previously described.
An Endocrine System: The pancreas The pancreas is an "endocrine" system because it releases hormones. Elevated blood glucose (stimulus) causes the pancreas to increase its production rate of the hormone insulin (response).
Like the visual system, the pancreatic glucose-insulin stimulus-response system has several different subsystems differentiated by size and connectivity.
Insulin is released from "Islets of Langerhans" into blood vessels. Each islet consists of thousands of insulin secreting cells called "beta" cells. Glucose causes a cascade of chemical events which open and close ionic channels in the cell membrane.
Intracellular and extracellular potassium and calcium concentrations change resulting in a complex electrical oscillation called "bursting". Below is the solution of a mathematical model of this phenomena showing the bursting oscillations (sequential series of rapid spikes) of the membrane potential and the calcium concentration (sawtooth pattern). Calcium is extremely relevant in the secretion and production of insulin.
Like the visual system, subsystems can be categorized by their size and connectivity. Much of the "connectivity" is electrical (currents through protein channels connecting beta-cells) while other is chemical (diffusion of glucose, potassium in extracellular regions, for instance).
Depending on what is measured, the beta cell may have glucose as a stimulus and any of voltage, calcium concentration or insulin secretion rate as a response. In some experiments, no glucose is added but an electrical stimulus externally applied by a probe (which makes physical contact with the cell) solicits similar responses.
In addition to the general facts pointed out for the visual system, note that:
- The stimulus is determined by the experimental conditions.
- A system may have several responses or a vector of measurable (and immeasureable) quantities
- Different responses may have dynamics occurring on highly disparate time scales.
For the last point note that duration of an electrical spike, calcium oscillation and blood insulin level occur on time scales of milliseconds, several seconds and hours, respectively.
Each muscle cell contains many "myofribrils" (schematic below) surrounded by a "sarcoplasmic reticulum" (SR).
The myofibrils are segemented into "sarcomeres". Within the sarcomere, "actin" and "myosin" filaments (shown below) slide against each other causing the muscle contraction.
The initial electrical stimulus from a neuron opens calcium channels in the cell and SR membranes. A calcium wave quickly propogates down the SR. The increase of calcium initiates a "conformational" (shape) change in the myosin molecules which "ratchet" against the actin molecules shortening the sarcomere.
In individual muscle cells, mechanical (tension) as well as electrical stimuli will initiate electrical activity of these cells. Like the beta-cells, the stimulus and response is determined by the particular experiment. Comparing the visual, pancreatic and muscle systems, stimuli can be electromagnetic (light), chemical, electrical or mechanical.
Neural: For the most part, neurons receive electrical stimuli and have an electrical response. The measured electrical potential is due to ionic concentration gradients (of sodium, potassium and calcium) across the cell membrane.
A depolarization (increase) of the cell body electrical potential initiates a wave of electrical depolarization (called an "action potential") which travels down "axons" to "synapses" where influx(?) of calcium initiates a complicated series of events ultimately depolarizing the receiving (post-synaptic) cell at its "dendrites" (axon or cell body in some cases).
Each neuron is a very complex system. Dendritic tree structure, location and number of synaptic contacts, and ionic channel and synaptic electro-chemistry all play a role in the post-synaptic response of a cell. Some synaptic input can tend to inhibit the receiving cell's ability to fire action potentials (shown below-voltage as a function of time). Other inputs tend to excite the receiving cell and initiate action potentials. In most neurons, several excitatory inputs (occuring at the same or different times) are required to initiate such an event.
In networks of connected neurons, the response of a given cell in the network will (in general) differ than its response when isolated from the network. The emergent complexity of the network response is a property of both the way the cells are connected and the properties of the cells themselves. Thus,
- A system response is not necessarily determined from subsystem behavior alone.