ReDiClus

ReDiClus - Receptor Diffusion & Cluster Model

Simulation Space

ReDiClus Model Space

ReDiClus is simulated on a 2D surface in 3D space

• The surface area represents a dendritic membrane with two synaptic spines
• Baseline dimensions are scaled to real-world values
  • these values are based on empirical observations of distal dendrites
  • base dimensions are set to 60x30 units

Scale

• 1 unit ≃ 100 nm

• 10 units ≃ 1 µm

• 2D space: 2.3 µm x 4.6 um
• PSD: 0.3 x 0.3 µm
• peri-PSD: 0.3 x 0.3 µm
• PSD separation: 2.0 µm

• The Z axis is only 2 levels: 0 and 1
  • 1 represents the membrane surface
  • 0 represents intracellular space

Particle Types

There are 2 types of particles in the simulation

• 'Red' particle dots represent AMPA receptors
  • Red dots can randomly diffuse anywhere on the X-Y plane
  • Red dots only diffuse on the surface Z = 0
• 'Blue' particle dots represent PSD-95 molecules
  • Blue dots are contained in predefined PSD areas and cannot leave
  • Blue dots can exist at the surface Z = 0 or intracellularly Z = -1

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Visual Representations

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{Box|font=120%|width=95%|float=left|text=12px|Particle Diffusion| Diffusion rates are at empirically relevant values

• The extrasynaptic diffusion rate D (D_es)
  • D_es ≃ 0.3 um²/s
• The PSD diffusion rates (D_psd) can be set manually to whatever we want, but usually:

• D_psd ≃ 0.03 um²/s

to

• D_psd ≃ 0.003 um²/s

The PSD diffusion rates (D_psd) can also be scaled automatically by the number of SAP molecules currently expressed in a cluster. For most simulations the starting SAP cluster size is 7x7 yielding 49 total SAP molecules. The amount of SAP dynamically fluctuates. It can hold a fairly steady number of about 50 SAPs, but it can also be made to grow and shrink to values ranging from 10 to 100 SAPs. The PSD diffusion rate can be scaled from these SAP values. We can make the curve by which it alters diffusion rate whatever we want, but right now it's simply {D_psd ≃ D_es/SAP}. Thus, given a range of 10 to 100 SAPs, we can see PSD diffusion rate values of (same range as manual values above):

• D_psd ≃ 0.3/10 ≃ 0.03 um²/s

to

• D_psd ≃ 0.3/100 ≃ 0.003 um²/s

}}

Physical Properties

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ReDiClus Physics

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two independent processes

In this model, there are two independently occurring processes.

• 1. Blue dots can be expressed at the surface or internalized within their PSD area
  • The Blue dot internalization/externalization rate properties are set by the Shouval cluster model equations.
• 2. Red dots diffuse on the X-Y plane with brownian motion
  • Each Red dot has an initial step size randomly drawn from a normal distribution with a mean = 1 and sd = .2

The step size for Red dots is dynamically altered when it's located in a PSD area

• In a PSD, the step size is reduced by a by some factor based on the number of Blue dots currently expressed at the surface of that PSD
• The more Blue dots at the surface, the more the step size is reduced
• The current step size function is:
  • f(R_step) = R * (10*(1 ⁄ B_n))
    • where R_step is the baseline Red dot step size
    • where B_n is number of Blue dots currently expressed at the PSD surface

Several screen shots of the dynamic graphs in the model

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MEAN SQUARED DISPLACEMENT

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Brownian Motion Mean Squared Displacement

• The goal of this calculation is to relate the simulated particle diffusion to real world values, namely velocity.
• Particle velocity will be a function of MSD x units ²⁄s which scales on space (units) and time (s) parameters.
• Space and time in the model are defined arbitrarily as Step_Size and Step where each Step a particle moves a distance randomly chosen from a normal distribution (µ=1,σ=.2)
• a step size of 1 unit/step will produce a brownian motion MSD of ~0.52 ±0.2 units ²/s
• empirical observations show that reasonable values for MSD are:
  • PSD 0.01 µm ²/s
  • synaptic 0.05 µm ²/s
  • extrasynaptic 0.1 µm ²/s

• given an MSD of 0.52 ±0.2 units ²/s at the current parameters: 1 step = 1 unit (at µ=1,σ=.2), the model will need to be scaled such that particles move at an extrasynaptic rate of 0.1 µm ²/s.
• spines are on average 1 to 10 µm apart, if the model is comparing two spines 1 µm apart, they should be separated by 5 units of model space. This is because the current particle diffusion rate of the model is .5 µm ²/s and the empirical MSD is .1 µm ²/s

Data Generation

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ReDiClus MODEL DATA RESULTS

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ReDiClusData

Neural Anatomy

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Quantitative Physiology of the Dendrite

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Quantitative Review

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Harris Website

The Size of Dendrites

adapted from Sheng and Hoogenraad (2007) ^FIG: {{#info

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• Dendrite: 1–10 spines per 10 μm
  
• Spines: 0.5–2 μm in length
  
• PSD: 100 - 300 nm diameter
  
• PSD95: within 12 nm of surface
  

adapted from Harris ^FIG: {{#info

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• proximal dendrite diameter: 1 - 3 µm
• distal dendrite diameter: 0.2 - 2 µm
• dendrite length: 2000 - 9000 µm
• dendrite tip to soma: 100 - 200 µm
• dendrites at soma: 1 - 5
• dendrite branches (granual): 10 - 30
• dendrite branches (purkinje): 400-500

Table of spine sizes, adapted from Harris 1992 ^FIG: {{#info

Harris 1992 Harris 1992 }}

Particle Counts

adapted from Sheng and Hoogenraad (2007) ^FIG: {{#info

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• PSD: 10,000 proteins (or 100 copies of 100 proteins)
  
• CaMKIIα: 7.4%
  
• CaMKIIβ: 1.3%
  
• SynGap: 2.1 pmol/20 μg
  
• NMDAR: 20 proteins
  
• AMPAR: 15 proteins
  
• GluR: 60 subunits, 15 tetramers, 80% or 12 GluR1/GluR2 heteromers
  
• PSD95: within 12 nm of surface
  

Diffusion Rates

from Choquet 2010 ^FIG: {{#info

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• extrasynaptic: 0.1 µm²⁄s
• synaptic: 0.05 µm²⁄s
• synaptic after glu/gly: 0.01 µm²⁄s

Images

From Sheng and Hoogenraad 2007

• Spine morphology ^FIG: {{#info: Error creating thumbnail: File missing{{{2}}} CLICK AWAY FROM IMAGE TO CLOSE }}

From Harris KM and Weinberg 2012

• Spine morphology ^FIG: {{#info: 3D reconstruction of a proximal CA3 pyramidal cell dendrite (blue) and a large mossy fiber bouton (translucent yellow). The cut-away in C2 shows synapses (red) onto multiple dendritic spines, some of which are highly branched. The bouton also forms nonsynaptic cell adhesion junctions (fuchsia). CLICK AWAY FROM IMAGE TO CLOSE }}
• Hippocampal dendrite ^FIG: {{#info: {{{2}}} CLICK AWAY FROM IMAGE TO CLOSE }}

Choquet 2007 Real Time Receptor Diffusion

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Choquet 2007 Real Time Receptor Diffusion Analysis

• The video represents a 10µm × 10µm section scaled to a 535px × 535px video.
  • 1_µm : 53.5_px
• The analysis below documents one instance of Qdot diffusion, between the 6s-7s time points.
• This instance was chosen because of the clarity of motion and no Qdot flicker.
• The Qdot (center) moves from pixel location (X:291, Y:302) at 6.78s to (X:319, Y346) at 6.98s
  • That is a distance of 52.2px in 200ms
  • Qdot velocity: Q_v ≈ 1_µm ⁄ 200_ms
  • Note this diffusion rate of 5µm/s is 10-fold higher than the median diffusion rate reported above.
  • An upper bound of 5µm/s means that receptors can move between synapses in fractions of a second.

Figures:

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Receptor Diffusion Rate Best Estimates

• GABAA: .01 - .05 µm²/s ^FIG: {{#info: Choquet 2010 CLICK AWAY FROM IMAGE TO CLOSE }}

Brain Data: Facts and Figures

Estimated Number of Neurons in the Brain of Humans & Other Animals

Average number of neurons and synapses in the human brain

Neurons: 100 billion (100,000,000,000; 1e11)

Synapses: 100 trillion (100,000,000,000,000; 1e14)

• The brain's weight composes ~2% of total body weight (150 pound human)
• Average brain width = 140 mm
• Average brain length = 167 mm
• Average brain height = 93 mm
• Intracranial contents by volume (1,700 ml, 100%): brain = 1,400 ml (80%); blood = 150 ml (10%); cerebrospinal fluid = 150 ml (10%)

(from Rengachary, S.S. and Ellenbogen, R.G., editors, Principles of Neurosurgery, Edinburgh: Elsevier Mosby, 2005)

• Average number of neurons in the brain = 100 billion
• Number of neurons in octopus brain = 300 million (from How Animals See, S. Sinclair, 1985)
• Number of neurons in honey bee brain = 950,000 (from Menzel, R. and Giurfa, M., Cognitive architecture of a mini-brain: the honeybee, Trd. Cog. Sci., 5:62-71, 2001.)
• Number of neurons in Aplysia nervous system = 18,000-20,000
• Number of neurons in each segmental ganglia in the leech = 350
• Volume of the brain of a locust = 6mm3 (from The Neurobiology of the Insect Brain, Burrows, M., 1996)

• Ratio of the volume of grey matter to white matter in the cerebral hemipheres (20 yrs. old) = 1.3 (Miller, A.K., Alston, R.L. and Corsellis, J.A., Variation with age in the volumes of grey and white matter in the cerebral hemispheres of man: measurements with an image analyser, Neuropathol Appl Neurobiol., 6:119-132, 1980)
• Ratio of the volume of grey matter to white matter in the cerebral hemipheres (50 yrs. old) = 1.1 (Miller et al., 1980)
• Ratio of the volume of grey matter to white matter in the cerebral hemipheres (100 yrs. old) = 1.5 (Miller et al., 1980)
• % of cerebral oxygen consumption by white matter = 6%
• % of cerebral oxygen consumption by gray matter = 94%

• Average number of glial cells in brain = 10-50 times the number of neurons (New research suggests the neuron-to-glia ratio may be much smaller, closer to 1:1)

(For more information about the number of neurons in the brain, see R.W. Williams and K. Herrup, Ann. Review Neuroscience, 11:423-453, 1988)

• Number of neocortical neurons (females) = 19.3 billion (Pakkenberg, B., Pelvig, D., Marner,L., Bundgaard, M.J., Gundersen, H.J.G., Nyengaard, J.R. and Regeur, L. Aging and the human neocortex. Exp. Gerontology, 38:95-99, 2003 and Pakkenberg, B. and Gundersen, H.J.G. Neocortical neuron number in humans: effect of sex and age. J. Comp. Neurology, 384:312-320, 1997.)
• Number of neocortical neurons (males) = 22.8 billion (Pakkenberg et al., 1997; 2003)
• Average loss of neocortical neurons = 85,000 per day (~31 million per year) (Pakkenberg et al., 1997; 2003)
• Average loss of neocortical neurons = 1 per second (Pakkenberg et al., 1997; 2003)
• Average number of neocortical glial cells (young adults ) = 39 billion (Pakkenberg et al., 1997; 2003)
• Average number of neocortical glial cells (older adults) =36 billion (Pakkenberg et al., 1997; 2003)
• Number of neurons in cerebral cortex (rat) = 21 million (Korbo, L., et al., J. Neurosci Methods, 31:93-100, 1990)
• Length of myelinated nerve fibers in brain = 150,000-180,000 km (Pakkenberg et al., 1997; 2003)
• Number of synapses in cortex = 0.15 quadrillion (Pakkenberg et al., 1997; 2003)
• Difference number of neurons in the right and left hemispheres = 186 million MORE neurons on left side than right side (Pakkenberg et al., 1997; 2003)

Proportion by Volume (%)

Rat vs Human

• Cerebral Cortex: 31 vs 77
• Diencephalon: 7 vs 4
• Midbrain: 6 vs 4
• Hindbrain: 7 vs 2
• Cerebellum: 10 vs 10
• Spinal Cord: 35 vs 2

(Reference: Trends in Neurosciences, 18:471-474, 1995)

• Total surface area of the cerebral cortex = 2,500 cm2 (2.5 ft2; A. Peters, and E.G. Jones, Cerebral Cortex, 1984)
• Total surface area of the cerebral cortex (lesser shrew) = 0.8 cm2
• Total surface area of the cerebral cortex (rat) = 6 cm2
• Total surface area of the cerebral cortex (cat) = 83 cm2
• Total surface area of the cerebral cortex (African elephant) = 6,300 cm2
• Total surface area of the cerebral cortex (Bottlenosed dolphin) = 3,745 cm2 (S.H. Ridgway, The Cetacean Central Nervous System, p. 221)
• Total surface area of the cerebral cortex (pilot whale) = 5,800 cm2
• Total surface area of the cerebral cortex (false killer whale) = 7,400 cm2

(Reference for surface area figures: Nieuwenhuys, R., Ten Donkelaar, H.J. and Nicholson, C., The Central nervous System of Vertebrates, Vol. 3, Berlin: Springer, 1998)

• Total number of neurons in cerebral cortex = 10 billion

(from G.M. Shepherd, The Synaptic Organization of the Brain, 1998, p. 6). However, C. Koch lists the total number of neurons in the cerebral cortex at 20 billion (Biophysics of Computation. Information Processing in Single Neurons, New York: Oxford Univ. Press, 1999, page 87).

• Total number of synapses in cerebral cortex = 60 trillion (yes, trillion)

(from G.M. Shepherd, The Synaptic Organization of the Brain, 1998, p. 6). However, C. Koch lists the total synapses in the cerebral cortex at 240 trillion (Biophysics of Computation. Information Processing in Single Neurons, New York: Oxford Univ. Press, 1999, page 87).

• Percentage of total cerebral cortex volume (human): frontal lobe = 41%; temporal lobe = 22%; parietal lobe = 19%; occipital lobe = 18%.

(Caviness Jr., et al. Cerebral Cortex, 8:372-384, 1998.)

• Number of cortical layers = 6
• Thickness of cerebral cortex = 1.5-4.5 mm
• Thickness of cerebral cortex (Bottlenosed dolphin) = 1.3-1.8 mm (S.H. Ridgway, The Cetacean Central Nervous System, p. 221)

• Rate of neuron growth (early pregnancy) = 250,000 neurons/minute
• Length of spiny terminals of a Purkinje cell = 40,700 micron
• Number spines on a Purkinje cell dendritic branchlet = 61,000
• Surface area of cerebellar cortex = 50,000 mm2 (from G.M. Shepherd, The Synaptic Organization of the Brain, 2004, p. 271)
• Weight of adult cerebellum = 150 grams (Afifi, A.K. and Bergman, R.A., Functional Neuroanatomy, New York: McGraw-Hill, 1998)
• Number of Purkinje cells = 15-26 million
• Number of synapses made on a Purkinje cell = up to 200,000
• Weight of hypothalamus = 4 g
• Volume of suprachiasmatic nucleus = 0.3 mm3
• Number of fibers in pyramidal tract above decussation = 1,100,000
• Number of fibers in corpus callosum = 250,000,000
• Area of the corpus callosum (midsagittal section) = 6.2 cm2

Species

Cerebellum Weight (grams) vs Body Weight (grams)

• Human: 142 vs 60,000
• Mouse: 0.09 vs 58
• Bat: 0.09 vs 30
• Flying Fox: 0.3 vs 130
• Pigeon: 0.4 vs 500
• Guinea Pig: 0.9 vs 485
• Squirrel: 1.5 vs 350
• Chinchilla: 1.7 vs 500
• Rabbit: 1.9 vs 1,800
• Hare: 2.3 vs 3,000
• Cat: 5.3 vs 3,500
• Dog: 6.0 vs 3,500
• Macaque: 7.8 vs 6,000
• Sheep: 21.5 vs 25,000
• Bovine: 35.7 vs 300,000

Source: Sultan, F. and Braitenberg, V. Shapes and sizes of different mammalian cerebella. A study in quantitative comparative neuroanatomy. J. Hirnforsch., 34:79-92, 1993.

Neurons

• Mass of a large sensory neuron = 10-6gram (from Groves and Rebec, Introduction to Biological Psychology, 3rd edition, Dubuque: Wm.C. Brown Publ., 1988)
• Number of synapses for a "typical" neuron = 1,000 to 10,000
• Diameter of neuron = 4 micron (granule cell) to 100 micron (motor neuron in cord)
• Diameter of neuron nucleus = 3 to 18 micron
• Length of Giraffe primary afferent axon (from toe to neck) = 15 feet
• Resting potential of squid giant axon = -70 mV
• Conduction velocity of action potential = 0.6-120 m/s (1.2-250 miles/hr)

• Single sodium pump maximum transport rate = 200 Na ions/sec; 130 K ions/sec
• Typical number of sodium pumps = 1000 pumps/micron2 of membrane surface (from Willis and Grossman, Medical Neurobiology, Mosby, St. Louis, 1981, p. 36)
• Total number of sodium pumps for a small neuron = 1 million
• Density of sodium channels (squid giant axon) = 300 per micron2 (from Hille, B., Ionic Channels of Excitable Membranes, Sinauer, Sunderland, 1984, p. 210.)
• Number of voltage-gated sodium channels at each node = 1,000 to 2,000 per micron2 (from Nolte, J., The Human Brain, Mosby, 1999, p. 163.)
• Number of voltage-gated sodium channels between nodes = 25 per micron2 (from Nolte, J., The Human Brain, Mosby, 1999, p. 163.)
• Number of voltage-gated sodium channels in unmyelinated axon = 100 to 200 per micron2 (from Nolte, J., The Human Brain, Mosby, 1999, p. 163.)
• Diameter of ion channel = 0.5 nanometer (Breedlove et al., Biological Psychology, 2007)
• Diameter of microtubule = 20 nanometer
• Diameter of microfilament = 5 nanometer
• Diameter of neurofilament = 10 nanometer
• Thickness of neuronal membrane = 5 nanometer (Breedlove et al., Biological Psychology, 2007)
• Thickness of squid giant axon membrane = 50-100 A
• Membrane surface area of a typical neuron = 250,000 um2 (Bear et al., 2001)
• Membrane surface area of 100 billion neurons = 25,000 m2, the size of four soccer fields (Bear, M.F., Connors, B.W. and Pradiso, M.A., Neuroscience: Exploring the Brain, 2nd edition)

• Typical synaptic cleft distance = 20-40 nanometers across (from Kandel et al., 2000, p. 176)
• % neurons stained by the Golgi method = 5%
• Slow axoplasmic transport rate = 0.2-4 mm/day (actin, tubulin)
• Intermediate axoplasmic transport rate = 15-50 mm/day (mitochondrial protein)
• Fast axoplasmic transport rate = 200-400 mm/day (peptides, glyolipids)
• Number of molecules of neurotransmitter in one synaptic vesicle = 5,000 (from Kandel et al., 2000, p. 277)
• Diameter of synaptic vesicle = 50 nanometer (small); 70-200 nanometer (large)
• Diameter of neurofilament = 7 - 10 nm
• Diameter of microtubule = 25 nm
• Internodal Length = 150 - 1500 microns (depends on fiber diameter)
• % composition of myelin = 70-80% lipid; 20-30% protein

Ion Concentration (mM) in Mammalian Neurons

Intracellular vs Extracellular

• Potassium: 140 vs 5
• Sodium: 10 vs 150
• Chloride: 10 vs 100
• Calcium: 0.0001 vs 1

Because of its large number of tiny granule cells, the cerebellum contains more neurons than the rest of the brain, but takes up only 10% of the total brain volume. The number of neurons in the cerebellum is related to the number of neurons in the neocortex. There are about 3.6 times as many neurons in the cerebellum as in the neocortex, a ratio that is conserved across many different mammalian species. What gives? Two things really: (1) The neocortex has a large proportion of pyramidal neurons which are much bigger than granule cells, and (2) Purkinje cells can make up to 200k synaptic connections (contrast that with 1k - 10k for "typical" neurons of other types).

Brain vs Computer

Facts and Figures

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Microprocessors

A microprocessor incorporates the functions of a computer's central processing unit on a single integrated circuit. It is a multipurpose, programmable device that accepts digital data as input, processes it according to instructions stored in its memory, and provides results as output.

Processor	Transistor count	Date of introduction	Manufacturer	Semiconductor device fabrication|Process	Area
Core 2 Duo Wolfdale3M	230,000,000	2008	Intel	45 nm	83 mm²
Core i7 (Quad)	731,000,000 (7e8)	2008	Intel	45 nm	263 mm²
POWER6	789,000,000	2007	IBM	65 nm	341 mm²
WDC 65C02	785,000,000	2009	western design center	0.22 µm	14 mm²
Six-Core Opteron 2400	904,000,000	2009	AMD	45 nm	346 mm²
16-Core SPARC T3	1,000,000,000 (1e9)	2010	Sun Oracle Corporation|Oracle	40 nm	377 mm²
Quad-Core plus GPU Sandy Bridge Core i7	1,160,000,000	2011	Intel	32 nm	216 mm²
Core i7 (Gulftown)	1,170,000,000	2010	Intel	32 nm	240 mm²
8-core POWER7 32M L3	1,200,000,000	2010	IBM	45 nm	567 mm²
8-Core AMD Bulldozer	1,200,000,000	2012	AMD	32nm	315 mm²
Quad-Core + GPU AMD Trinity	1,303,000,000	2012	AMD	32 nm	246 mm²
z196	1,400,000,000	2010	IBM	45 nm	512 mm²
Core i7	1,400,000,000	2012	Intel	22 nm	160 mm²
Dual-Core Itanium 2	1,700,000,000	2006	Intel	90 nm	596 mm²
Six-Core Xeon 7400	1,900,000,000	2008	Intel	45 nm	503 mm²
Tukwila	2,000,000,000 (2e9)	2010	Intel	65 nm	699 mm²
8-core POWER7 80M L3	2,100,000,000	2012	IBM	32 nm	567 mm²
Six-Core Core i7 and 8-Core Xeon E5	2,270,000,000	2011	Intel	32 nm	434 mm²
Nehalem-EX	2,300,000,000	2010	Intel	45 nm	684 mm²
10-Core Xeon Westmere-EX	2,600,000,000	2011	Intel	32 nm	512 mm²
zEC12	2,750,000,000	2012	IBM	32 nm	597 mm²
Poulson	3,100,000,000 (3e9)	2012	Intel	32 nm	544 mm²
15-Core Xeon Ivy Bridge-EX	4,310,000,000 (4e9)	2014	Intel	22 nm
62-Core Xeon Phi	5,000,000,000	2012	Intel	22 nm
Xbox One Main SoC	5,000,000,000 (5e9)	2013	Microsoft/AMD	28 nm	363 mm²

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Molecular Methods

Quantum Dots

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Brownian Motion

Malinow

Molecular Methods

Quantum Dots

Choquet

AMPAR