Neurophysiology Flashcards
1
Q
Why are sensory receptors known as transducers?
A
Convert physical/chemical stimulus into electrical impulse
2
Q
How do sensory receptors allow the localisation of sensory stimuli?
A
Receptive field
3
Q
What are receptor potentials?
A
Electrical impulse transduced by sensory receptors
4
Q
How are (i) receptor potential (ii) firing frequency and (iii) sensory stimuli related?
A
Magnitude of sensory stimulus encodes for duration and intensity of APs
- ↑stimulus → ↑receptor potential → ↑freq. of AP (> exceed threshold)
5
Q
In order to generate an action potential, the depolarisation of the membrane at the sensory receptor must reach a ______________.
A
Threshold potential
6
Q
Odorants generate (fast/slow) receptor potential within cilia?
A
Slow
7
Q
True or false. Odorants trigger a series of receptor potentials that propagate continuously along olfactory nerve axons.
A
False.
Odorants → slow RP in cilia
→ RP along dendrite
→ series of AP within soma
→ AP along axon
8
Q
What are 4 sensory stimuli that are sensed by exteroceptors?
A
1) Pain
2) Temperature
3) Touch
4) Pressure
9
Q
Where are proprioceptors located?
A
1) Muscles
2) Tendons
3) Joints
10
Q
What are 5 modes of sensory detection?
A
1) Chemoreceptors
2) Photoreceptor
3) Thermoreceptors
4) Mechanoreceptors
5) Nociceptors
11
Q
In the visual sensory system, what are the
i) modality
ii) stimulus
iii) receptor class
iv) receptor cell type
A
Visual:
i) Vision
ii) Light
iii) Photoreceptor
iv) Rods, cones
12
Q
In the auditory sensory system, what are the
i) modality
ii) stimulus
iii) receptor class
iv) receptor cell type
A
Auditory:
i) hearing
ii) sound
iii) mechanoreceptors
iv) hair cells (cochlea)
13
Q
In the vestibular sensory system, what are the
i) modality
ii) stimulus
iii) receptor class
iv) receptor cell type
A
Vestibular:
i) balance
ii) gravity
iii) mechanoreceptors
iv) hair cell (vestibular labyrinth)
14
Q
In the gustatory sensory system, what are the
i) modality
ii) stimulus
iii) receptor class
iv) receptor cell type
A
Gustatory:
i) taste
ii) chemical
iii) chemoreceptor
iv) taste buds
15
Q
In the olfactory sensory system, what are the
i) modality
ii) stimulus
iii) receptor class
iv) receptor cell type
A
Olfactory:
i) smell
ii) chemical
iii) chemoreceptor
iv) olfactory sensory receptors
16
Q
For touch sensation in the somatosensory system, what are the
i) stimulus
ii) receptor class
iii) receptor cell type
A
i) Pressure
ii) Mechanoreceptor
iii) Cutaneous mechanoreceptors
17
Q
For proprioceptive sensation in the somatosensory system, what are the
i) stimulus
ii) receptor class
iii) receptor cell type
A
i) Displacement
ii) Mechanoreceptor
iii) Muscle and joint receptors
18
Q
For temperature sensation in the somatosensory system, what are the
i) stimulus
ii) receptor class
iii) receptor cell type
A
i) Thermal
ii) Thermoreceptor
iii) Cold and warm receptors
19
Q
For pain sensation in the somatosensory system, what are the
i) stimulus
ii) receptor class
iii) receptor cell type
A
i) Chemical, thermal, mechanical
ii) Chemoreceptor, thermoreceptor, mechanoreceptor
iii) Polymodal, thermal, mechanical nocireceptor
20
Q
For itch sensation in the somatosensory system, what are the
i) stimulus
ii) receptor class
iii) receptor cell type
A
i) chemical
ii) chemoreceptor
iii) chemical nociceptor
21
Q
Are spinal and intracranial neurons sensitive to sensory stimuli eg. touch, sound, light, odor?
A
No.
Each stimuli must be transduced by specialised sensory cells
22
Q
True or false:
As a neuronal action potential is summative, the intensity of a stimulus can be directly calculated from a single sensory neuron action potential.
A
False.
Single neuron → “All or nothing” (threshold)
Intensity coded by (i) no. activated receptors (ii) freq. of AP from those receptors
23
Q
What are the 2 modes of sensory receptor adaptation?
A
1) Tonic
- slowly adapting
- responsive during long stimuli
- for monitoring unchanging stimuli (eg. pressure)
2) Phasic
- rapidly adapting
- only detect onset of stimulus
- for detecting rapid changes in stimuli (eg. vibration)
24
Q
What is receptor adaptation?
A
Sensory receptors become less responsive to a stimulus over time
25
How do neurons differentiate between new or changing stimuli rather than constant, unchanging ones?
Phasic receptors:
Once the stimulus reaches a steady state, phasic receptors adapt and "turn off," effectively ignoring the continuous presence of the stimulus.
(only stimulated by "new" or different stimuli)
26
Sensory neurons that innervate sensitive areas have (larger/smaller) receptive fields.
Smaller
27
What is the physiology of two-point touch discrimination?
Less convergence of receptive fields by:
i) Smaller secondary receptive fields
ii) Less converges of primary neurons
→ 2 stimuli more likely to actively separate pathways
→ perceived as distinct stimuli
→ 2-point discrimination
28
How does lateral inhibition isolate/enhance contrast between stimuli?
Group of primary neurons stimulated
→ primary neuron with greatest stimulation → greatest response
Pathway of primary neuron with greatest response inhibits adjacent pathway → ↑SNR
29
What is labeled line coding?
1:1 association of a receptor with a sensation
(each receptor has a distinct pathway from receptor surface to brain)
30
True or false:
Labeled line coding is applicable for all sensory systems.
False:
Not applicable for auditory
- timing differences rather than labeled line coding to localise sound
31
True or false: Neurons in the ears have very small receptive fields to accurately localise auditory stimuli.
False:
- sensitive to different frequencies but no receptive fields
- geographical activation provides no information of location of sound → relies on delay of stimuli between left and right ear
32
Which sensory pathway does not synapse in the thalamus?
Olfactory
33
Most sensory pathways project to the ______ where they synapse and information is modified before being relayed to the relevant cortical centers.
Thalamus
34
Equilibrium pathways project primarily to the ____________.
Cerebellum
35
What are the 5 sensations that make up "taste"?
1) Sweet
2) Sour
3) Salty
4) Bitter
5) Umami
36
Each taste cell is a non-neural polarised ___________ cell that only has a tiny tip that protrudes into the oral cavity through a ______________.
Taste cell:
- non-neural polarised epithelial cell
- tiny tip protrudes through taste pore
37
What are 2 ways by with the apical membrane/ends of taste buds are adapted for its function?
1) Tight junctions link adjacent cells → limit movement of molecules between cells
2) Apical microvilli → ↑SA:Vol
38
How are taste particles transduced into action potentials in primary neurons?
1) Dissolve in saliva/mucus of mouth
2) Dissolved taste ligands interact with apical receptor/channel on taste cell
3) Signal transduction cascade initiated → AP in 1° neuron
39
How do the signal transduction mechanisms differ for salt, sour, bitter, sweet and "umami" tastants?
1) Stimuli (Na+/H+/tastant ligands)
2) Membrane receptors/ channels
- salt and sour: channel proteins
- bitter, sweet, umami: GPCR
3) Transmitter:
- salt and sour: serotonin via external Ca2+ influx
- bitter, sweet umami: ATP via internal Ca2+ → external Na+ influx
40
Describe the transduction mechanisms of salt and sour tastants.
Tastant ions either (i) pass directly through respective membrane channels or (ii) block them
→ membrane depolarisation
→ opening of voltage gated Na+ and Ca2+ channels → influx
→ exocytosis of serotonin from synaptic vesicles
→ gustatory afferent axon
41
Describe the transduction mechanisms for bitter, sweet and umami tastants.
Tastants bind to GPCR
→ activate Phospholipase C → ↑IP3
→ triggers intracellular release of Ca2+
→ open taste-specific ion channel → ↑Na+ influx
→ depolarisation → ATP release
→ ATP diffuse through ATP-permeable channels → gustatory afferent axon
42
What is the typical life span of an olfactory neuron?
2 months
- replaced by new cells whose axons must find their way to the olfactory bulb
43
The olfactory epithelium is located _______________________ and comprises of ____________ cells which project into the olfactory bulb.
Olfactory epithelium
- high within nasal cavity
- olfactory cells (1° sensory neurons) → project into olfactory bulb
44
How are olfactory receptors replaced?
By basal cell layer beneath lamina propria of olfactory epithelium
45
Describe the mechanism of olfactory transduction.
Odorant dissolves in apical mucus layer
→ binds to odorant receptor protein of Golf-protein (GCPR)
→ activate adenylyl cyclase → ↑cAMP
→ open Ca2+ and Na+ channels → influx
→ ↑Ca2+ → Cl- efflux
→ membrane depolarisation
46
What are the constituents of the external ear?
1) Outer ear
2) Pinna
3) Ear canal
47
What is the function of the pinna?
Directs sounds waves into the ear
48
The ear canal is sealed at its internal end by ______________________.
Tympanic membrane (eardrum)
- thin membranous sheet of tissue
49
What structure separates the external ear from the middle ear?
Tympanic membrane
50
What is the middle ear?
Air-filled cavity that connects with the pharynx through the eustachian tube
51
Describe the regulation of middle ear pressure.
Eustachian tube
- normally collapsed → seal off middle ear
- opens transiently to allow middle ear pressure to equilibrate with atmospheric pressure during eg. chewing, swallowing, yawning
52
What is otitis media?
Infection of the middle ear
53
What structure separates the fluid-filled inner ear from the air-filled middle ear?
Oval and round window
- membranous discs
54
What are the 3 bones of the middle ear?
1) Malleus (hammer)
2) Incus (anvil)
3) Stapes (stirrup)
55
How are the 3 bones of the middle ear related?
Connected by biological "hinges"
- 1 end of malleus attached to tympanic membrane
- stirrup end of stapes attached to thin membrane separating middle ear from inner ear
56
What are the 2 major sensory structures of the inner ear?
1) Vestibular apparatus
- sensory transducer
- semicircular canals
2) Cochlea
- contains sensory receptors
- membranous tube coiled like snail shell within bony cavity
57
Which nerve leads from the inner ear to the brain to transmit sensory stimuli to the vestibular and cochlear nuclei of the pons and medulla oblongata.
Vestibulocochlear nerve
- branches of CNVIII
58
Sound waves are distinguished by their ______________.
1) Amplitude (dB)
2) Frequency (Hz)
59
Intensity is measured on a ________ scaled in (units) and is a function of wave _____________.
Intensity
- measured logarithmic scale in dB
- function of wave amplitude
60
What is the typical audible ranges of frequency and noise level?
Frequency:
- 20-20000Hz
Noise level:
~60dB (depends on sensitivity of individual ear)
61
Describe the process of sound transmission through the ear?
1) Sound waves strikes tympanic membrane → vibrations
2) Sound wave energy transferred to 3 bones of middle ear → vibrate
3) Stapes transmit vibration to fluid within cochlea through membrane of oval window
4) Fluid waves push on flexible membranes of the cochlear duct → hair cells bend → open ion channels
5) Depolarisation → NT release → sensory neurons → AP through cochlear nerve to brain
6) Wave energy transfers across cochlear duct into tympanic duct and dissipated back into middle ear at round window
62
What are the 3 ducts of the inner ear?
1) Vestibular duct (perilymph)
2) Cochlear duct (endolymph)
3) Tympanic duct (perilymph)
63
Hair cells are (neural/non-neural) receptor cells.
Non-neural
64
Describe the process of signal transductions in the hair cells.
At rest:
- ~10% ion channels open → tonic signals
Excitation:
- hair cells bend → depolarisation → ↑AP freq. in associated sensory neuron
Inhibition:
- hair cells bend in opposite direction → ion channels close → hyperpolarisation → ↓AP
65
Describe the process of sensory coding for pitch.
Primarily by basilar membrane:
- tiff & narrow near round/oval window attachments, distal & flexible near distal end
- frequency determines displacement of basilar membrane
→ location of maximal displacement/active hair cells
→ differential response to frequency
→ transform temporal aspect (pitch and frequency) into spatial (along basilar membrane) coding for pitch
66
Where are the sensory cell bodies in the PNS located?
Spinal ganglion of each spinal nerve
67
Where is the spinal cord are lower motor neurons found?
Anterior horn
68
Where are the the cell bodies and exit paths of primary efferent autonomic fibers?
Cell bodies → lateral horn
Leave through anterior root
69
Where in the spinal cord do afferent autonomic and somatic fibres travel?
Posterior root
70
Describe the general pathway for somatic perception.
1) Spinothalamic tract:
- Pain, temperature, coarse touch decussate in spinal cord
2) DCML pathway:
- Fine touch, vibration, proprioception decussate in medulla
3) Sensory pathways synapse in thalamus
4) Sensations perceived in primary somatic sensory cortex
71
The amount of space/size of the somatosensory cortex devoted to each body part is proportional to _____________________.
Sensitivity of that part
72
The receptive fields of Meissner's corpuscles are relatively (bigger/smaller) than that of Pacinian corpuscle
Meissner's (fine touch) < Pacinian (vibration)
73
What are 3 modalities by which mechanosensitive ion channels transduce sensory stimuli into electrochemical gradients?
1) Sensitive to stretch of lipid membrane
2) Linked to extracellular peptides (sensitive to force)
3) Linked to intracellular proteins (eg. cytoskeleton)
74
What are 2 types of temperature receptors?
1) Cold receptors
- sensitive to body temp
75
How does temperature above a certain level create a pain sensation?
Beyond ~45° → warm + nociceptor activation
76
Which thermosensitive TRP channel is responsive to menthol?
TRPM8
77
Which thermosensitive TRP channel is responsive to capsaicin?
TRPV1
78
Which type of receptor is more prevalent, cold or warm receptors?
Cold > warm
79
How does the brain differentiate between changing and ambient temperature?
Temperature receptors slowly adapt between 20°C and 40°C
- initial response → temp is changing
- sustained response → ambient temperature
80
Do thermoreceptors adapt beyond ~40°C?
No, likelihood of tissue damage is greater
81
Cold receptors are coupled to ___________ fibers while warm receptors are coupled to _________________ fibers.
Cold: A-δ, C fibres
Warm: C fibres
82
Are thermoreceptors more responsive to sudden or slow changes in temperature?
Sudden
- adapt over several seconds
83
The diameter of an axon is correlated with its ____________________________.
1) Conduction velocity
2) type of sensory receptor to which it is connected
84
What are the different nerve fibre groups and which are myelinated?
Myelinated:
1) A-α
2) A-ß
3) A-δ
Unmyelinated:
4) C
85
Thicker nerve fibers transmit information (more/less) quickly?
Thicker → faster
86
What is the somatosensory cortex?
part of the brain that recognizes where ascending sensory tracts originate/processes sensory information
87
What is the homunculus and how is it related to the organisation of sensory pathways in the somatosensory cortex?
Mapping of the geographical sensory tributaries onto the cortex
- columnar arrangement → maintain association with receptors and sensory modality
88
What is the physiological mechanism behind phantom limb pain?
Somatotropic map plasticity
- portion of the somatosensory cortex devoted to the missing structure begins to be taken over by sensory fields of adjacent structures.
89
What are the 2 sensations perceived upon nociceptor activation?
Pain and itch
90
How is sharp pain differentiated from dull pain?
Primary vs secondary pain
Primary
- A-δ fibres → well localised sharp pain
Secondary
- C fibres → poorly localised dull pain
91
How does tissue injury cause pain?
Tissue injury
→ release of bradykinin, 5-HT, prostaglandins, K+
→ stimulate C-fibres
92
How do active C-fibers aid in tissue inflammation?
Release CGRP and substance P →
i) Stimulate mast cells → histamine
ii) Vasodilation
93
What are the 2 types of synaptic targets of A-δ and C fibres?
1) Nociceptive-specific (NS) cells
- only synapse with A-δ and C fibers
2) Wide dynamic range (WDR) neurons
- synapse with all types of sensory fibers
94
What are the neurotransmitters and their respective receptors in a posterior horn nociceptive synapse?
1) Glutamate → AMPA, NMDA , mGLu
2) Substance P → NK1
3) CGRP → CGRP
95
Nociceptive synapses in the posterior horn are (excitatory/inhibitory).
Excitatory
96
How is the intensity of dull pain transmitted to the brain?
C-fibers → WDR neurons
- WDR can fire APs in graded fashion: "wind-up" → progressive amplification of repetitive C-fibre stimulated APs
∴ ↑pain/stimulation → ↑freq. of C-fibre discharge → ↑WDR neuron response
97
What is "wind-up" in the spinal cord and how does it happen?
Amplification in response to repetitive excitatory stimulation of WDR neurons from nociceptive input from C-fibers
1) ↑repetitive C-fiber input → ↑AP freq. + sustained membrane depolarisation
2) Usual blockade of NMDA receptor by Mg2+ released by sustained depolarisation
3) NMDA activated by glutamate → Ca2+ influx
4) Insertion of Na+ channels + block K+ → ↑Na and K+ in cell → ↑depolarisation and ↓hyperpolarisation/refraction
→ ↑ neuronal excitability / response to C-fibre input
98
What is the difference between hyperalgesia and allodynia?
Hyperalgesia
- heightened response to normally painful stimulus
Allodynia
- normally non-painful stimulus perceived as painful
99
What are the 2 ascending pain pathways and how do they differ?
1) Lateral sensory-discriminative
- organised somatotropically → pain localisation in 1° somatosensory cortex
2) Medial affective-motivational pathways
- dull, poorly localised pain
- influences:(i) emotional (ii) visceral (iii) descending pain modulation
100
Using gate-control theory, explain why rubbing a bumped elbow lessens the perceived pain.
Rubbing → non-painful stimulus → activate A-ß fibres → synapse on inhibitory interneurons
→ enhance tonic inhibition of ascending pain pathway
∴ Partial inhibition of summative ascending pathway stimulation even with C-fibre stimulation → relief of pain
101
What is the function of the endogenous opioid system?
Provide modulatory influence on cortical pain process
102
What are 3 endogenous molecules that physiologically activate opioid receptors?
1) Enkephalins
2) Endorphins
3) Dynorphins
103
How does the endogenous
opioid system provide analgesia?
Release of (i) enkephalins (ii) endorphins (iii) dynorphins
→ activation of opioid receptors
→ inhibit Ca2+ and/or open K+ channels
→ hyperpolarisation + ↓neuronal excitability
104
What are the 4 types of pain?
1) Radicular
- dermatome
2) Referred
- viscerosomatic convergence
3) Phantom pain
- pain in absent of insensate (by nerve severance) part of body
4) Central pain
- from lesion in thalamus or cortex → pain in corresponding mapped body part
105
What is the difference between aphasia, dysarthria, speech ataxia and cognitive-communication defects?
Aphasia:
- impaired ability to understand and produce language
Dysarthria:
- ↓intelligibility due to weakness in speech muscles
Speech apraxia:
- difficulty coordinating the movements needed for speech, despite having no weakness in the speech muscles themselves
Cognitive-communication defects:
- difficulties in communicating in higher level with corresponding deficits in cognitive functions and pragmatics
106
Which germ layer and part of the pharyngeal apparatus is the external ear canal from?
Ectoderm
1st pharyngeal cleft
107
Which germ layer and part of the pharyngeal apparatus is the tympanic membrane from?
Mesoderm of 1st arch
108
Which germ layer and part of the pharyngeal apparatus is the eustachian tube from?
Endoderm
1st pharyngeal pouch
109
Which part of the pharyngeal apparatus are the ear ossicles from?
Malleus + Incus' short process and body ← 1st arch
Incus' long process + Stapes cura ← 2nd arch
110
How does the external ear help us with hearing?
Amplification and localisation
111
Why is impedance matching important in hearing?
Reflection coefficient for terrestrial animals very high (specific acoustic impendence difference very big between air and liquid in cochlear) → need matching to transmit more energy to inner ear for sensing
112
What are 3 features of the middle ear that help with impedance matching?
1) Tympanic membrane to oval window ratio (high→20x)
2) Lever action of ossicles
- malleus 30% longer than incus → 1.3x by lever action
3) Buckling action of tympanic membrane
- 2x amplfication
Total: 2x20x1.3=52x amplification
113
Which part of the inner ear are cochlear hair cells located?
Organ of Corti
114
How are the cochlear hair cells arranged?
3 outer rows:
- amplify sound
- signal modulation
1 inner row
- main signal transducer
115
Describe the tonotropic arrangement of the cochlear.
Hair cells sensitive to higher pitch → base
Hair cells sensitive to lower pitch → apex
116
Which lobe is the auditory cortex found in?
Temporal
117
The cochlear nucleus receives (ipsi/contra/bilateral) contribution before decussating.
Bilateral
118
How would a px with age-related hearing loss commonly present on an audiometry?
Sloping, hearing loss accentuated at higher frequencies
119
What are 4 forms of hearing tests?
1) Audiometry
2) Auditory brainstem response (ABR) testing
3) Otoacoustic emission (OAE) testing
4) Weber's test
5) Rinne's test
120
What are 2 treatment modalities for conductive hearing loss?
1) Myringotomy and tube insertion (if effusion into middle ear)
2) Ossiculoplasty (if ossicles absent)
3) MAHA (bone conduction device)
121
What are 2 treatment modalities for sensorineural hearing loss?
1) Cochlear implants
2) Hearing aids
122
What are the transparent mediums of the eye?
1) Cornea
2) Lens
123
How is the transparency of the cornea maintained?
Regular arrangement of collagen layers
- by constant level of hydration between evaporation and active transport by carbonic anhydrase pump of endothelium
124
The lens is a bi(concave/convex) structure that is manipulated by the ciliary body and suspensory ligaments to allow for focusing.
Biconvex
125
What it the "near triad" for viewing near objects?
1) Accommodation
- ciliary muscles contract → suspensory ligaments relax → lens more convex (↑AP diameter → ↑refraction)
2) Convergence
3) Miosis
126
What are 3 forms of refractive error in the eye?
1) Myopia
- axial length too long/refractive medium too strong → light focused in front of retina → distant blur
- correct with divergent lens
2) Hyperopia
- axial length too short → light focused behind retina → accommodation needed for distant vision → near/distant blur
- correct with convergent lens
3) Presbyopia
- failure in accommodation → near/far blur
- correct with convergent lens
4) Astigmatism
- refractive surfaces have different radii of curvature → 2 points of focus
- correct with cylindrical lens
127
What does the retinal pigment epithelium layer do?
1) Contains melanin → absorbs light and reduces scatter
2) Vitamin A cycle
- regeneration of visual pigment (11-cis-retinal)
128
Describe the biosignalling mechanism when light strikes the retina.
1) Light strikes Rhodopsin
11-cis-retinal → all-trans-retinal
2) Hyperpolarisation of photoreceptors
3) ↓inhibitory NTs to bipolar cells → depolarisation
4) Bipolar synapse with retinal ganglion cells → AP to brain
129
What does 6/6 vision mean?
A subject can, at 6m, read a letter that subtends 5'/arc
130
The different cones have the same ___________ but different __________, leading to different maximum sensitivity to RGB wavelengths respectively.
Same vitamin A chomophore
Different opsin protein
131
What visual defect is caused by vitamin A deficiency?
Night blindness
- insufficient chromophore/retinal → loss of night vision
132
What visual defect is caused by macular edema/submacular hemorrhage?
Loss of normal acuity but not blindness
133
What visual defect is caused by rod-cone dystrophies?
Genetic defects in opsin protein
- inability to detect light → poor night vision and visual acuity
134
What are 5 functional brain areas for vision?
V1: 1° visual cortex
V2: 2° visual cortex
V3: Dorsal → motion, Ventral → colour
V4: Extrastriate → colour
V5: Middle temporal cortex/lingual gyrus → motion, facial recognition
6) Inferotemporal cortex → shapes
7) Hippocampus → visual memory
135
What is the primary action of the medial rectus?
Adduction
136
What is the primary action of the lateral rectus?
Abduction
137
What are the (i) primary (ii) secondary and (iii) tertiary actions of the superior rectus?
i) Elevation
ii) Intorsion
iii) Adduction
138
What are the (i) primary (ii) secondary and (iii) tertiary actions of the inferior rectus?
i) Depression
ii) Extorsion
iii) Adduction
139
What are the (i) primary (ii) secondary and (iii) tertiary actions of the superior oblique?
i) Intorsion
ii) Depression
iii) Abduction
140
What are the (i) primary (ii) secondary and (iii) tertiary actions of the inferior oblique?
i) Extorsion
ii) Elevation
iii) Abduction
141
What are 2 forms of anisocoria?
1) Parasympathetic/ constriction failure
- more apparent in light
- eg. Adie's tonic pupil, CNIII palsy, pharmacologic
2) Sympathetic/ dilation failure
- more apparent in dark
- eg. physiologic, Horner's
