imtoken钱包下载推荐|rrw
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2024-03-07 20:55:07
RRW Off Road | Relations Race Wheels: Strong, Well Built Rims & More
RRW Off Road | Relations Race Wheels: Strong, Well Built Rims & More
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Shop by Part RR5-S 16x8 RR5-V 16x8 RR6-S 17x7.5 RR6-H 17x8.5 Hybrid Beadlock RR7-H 17x8.5 Hybrid Beadlock Clearance Sale Floor Mats Lug Nuts Molle Panels Pre-Order
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Subtotal Go to cart Home Shop by Part Shop by Vehicle Contact RR5-S 16x8 RR5-V 16x8 RR6-S 17x7.5 RR6-H 17x8.5 Hybrid Beadlock RR7-H 17x8.5 Hybrid Beadlock Clearance Sale Floor Mats Lug Nuts Molle Panels Pre-Order
Chevy Colorado / ZR2 Silverado 1500 Ford Bronco Bronco Sport F150 / Raptor Maverick Ranger Transit GMC Canyon Jeep Gladiator Wrangler JK / JL Lexus GX460 / GX470 Subaru Crosstrek Forester SJ 4th Gen Forester SK 5th Gen Outback Toyota 4Runner FJ Cruiser Rav4 Tacoma Tundra (2021-older) Tundra (2022+)
Chevy Colorado / ZR2 Silverado 1500
Ford Bronco Bronco Sport F150 / Raptor Maverick Ranger Transit
GMC Canyon
Jeep Gladiator Wrangler JK / JL
Lexus GX460 / GX470
Subaru Crosstrek Forester SJ 4th Gen Forester SK 5th Gen Outback
Toyota 4Runner FJ Cruiser Rav4 Tacoma Tundra (2021-older) Tundra (2022+)
New Wheels Accessories
Read our Latest Blogs Add up to five columns
New Wheels Accessories
Read our Latest Blogs Add up to five columns
Monoforged Wheels RS2-H Monoforged Wheel RS2-S MonoForged RS4-H Hybrid MonoForged RS4-S MonoForged RS5-H Hybrid MonoForged RS6-H Hybrid MonoForged RS7-H Hybrid MonoForged RS7-S MonoForged Wheel Wheels RR2-S RR2-V RR5-S RR5-V RR6-S RR6-V NEW Flow Form RR7-S Flow Form RR7-H Flow Form Hybrid Beadlock Wheels RR5-H RR6-H Hybrid Wheel Accessories Protection Ring Billet Protection Rings True Beadlock Ring Spacer for True Beadlock Ring Interior Floor Liners Suspension Upper Control Arms - Tacoma/4Runner/GX Upper Control Arms - Tundra (22+) Accessories ABS Center Caps + Decals Billet Caps Hub-Centric Rings Protection Rings + Beadlock Rings + Spacers Lug Nuts & Locks Replacement Bolts + Hardware
Monoforged Wheels RS2-H Monoforged Wheel RS2-S MonoForged RS4-H Hybrid MonoForged RS4-S MonoForged RS5-H Hybrid MonoForged RS6-H Hybrid MonoForged RS7-H Hybrid MonoForged RS7-S MonoForged Wheel
Wheels RR2-S RR2-V RR5-S RR5-V RR6-S RR6-V
NEW Flow Form RR7-S Flow Form RR7-H Flow Form
Hybrid Beadlock Wheels RR5-H RR6-H
Hybrid Wheel Accessories Protection Ring Billet Protection Rings True Beadlock Ring Spacer for True Beadlock Ring
Interior Floor Liners
Suspension Upper Control Arms - Tacoma/4Runner/GX Upper Control Arms - Tundra (22+)
Accessories ABS Center Caps + Decals Billet Caps Hub-Centric Rings Protection Rings + Beadlock Rings + Spacers Lug Nuts & Locks Replacement Bolts + Hardware
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THE NEW GENERATION OF OFFROAD WHEEL SHOP MONOFORGED
unleash your suspension shop upper control arms
air down without worries shop beadlock rings
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Built Tough RRW offroad truck wheels are guaranteed to last the lifetime of your truck. Our metal parts and accessories are built for functionality and to withstand any terrain. Company Home About Catalog Wholesale and Services Gallery Customer Service Customer Login Contact Us Military / First Responder Discount Frequently Asked Questions Financing Return Policy Shipping Policy
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Rww watch 全新錶 | 二手錶 | 高價收錶 | 二手錶買賣 | 勞力士
Rww watch 全新錶 | 二手錶 | 高價收錶 | 二手錶買賣 | 勞力士
About Us | RRW - Relations Race Wheels
About Us | RRW - Relations Race Wheels
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Shop by Part RR5-S 16x8 RR5-V 16x8 RR6-S 17x7.5 RR6-H 17x8.5 Hybrid Beadlock RR7-H 17x8.5 Hybrid Beadlock Clearance Sale Floor Mats Lug Nuts Molle Panels Pre-Order
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Subtotal Go to cart Home Shop by Part Shop by Vehicle Contact RR5-S 16x8 RR5-V 16x8 RR6-S 17x7.5 RR6-H 17x8.5 Hybrid Beadlock RR7-H 17x8.5 Hybrid Beadlock Clearance Sale Floor Mats Lug Nuts Molle Panels Pre-Order
Chevy Colorado / ZR2 Silverado 1500 Ford Bronco Bronco Sport F150 / Raptor Maverick Ranger Transit GMC Canyon Jeep Gladiator Wrangler JK / JL Lexus GX460 / GX470 Subaru Crosstrek Forester SJ 4th Gen Forester SK 5th Gen Outback Toyota 4Runner FJ Cruiser Rav4 Tacoma Tundra (2021-older) Tundra (2022+)
Chevy Colorado / ZR2 Silverado 1500
Ford Bronco Bronco Sport F150 / Raptor Maverick Ranger Transit
GMC Canyon
Jeep Gladiator Wrangler JK / JL
Lexus GX460 / GX470
Subaru Crosstrek Forester SJ 4th Gen Forester SK 5th Gen Outback
Toyota 4Runner FJ Cruiser Rav4 Tacoma Tundra (2021-older) Tundra (2022+)
New Wheels Accessories
Read our Latest Blogs Add up to five columns
New Wheels Accessories
Read our Latest Blogs Add up to five columns
Monoforged Wheels RS2-H Monoforged Wheel RS2-S MonoForged RS4-H Hybrid MonoForged RS4-S MonoForged RS5-H Hybrid MonoForged RS6-H Hybrid MonoForged RS7-H Hybrid MonoForged RS7-S MonoForged Wheel Wheels RR2-S RR2-V RR5-S RR5-V RR6-S RR6-V NEW Flow Form RR7-S Flow Form RR7-H Flow Form Hybrid Beadlock Wheels RR5-H RR6-H Hybrid Wheel Accessories Protection Ring Billet Protection Rings True Beadlock Ring Spacer for True Beadlock Ring Interior Floor Liners Suspension Upper Control Arms - Tacoma/4Runner/GX Upper Control Arms - Tundra (22+) Accessories ABS Center Caps + Decals Billet Caps Hub-Centric Rings Protection Rings + Beadlock Rings + Spacers Lug Nuts & Locks Replacement Bolts + Hardware
Monoforged Wheels RS2-H Monoforged Wheel RS2-S MonoForged RS4-H Hybrid MonoForged RS4-S MonoForged RS5-H Hybrid MonoForged RS6-H Hybrid MonoForged RS7-H Hybrid MonoForged RS7-S MonoForged Wheel
Wheels RR2-S RR2-V RR5-S RR5-V RR6-S RR6-V
NEW Flow Form RR7-S Flow Form RR7-H Flow Form
Hybrid Beadlock Wheels RR5-H RR6-H
Hybrid Wheel Accessories Protection Ring Billet Protection Rings True Beadlock Ring Spacer for True Beadlock Ring
Interior Floor Liners
Suspension Upper Control Arms - Tacoma/4Runner/GX Upper Control Arms - Tundra (22+)
Accessories ABS Center Caps + Decals Billet Caps Hub-Centric Rings Protection Rings + Beadlock Rings + Spacers Lug Nuts & Locks Replacement Bolts + Hardware
Add description, images, menus and links to your mega menu A column with no settings can be used as a spacer Link to your collections, sales and even external links Add up to five columns Add description, images, menus and links to your mega menu A column with no settings can be used as a spacer Link to your collections, sales and even external links Add up to five columns
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About Us
Relations Race Wheels (RRW) was founded in 2016 with the commitment to design and develop gorgeous wheels for consumer trucks. We believe in not only enhancing the look and function of your truck but also in NEVER developing a product that would downgrade its performance. We steer clear of obnoxious, over-sized heavy wheels that are made of low-quality material that deteriorate the handling and appearance of a truck. Instead, our designs are inspired by simplicity, ruggedness and, most importantly, functionality.
Quality over QuantityRRW is lead by a small group of individuals with a passion for the outdoors and changing the norm. In order to keep prices competitive, we do everything we can to cut out the middleman. This lets us bring a product to the market that's of the highest quality but also at a reasonable price. We strive each day to learn more and excel in providing products that enhance the functionality of late model luxury trucks.
Our wheels are thoroughly stress tested in both 3D simulations and in real life before a new design is finalized and ready for production. RRW takes pride in our work and strives to outperform every competitor. We believe in our customers getting the most value for their hard earned money. We run our business operations lean and keep overhead low so that we can continue to pass the savings to our customers. We never compromise quality and craftsmanship in our products.
Today, we are developing more than just wheels. We are currently CAD designing a full array of new products. We're excited to continue our journey and expand our inventory of products.
Be sure to check out our store and reach out to us with any questions. We'd love to hear from you.
Don't Miss Out Sign up to get the latest on sales, new releases and more
Built Tough RRW offroad truck wheels are guaranteed to last the lifetime of your truck. Our metal parts and accessories are built for functionality and to withstand any terrain. Company Home About Catalog Wholesale and Services Gallery Customer Service Customer Login Contact Us Military / First Responder Discount Frequently Asked Questions Financing Return Policy Shipping Policy
Currency
USD $
CAD $
USD $
© 2024 Relations Race Wheels. Powered by Shopify Visa Mastercard Discover American Express Google Pay Apple Pay Klarna Shop Pay
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Toyota Tacoma Truck Wheels and Offroad Parts | RRW - Relations Race Wheels
Toyota Tacoma Truck Wheels and Offroad Parts | RRW - Relations Race Wheels
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Shop by Part RR5-S 16x8 RR5-V 16x8 RR6-S 17x7.5 RR6-H 17x8.5 Hybrid Beadlock RR7-H 17x8.5 Hybrid Beadlock Clearance Sale Floor Mats Lug Nuts Molle Panels Pre-Order
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Subtotal Go to cart Home Shop by Part Shop by Vehicle Contact RR5-S 16x8 RR5-V 16x8 RR6-S 17x7.5 RR6-H 17x8.5 Hybrid Beadlock RR7-H 17x8.5 Hybrid Beadlock Clearance Sale Floor Mats Lug Nuts Molle Panels Pre-Order
Chevy Colorado / ZR2 Silverado 1500 Ford Bronco Bronco Sport F150 / Raptor Maverick Ranger Transit GMC Canyon Jeep Gladiator Wrangler JK / JL Lexus GX460 / GX470 Subaru Crosstrek Forester SJ 4th Gen Forester SK 5th Gen Outback Toyota 4Runner FJ Cruiser Rav4 Tacoma Tundra (2021-older) Tundra (2022+)
Chevy Colorado / ZR2 Silverado 1500
Ford Bronco Bronco Sport F150 / Raptor Maverick Ranger Transit
GMC Canyon
Jeep Gladiator Wrangler JK / JL
Lexus GX460 / GX470
Subaru Crosstrek Forester SJ 4th Gen Forester SK 5th Gen Outback
Toyota 4Runner FJ Cruiser Rav4 Tacoma Tundra (2021-older) Tundra (2022+)
New Wheels Accessories
Read our Latest Blogs Add up to five columns
New Wheels Accessories
Read our Latest Blogs Add up to five columns
Monoforged Wheels RS2-H Monoforged Wheel RS2-S MonoForged RS4-H Hybrid MonoForged RS4-S MonoForged RS5-H Hybrid MonoForged RS6-H Hybrid MonoForged RS7-H Hybrid MonoForged RS7-S MonoForged Wheel Wheels RR2-S RR2-V RR5-S RR5-V RR6-S RR6-V NEW Flow Form RR7-S Flow Form RR7-H Flow Form Hybrid Beadlock Wheels RR5-H RR6-H Hybrid Wheel Accessories Protection Ring Billet Protection Rings True Beadlock Ring Spacer for True Beadlock Ring Interior Floor Liners Suspension Upper Control Arms - Tacoma/4Runner/GX Upper Control Arms - Tundra (22+) Accessories ABS Center Caps + Decals Billet Caps Hub-Centric Rings Protection Rings + Beadlock Rings + Spacers Lug Nuts & Locks Replacement Bolts + Hardware
Monoforged Wheels RS2-H Monoforged Wheel RS2-S MonoForged RS4-H Hybrid MonoForged RS4-S MonoForged RS5-H Hybrid MonoForged RS6-H Hybrid MonoForged RS7-H Hybrid MonoForged RS7-S MonoForged Wheel
Wheels RR2-S RR2-V RR5-S RR5-V RR6-S RR6-V
NEW Flow Form RR7-S Flow Form RR7-H Flow Form
Hybrid Beadlock Wheels RR5-H RR6-H
Hybrid Wheel Accessories Protection Ring Billet Protection Rings True Beadlock Ring Spacer for True Beadlock Ring
Interior Floor Liners
Suspension Upper Control Arms - Tacoma/4Runner/GX Upper Control Arms - Tundra (22+)
Accessories ABS Center Caps + Decals Billet Caps Hub-Centric Rings Protection Rings + Beadlock Rings + Spacers Lug Nuts & Locks Replacement Bolts + Hardware
Add description, images, menus and links to your mega menu A column with no settings can be used as a spacer Link to your collections, sales and even external links Add up to five columns Add description, images, menus and links to your mega menu A column with no settings can be used as a spacer Link to your collections, sales and even external links Add up to five columns
Add description, images, menus and links to your mega menu A column with no settings can be used as a spacer Link to your collections, sales and even external links Add up to five columns Add description, images, menus and links to your mega menu A column with no settings can be used as a spacer Link to your collections, sales and even external links Add up to five columns
Home / Toyota Tacoma Toyota Tacoma All Toyota Tacoma 22+ Toyota Tundra 6 139.7 6 5.5 6 on 139.7 6 on 5.5 6x139.7 6x5.5 Accessories Ford Bronco Ford Bronco Sport Ford F150 Ford F150 Raptor Ford Ranger Hub-Centric Jeep Gladiator Jeep Wrangler Lexus GX460 Lexus GX470 Monoforged New RR2-S 17x8.5 RR2-V 17x8.5 RR5-H 17x8.5 RR5-S 16x8 RR5-V 17x8.5 RR6-H 17x8.5 RR7-H FF RR7-S FF Toyota 4Runner Toyota FJ Cruiser Toyota Rav4 Toyota Tacoma Toyota Tundra Featured Best Selling Alphabetically: A-Z Alphabetically: Z-A Price: Low to High Price: High to Low Date: New to Old Date: Old to New
Outfit your Tacoma in 17" wheels that are designed with a 106.1 mm center bore for a hub-centric fit. RRW has everything you'll need to make your Tacoma perform as good as it'll look.
Sale
Sale
CNC Billet Upper Control Arm (UCA) | Toyota Tacoma 4Runner GX470
$ 1,300.00
$ 1,500.00
Sale
Sale
RS6-H Hybrid 17x8.5 MonoForged Wheel from
$ 2,000.00
$ 3,000.00
Sale
Sale
RS7-S 17x8.5 MonoForged Wheel
$ 2,000.00
$ 3,000.00
Sale
Sale
RS7-H Hybrid 17x8.5 MonoForged Wheel from
$ 2,000.00
$ 3,000.00
RR7-H FLOW FORM 17x8.5 (6x5.5 | 6x139.7) Hybrid Beadlock | Toyota Tacoma / 4Runner
$ 325.00
RR7-S FLOW FORM 17x8.5 (6x5.5 | 6x139.7) | Toyota Tacoma / 4Runner
$ 325.00
RR2-S 17x8.5 (6x5.5 | 6x139.7) | Toyota Tacoma / 4Runner
$ 275.00
RR2-V 17x8.5 (6x5.5 | 6x139.7) | Toyota Tacoma / 4Runner
$ 275.00
RR6-H 17x8.5 (6x5.5 | 6x139.7) Hybrid Beadlock | Toyota Tacoma / 4Runner
$ 295.00
RR5-S 17x8.5 (6x5.5 | 6x139.7) | Toyota Tacoma / 4Runner
$ 275.00
RR2-V 17x8.5 (6x5.5 | 6x139.7) | Toyota Tacoma / 4Runner
Sold out
RR5-S 16x8 (6x5.5 | 6x139.7) | Toyota Tacoma (2005+)
$ 250.00
RR5-V 17x8.5 (6x5.5 | 6x139.7) | Toyota Tacoma / 4Runner
$ 275.00
Sale
Sale
RR5-H 17x8.5 (6x5.5 | 6x139.7) Hybrid Beadlock | Toyota Tacoma / 4Runner
$ 225.00
$ 295.00
Sale
Sale
RS2-S 17x8.5 MonoForged Wheel
$ 2,000.00
$ 3,000.00
Sale
Sale
RS2-H Hybrid 17x8.5 MonoForged Wheel
$ 2,000.00
$ 3,000.00
Sale
Sale
RS4-H Hybrid 17x8.5 MonoForged Wheel
$ 2,000.00
$ 3,000.00
Sale
Sale
RS4-S 17x8.5 MonoForged Wheel
$ 2,000.00
$ 3,000.00
Sale
Sale
RS5-H Hybrid 17x8.5 MonoForged Wheel
$ 2,000.00
$ 3,000.00
Spline Closed End Lug Nuts (12x1.5 ET) | Toyota / GX / Bronco / Ranger
Sold out
Hex Closed End Lug Nuts (12x1.5 ET) | Tacoma / 4Runner / GX / Bronco / Ranger
$ 60.00
Billet Aluminum Center Cap
$ 50.00
Open end Spline Lug Locks | Toyota / Lexus / Ford
$ 25.00
Don't Miss Out Sign up to get the latest on sales, new releases and more
Built Tough RRW offroad truck wheels are guaranteed to last the lifetime of your truck. Our metal parts and accessories are built for functionality and to withstand any terrain. Company Home About Catalog Wholesale and Services Gallery Customer Service Customer Login Contact Us Military / First Responder Discount Frequently Asked Questions Financing Return Policy Shipping Policy
Currency
USD $
CAD $
USD $
© 2024 Relations Race Wheels. Powered by Shopify Visa Mastercard Discover American Express Google Pay Apple Pay Klarna Shop Pay
Search
Relations Race Wheels (RRW) Review on 4Runner/Tacoma
lations Race Wheels (RRW) Review on 4Runner/Tacoma Skip to content HOMESHOPBLOGCONTACT Get StartedMods 1 – Getting StartedMods 2 – Tire Size GuideMods 3 – Tire Buying GuideMods 4 – PerformanceMods 5 – Lift & Level KitsMods 6 – Grille KitsMods 7 – HeadlightsMods 8 – Fog LightsMods 9 – Rock SlidersMods 10 – Roof RacksMods 11 – Front BumpersMods 12 – Rear BumpersMods 13 – Skid PlatesMods 14 – Wheels5th Gen ModsSuspensionElectricalSwitch SystemsRoof RacksRooftop TentsAwningsLightingHeadlightsFog LightsLED BulbsAcc LightingTail LightsSwitch SystemsArmorRock SlidersSkid PlatesFront BumpersRear BumpersAccessoriesGearRecovery GearOff-RoadOverlandRooftop TentsAwningsRefrigeratorsInstallsReviewsTrail TestedMaintenance 5th Gen Mods, Accessories, ReviewsRelations Race Wheels – RR5-S 17X8.5 Wheels Posted on August 17, 2019August 29, 2019 Last Updated Thursday, August 29, 2019 Read Time: 5 mins By Brenan GreeneRelations Race Wheels (RRW) – RR5-S 17X8.5 (6X5.5 | 6X139.7)For our newest 4Runner in the family, we grabbed a set of the RR5-S 17X8.5 (6X5.5 | 6X139.7) Hub-Centric wheels with 0 offset and wrapped those in a set of 285/70R17 Guard Dog TreadWrights.If you are looking push your wheel outside the well a bit more, they do offer this wheel in a -12 offset and other wheel options up to -25 offset.The wheels we bought (RR5-S) are the same design as the RR5-V without the faux beadlocks.We wanted to go with a lightweight wheel with a minimal offset due to the purpose of our build. We have run a few different -offsets on our other 4Runners but we wanted to find a setup that would answer the most common question amongst 4Runner drivers.Shop RRWShop RR Wheels: Check Website (Coupon Code: Trail4R)What is RR5-S?Modeling after our best selling and most popular RR5-V beadlock, RRW’s brand new RR5-S is an updated take on the design that gives the illusion of smoother lines and more cohesiveness between the wheel and the tire. The RR5-S is now available in Matte Black, Matte Bronze and Matte Gunmetal and a 0 or -12 offset.Faux Beadlock Wheels?Relations Race Wheels offers a few different models of their wheels in this pattern.They have a couple of different color options and then you can choose between the faux beadlocks or no faux beadlocks.If you are looking for a set of their wheels, odds are they have an option either with or without the beadlock look. That is rare. Usually, companies make it with or without the beadlock look.RR5-S = without beadlocksRR5-V = with beadlocksRR5-S Wheel SpecsSize: 17×8.5Weight: 22lbs per wheelOffset: 0 offset and -12 offsetBackspacing: 4.75″Bolt Pattern: 6×139.7 / 6×5.5Center bore: 106.1 mm (hub-centric for Toyota trucks)Load Rating: 2500 lbsCompatible with TPMSThere are many great characteristics of the RRW wheel lineup but I wanted to touch on a few of the most important ones.Weight and width.Sitting at 22lbs per tire, the RRW wheels are lighter than the industry known TRD SEMA wheels at 25lbs. They’re 8.5″ width also makes them wider than the TRD wheels at 7″.If you are running a smaller tire (265 0r 275), you should be fine with a smaller wheel. If however, you are looking to run larger tires (285 or 295+), then a wider wheel is recommended.For my needs, RRW wheels have the perfect width and feature a great weight. Most off-road wheels are in the 23-26lbs range.Sitting at only 22lbs, these RRW wheels are pretty light.Offset & BackspaceBoth backspace and offset affect how much you are pushing your wheel out of the well, getting that aggressive stance and helping to mitigate lift changes.When you lift your truck, the shocks get taller which forces the control arms to pull the wheel hub assembly inside the wheel well. Less backspace and lower offset push your wheel out of the well further. To help me understand the difference between backspace and offset, I usually reference this guide.If you want to push your wheels outside the wheel well and get a more aggressive stance, then wheels with -offset or wheel spacers are what you want.Most of us install these common wheel spacers which are measured at 1.25″ which means they push wheels outside 1.25″.Offset Options-0mm offset = almost flush with fender flares-12mm offset = .47″-25mm offset = .98″-31mm offset = 1.25″ Wheel SpacersBackspace and offset do the same thing as wheels spacers, it’s just built into the wheel.Two Options for Offset (-0mm & -12mm)Featuring two options for an offset on this design (RR5-S and RR5-V), this wheel is a great option for our 4Runners, Tacomas and Tundras. RRW makes this wheel in a 0, and -12 offset option. They even make other models in a -25 offset, which is huge.The 4.0″ – 5.0″ backspace is somewhat standard around town with off-road wheels. Again, the smaller the backspace, the more your wheel is being pushed out. RRW backspace is 4.5 which is right in the middle. Good backspacing.We chose 0 offset because I originally planned on keeping this truck as close to stock as possible. BUT, looking back I might have decided to go with -12 offset or even another design to get the -25 offset. It’s nice when the offset is built into the wheel and you don’t need to buy spacers to push the wheels out.If we do decide to lift this 4Runner up 3″+ we will buy some wheel spacers.Final Thoughts?Their wheels are also hub-centric which is nice. Hub-centric wheels are where the center hole of the wheels is the actual center bore of the wheel. This is pretty standard on most wheels these days.If you are looking for a good off-road wheel, RRW makes some good options. Not only are their designs pretty fire, but their specs are also on point as well.Looking for some Relations Race Wheels Inspiration? Here are some additional shots of other Tacomas and 4Runners. RRW really does make some killer wheels. I am stoked we went this route.RR2-V 17X8.5 on MGM 4RunnerGunmetal RR5-S on Cement TacomaGold RR5-V on White TacomaMatte Bronze RR4-V on Cement Tacoma This entry was posted in 5th Gen Mods, Accessories, Reviews. Bookmark the permalink. Brenan GreeneBrenan is the founder of Trail4R.com, Toyota guy through and through, verified nature lover, lightweight photographer, exploration enthusiast, front-end web designer, graphic designer, and certified serial blogger. Anytime Backup & Front Camera (Updated 2022 Version)Trail Intro: C4 Fabrication Front Bumpers for the 5th Gen 4Runner Subscribe LoginNotify of new follow-up commentsnew replies to my comments Label {} [+] Name* Email* Δ Label {} [+] Name* Email* Δ 25 Comments Inline FeedbacksView all comments Robert G. 5 months ago Hi Brenan. Just wanted to hear what you had to say about this to help my decision process. I’m looking at the RR5-S wheel in your pics. It looks more satin”ish” in those. If you look at it on the website, it only offers a black gloss or bronze. The website pic of that wheel looks much more glossy than any of the pics I have seen where they are installed. Are they actually a shiny gloss, or more of a satin tone. I love the wheels in all of the pics, but I don’t like the wheel in its stock photo on the website. I appreciate your feedback. Thanks for being awesome! 0 Reply Bret 1 year ago Hey I got a 2014 Tacoma and looking at installing the rr6 or rr7 -12 offset on 265/70/17 how much lift do I need to not rub. 0 Reply Vince 2 years ago Hey Brennan, I’m thinking of going with these in the same “0” offset. My lift up front is about the same as yours, 2.4″ but with 6112s. I’m currently running 285/70R17 KO2s on the stock Off Road wheels. Did you experience any rubbing with the RRWs and Guard Dog 285s? Do you think a simple fender liner mod. is needed in my case or a BMC? I see the KO2s are slightly larger than the Dogs so I’m hoping I can get away with just a fender mod. Thanks, 0 Reply Sean 3 years ago Hey Brennan, I’m having an issue using the stock lugs with these wheels. Do you have an alternate lug that would fit the narrower channel? Thanks! 0 Reply AuthorScout Brenan Greene 3 years ago Reply to Sean We are running the lugs from Relations Race Wheels. I usually always buy lugs from the company I buy wheels from for that reason. https://www.relationsracewheels.com/collections/lug-nuts 1 Reply Daniel 3 years ago Thinking of getting a set of RR5-S wheels with +0 offse with stock size AT3Ws, do you think they will be any running on an otherwise stock 2021 Off-road Premium? 0 Reply AuthorScout Brenan Greene 3 years ago Reply to Daniel Not with a zero offset, no. You should clear those just fine. 0 Reply Jeff Mangels 3 years ago Hey Brenan, I’m picking up my first 4Runner this week and absolutely love these wheels. In the pictures of your MGM in this article, is it lifted? Trying to get a feel for fitment/look on a stock 4Runner.I’ve thoroughly enjoyed browsing the trail4runner website and educating myself. Keep up the great work! 0 Reply AuthorScout Brenan Greene 3 years ago Reply to Jeff Mangels Yeah, this lift was a Falcon +2.5″ lift. You can see that post here. 0 Reply shafeek 3 years ago the RR5-V model does it have the function to lock with the tyre ?. or is it just the beadlock LOOK ?… 0 Reply AuthorScout Brenan Greene 3 years ago Reply to shafeek They now make the beadlock versions. They are referred to as hybrid wheels. You can see the new forged beadlock wheels here. 0 Reply Wylie Clare 3 years ago Hi Brenan , i bought these wheels with the -12 offset, i have an icon stage 2 lift 2.5 ” in front and 2″ in back, do you think i will need a BMC to rock 285 /70 ko2s because of the offset? thanks for all the info you share with the community 0 Reply AuthorScout Brenan Greene 3 years ago Reply to Wylie Clare Wylie, it’s not going to be needed for daily driving but for off-road, I would plan for it. 1 Reply James 4 years ago Brenan I’ve got a 2018 trd pro with a 2/1.5 Cornfed spacer level kit installed. Really considering a new set of these wheels to be able to run a larger tire than stock 265 nittos. 285/70 would be the goal but wondering if I would need a body mount chop or any serious trimming based on your experience! 0 Reply Brenan - @Trail4R 4 years ago Reply to James Everything you need is here: https://trail4runner.com/2019/07/14/fender-liner-push-back-trimming-on-4runner/ 0 Reply WCB 4 years ago Beware of their lead times and communication issues as well. I ordered sliders on August 16th, which on their website states 10-12 week lead time – expected for a custom fab item. As of 12/03 they still cannot and will not give me a completion date. Attempted to cancel the order but they are being very resistant and not giving me any updates or definite completion date. I am probably going to have to file a fraud charge on my credit card since I cannot get them to refund either. 4 Reply Jason 4 years ago Can you confirm the weight of these wheels? Their website says 28lbs…confused because I really want them to be 22lbs like you say. Thanks! 0 Reply AuthorScout Brenan Greene 4 years ago Reply to Jason Jason, I would call them. Last time I checked their website said 22lbs. Maybe they changed their manufacturing process? Not 100% sure but that 22lbs per wheel was really attractive at the time of writing this. I will reach out and see what’s going on. 0 Reply JASON 4 years ago Reply to Brenan Greene What is your opinion on the -12 offset version of this wheel? I really wanted the 0 offset but they’re sold out. Thanks! 0 Reply AuthorScout Brenan Greene 4 years ago Reply to JASON I would rather have -12mm over 0mm on this build, that way the wheel sticks out past the fender wells. And, at -12 it will be very minimal (compared to spacers) but at least something if you going for a wide stance. Check out this lifted 4Runners post, where a build featured has -38mm (1.49″) which is huge offset for a 17″ wheel in our world. That’s big enough to where you probably don’t need spacers if you are going for a stout/wide stance. I have -6mm with 2″ spacers on another build (the white one) and feel like I am at a good spot but I need a wide stance with fiberglass fenders and upcoming 35X12.5 tires. It really depends on the look you are going for though. 0 Reply Jason 4 years ago Reply to Brenan Greene Is there more of a chance for rubbing with -12, alignment issues, etc. I’m not doing a crazy build…just mild. Thanks 0 Reply AuthorScout Brenan Greene 4 years ago Reply to Jason Yeah, you can possibly rub more with -12mm over 0 but it will be minimal. Again, it all depends on the look you are going for. The 0 doesn’t look bad at all. 0 Reply JMIC 4 years ago Buyer beware. I purchased a set of RRW and the hub bore had a manufacturing defect and would not fit over the front hub dust caps. RRW would not send me new wheels, and I was forced to run Spidertrax spacers to resolve the problem. Not pleased. 10 Reply Matthew Turner 4 years ago How much lift do you have for 285 to fit? 0 Reply AuthorScout Brenan Greene 4 years ago Reply to Matthew Turner Current lift here is a Falcon Suspension +2.5” in the front and 1″ in the rear. 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Leave this field empty if you're human: We will never spam your inbox. Our content is pretty fire! We will also never sell out and sell your data. x Get Paid for Reviewing PartsWe send free parts & pay you cash.Apply Today xRRW: repeated random walks on genome-scale protein networks for local cluster discovery | BMC Bioinformatics | Full Text
RRW: repeated random walks on genome-scale protein networks for local cluster discovery | BMC Bioinformatics | Full Text
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RRW: repeated random walks on genome-scale protein networks for local cluster discovery
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Research article
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Published: 09 September 2009
RRW: repeated random walks on genome-scale protein networks for local cluster discovery
Kathy Macropol1, Tolga Can2 & Ambuj K Singh1
BMC Bioinformatics
volume 10, Article number: 283 (2009)
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141 Citations
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AbstractBackgroundWe propose an efficient and biologically sensitive algorithm based on repeated random walks (RRW) for discovering functional modules, e.g., complexes and pathways, within large-scale protein networks. Compared to existing cluster identification techniques, RRW implicitly makes use of network topology, edge weights, and long range interactions between proteins.ResultsWe apply the proposed technique on a functional network of yeast genes and accurately identify statistically significant clusters of proteins. We validate the biological significance of the results using known complexes in the MIPS complex catalogue database and well-characterized biological processes. We find that 90% of the created clusters have the majority of their catalogued proteins belonging to the same MIPS complex, and about 80% have the majority of their proteins involved in the same biological process. We compare our method to various other clustering techniques, such as the Markov Clustering Algorithm (MCL), and find a significant improvement in the RRW clusters' precision and accuracy values.ConclusionRRW, which is a technique that exploits the topology of the network, is more precise and robust in finding local clusters. In addition, it has the added flexibility of being able to find multi-functional proteins by allowing overlapping clusters.
BackgroundIn recent years, much effort has gone into finding the complete set of interacting proteins in an organism [1]. Such genome-scale protein networks have been realized with the help of high throughput methods, like yeast-two-hybrid (Y2H) [2, 3] and affinity purification with mass spectrometry (APMS) [4, 5]. In addition, information integration techniques that utilize indirect genomic evidence have provided both increased genome coverage by predicting new interactions and more accurate associations with multiple supporting evidence [6–9].Complementary to the availability of genome-scale protein networks, various graph analysis techniques have been proposed to mine these networks for pathway or molecular complex discovery [10–15], function assignment [16–18], and complex membership prediction [19, 20]. Bader and Hogue [21] propose a clustering algorithm to detect densely connected regions in a protein interaction network for discovering new molecular complexes. Spirin and Mirny [22] use superparamagnetic clustering (SPC) and a Monte Carlo (MC) algorithm to cluster a given protein interaction network. These algorithms work on undirected unweighted graphs and partition the network of proteins into non-overlapping clusters. However, genome-wide networks constructed with multiple supporting evidence have edges with varying degrees of confidence. The strength of confidence should be considered when identifying strongly connected proteins. Also, it is known that there are many multi-functional proteins which may play important roles in different functional modules. Therefore, a biologically more sensitive cluster identification technique should report clusters that may sometimes overlap. Several clustering techniques have since been proposed that take into account the given edge confidence [23] or overlapping clusters [24, 25]. However, these algorithms all account for the two problems separately, and do not both use given biological edge confidences and find overlapping clusters at the same time.In this paper, we propose a novel algorithm, repeated random walk (RRW for short), for molecular complex and functional module discovery within genome-scale protein interaction networks. This new algorithm utilizes both given edge weights and can find overlapping clusters. The idea is based on expansion of a given cluster to include the protein with the highest proximity to that cluster. Starting with a cluster of size one (any protein in the network), this iterative process is repeated either k times, or until a stopping condition is met, to obtain clusters of size ≤ k. All significant overlapping clusters are recorded and post-processed to remove redundant clusters based on a given overlap threshold. We use random walks with restarts to find the closest proteins to a given cluster. To increase the algorithm's speed, the random walk results from a given cluster are computed using linear combinations of precomputed random walk results obtained starting from single proteins. Unlike other techniques proposed for pathway discovery, the random walk method implicitly exploits the global structure of a network by simulating the behavior of a random walker [26].We apply RRW on a genome-scale functional network of yeast genes and accurately identify statistically significant clusters of proteins. We validate the biological significance of the results by comparison to known complexes in the MIPS complex catalogue database [27]. By comparison to an existing clustering technique, we show that using edge weights in addition to connectivity information and allowing certain amounts of overlap between clusters are the key characteristics of RRW for finding biologically more significant clusters.Results and discussionProblem statement and algorithmLet G = (V, E) be the graph representing a genome scale protein interaction network, where V is the set of nodes (proteins), and E is the set of weighted undirected edges between pairs of proteins. The edges are weighted by the strength of supporting evidence for functional association.Problem definitionGiven a physical protein interaction or predicted functional network of an organism, our goal is to find biologically significant groups of proteins in the network. Here, the definition of a biologically significant group entails proteins that function together in a biological pathway or are members of a protein complex. Moreover, significant clusters may contain proteins from different complexes, therefore revealing modular interactions at a higher level.The problem can be stated formally as follows: Given an undirected weighted graph G = (V, E), find top-m connected clusters of vertices of size at most k where the ranking is based on statistical significance. (Assessment of statistical significance is discussed in detail at the end of this section.) Evaluating all possible sets of proteins for biological significance is obviously intractable, O(2|V|). Therefore, we propose a heuristic based on random walks on graphs. The idea is based on expansion of a given cluster to include the protein with the highest proximity to that cluster. Starting with a cluster of size one, this iterative process is repeated either k times, or until the next closest protein's distance is not within a given cutoff. In this way, clusters of size ≤ k are obtained (all intermediate clusters are also assessed for biological significance). Table 1 contains a reference of the various notations and symbols used throughout the paper.Table 1 List of notations usedFull size tableRandom walks with restartsWe use random walks with restarts for finding the highest affinity protein to a given cluster. The random walk technique exploits the global structure of a network by simulating the behavior of a random walker [26]. The random walker starts on an initial node (or a set of source nodes simultaneously), and moves to a neighboring node based on the probabilities of the connecting edges. The random walker may also choose to teleport to the start nodes with a certain probability, called the restart probability, α. The walking process is repeated at every time tick for a certain amount of time. At the end, the percentage of time spent on a node is proportional to its proximity to the starting nodes. The percentage of time spent is a probability distribution over the set of all nodes and changes in this distribution are modeled as a Markov chain. We refer to the stationary vector of the Markov chain as the affinity vector. The restart probability α enforces a restriction on how far the random walker moves away from the starting nodes. In other words, if α is close to 1, the local structure around starting nodes is analyzed, and as α gets close to 0, a more global view is observed. We use α = 0.7 for the results reported in this paper. A sketch of the random walk algorithm for finding the closest protein to a single protein is given in the Methods Section (Figure 1).Figure 1Random walk algorithm. Pseudocode for a random walk with restarts from a single vertex.Full size imageRepeated random walk algorithmThe random walk algorithm finds proteins that are in close proximity to a start node. Below we describe a linear combination technique to simulate a random walk starting from a set of proteins.We can add the closest protein to the start set and repeat the random walk. Successive iterations can be used to identify clusters of any given size. Repeated random walks is based on this idea. However, the large number of random walks necessary to obtain a cluster in this way greatly reduces the speed of the algorithm. To lower the computational costs, the number of random walks performed can be reduced and the affinity vectors found using an alternative method.Precomputed random walk results starting from single proteins in the set can be linearly combined to obtain the affinity vector for larger clusters starting from multiple proteins, as shown below.Theorem 1 Let P be the row normalized adjacency (transition) matrix defined by the graph, G.Let sC be the restart vector for a set of nodes, C, that contains a value of in all entries corresponding to nodes in C, and 0 for other entries. Then, the stationary vector, x
C
, for a random walk with restarts starting from the set of nodes, C, is , where xi is the stationary vector of random walk with restarts from node i.Proof The stationary vector xi of a random walk with restarts beginning from any single vertex, i, by definition, follows equation [28]:
(1)
Summing the above for all the nodes in C and dividing by |C|, we obtain,
(2)
Now, the stationary vector xC is defined to satisfy the equation,
(3)
Noting the form of Equations 2 and 3, and since the stationary vector is unique, we conclude that ■A sketch of the repeated random walk (RRW) and ClusterRWSimulation algorithms is given in the Methods Section (Figures 2 and 3). Starting from every node in the network, the RandomWalk method is run, and the resulting affinity vectors associated with each single node are saved. Sets of strongly connected proteins are then found by again starting from every node in the network and expanding the clusters repeatedly using the ClusterRWSimulation method. This method utilizes the vectors found in the RandomWalk method to quickly obtain the random walk affinity vectors, and the closest protein to the current cluster is found. This protein is added to the cluster, its score remembered, and resulting in a new cluster to be further expanded. This process is continued until either the next protein to be added's score is not within a given percentage, λ (the early cutoff), of the previously added protein's score, or we reach the maximum cluster size k. All clusters created during expansion are saved.Figure 2Repeated random walk (RRW) algorithm. Pseudocode for the overall RRW algorithm used to create significant clusters in the network.Full size imageFigure 3Random walk from a cluster algorithm. Pseudocode for the algorithm used to simulate a random walk with restarts from a cluster of vertices.Full size imageThese expanded clusters are afterwards post-processed based on a given overlap threshold. The less significant of highly overlapping (redundant) clusters are then discarded. The overlap ratio between two clusters, C1 and C2, is given by |C1 ∩ C2|/min {|C1|, |C2|} and is between 0.0 and 1.0.The complexity of the Random Walk algorithm is linear in the size of the graph and maximum cluster size, O (|V|·R + |V|·k), where R is the complexity of the RandomWalk algorithm, and the complexity of post-processing is O(n2) where n are the number of clusters created. The bottleneck for the RRW algorithm, in large graphs, are the calls to the RandomWalk method done in the beginning. On a protein network with |V | = 4,681 and |E| = 34,000, the random walk calls take about fifteen minutes in total (using a machine with a 3.2 GHz Intel Xeon CPU and 8 GB of RAM running the Ubuntu 8.04 operating system), versus less than a minute spent computing the clusters using the linear combination method after the Random Walk affinity vectors have been computed and stored.In order to reduce this complexity, one can skip using the RandomWalk and simply use the best neighbors based solely on edge weights. However, this naïve nearest neighbor approach does not capture the structure of the network around starting nodes. Our experiments show that this is indeed the case.Statistical significance of a clusterGiven a set of proteins that form a cluster in a genome-scale protein network, we assign a statistical significance to that set. To create a quantitative representation of a cluster, we compute a score which is the average value of the random walk distance between all nodes in the cluster. (Since the affinity vectors from each node in the graph are already precomputed and stored during the RRW computations, this can be done quickly and efficiently.) Since the "distances" are the stationary probabilities, the average score value will range from 0 to 1.The computation of significance of a score requires estimating the cdf of scores and computing p-value(s) = 1 - cdf(s). Score distributions can be computed empirically by sampling clusters of different sizes. However, we found that the typical scores we worked with had very small tail probabilities. For example, for a cluster size of 10, the mean was 3.27·10-5, the standard deviation was 1.28·10-4, and the tail probability had to be computed for a score of .0359, which is about 280 times the standard deviation removed from the mean. It is difficult to apply sampling to compute these small tail probabilities.For our purposes, we assumed a simple relationship between the cdf, scores, and cluster sizes. Clearly, the cdf value of a score is monotonic in score. It is also monotonic in cluster size since the probability of a cluster having an average score less than a threshold increases with cluster size. We attempted a number of different estimates of cdf-values: (score·log |C|), (score·), and (score·|C|). Both (score·) and (score·|C|) were correlated significantly with biological significance in MIPS clusters (the percent of proteins in the cluster that belong to the same MIPS complex). For a sample size of 1,855 clusters, the Pearson Correlation Coefficient between the biological significance and (score·log |C|), (score·), and (score·|C|) was 0.00787, 0.158 and 0.229, respectively. Since the critical value of the correlation coefficient p for 1,855 items is 0.0763 at 0.001 probability, it can be seen that (score·) and (score·|C|) are both significantly correlated to biological significance.In our experiments, a slower growing function of |C| (such as ) led to better precision and worse recall than a faster growing function of |C| (such as |C|). Choosing clusters with higher precision over recall, we adopted the function and present results for p-value = 1 - (score·).Experimental resultsIn this section, we report our experimental results conducted on different variants of a S. cerevisiae protein interaction network, setting λ to be 0.6, k to be 11, and the overlap threshold to be 0.2. Varying the overlap threshold between 0.01 to 0.4 was found experimentally to affect the reported results only slightly, and so a value of 0.2 (one overlapping protein allowed in a cluster of size 5) was chosen. The values for λ and k were found to not significantly alter the majority of returned results as well, as the returned clusters tended to favor smaller sizes (on average 5-6 proteins). These values, however, were chosen after evaluating various parameter settings. For the model organism S. cerevisiae, we used the WI-PHI network by Kiemer et al. [29]. WI-PHI is a weighted undirected protein interaction network encompassing a large majority of yeast proteins. It is constructed by integration of various heterogeneous data sources such as application of tandem affinity purification coupled to MS (TAP-MS), large-scale yeast two-hybrid studies, and results of small-scale experiments stored in dedicated databases. The network contains 50,000 interactions for 5,955 yeast proteins. The weights, included in the original file, are determined by assessing each data source's performance in reproducing the results of a high confidence benchmark interactome. We also created noisy versions of these networks to demonstrate the robustness of RRW under noise.Comparison to known MIPS complexesIn order to evaluate the performance of RRW, we use protein complexes from the MIPS complex catalog [27]. All proteins belonging to the same MIPS complex are determined to be interacting with each other. Two statistical results are obtained. First, the quality of a cluster is assessed by finding the percentage of proteins belonging to the same MIPS complex within that cluster. If multiple complex annotations are mapped to the same cluster, the annotation with the highest number of proteins contained in the cluster is chosen. In addition, benchmark protein complexes from the MIPS catalog were used to obtain precision, recall, and accuracy measures. The MIPS benchmark contains 49 protein complexes each of which contains 5 to 10 proteins. The goal was to find clusters as close as possible to the actual complex or pathway, as measured by: precision = number of true positives/local cluster size, recall = number of true positives/size of complex or pathway, and accuracy = where true positives are proteins in the same benchmark complex which are found in the local cluster.We compare our results to MCL [30] (using an inflation value of 2.5), as well as a naïve cluster expansion method we implemented. MCL has been identified as currently being the strongest graph clustering technique in two recent clustering survey papers [31, 32], and so we focus our comparisons to this technique. The MCL inflation parameter was chosen after evaluating various parameter settings, as shown in Table 2. In the naïve expansion method, clusters are expanded by including the neighbors that are connected to the cluster with the largest weight edges. The main difference between this approach and the repeated random walk is that the naïve method chooses the closest neighbors based on local similarity, whereas RRW chooses the closest neighbors based on the global structure of the network.Table 2 Precision, recall, & accuracy on pre-selected MIPS clusters with various MCL inflation parameter valuesFull size tableIgnoring uncharacterized proteins and clusters less than 5 characterized proteins in size, 50% of all the reported clusters from RRW on the original network had at least 90% of their members from the same MIPS complex, significantly higher compared to the 17% in MCL or 7.8% in naïve, as can be seen from Table 3. In addition, three types of noisy networks were generated to observe the effect of false negatives (FN40), false positives (FP40), and edge shuffling (Rewire40) separately. FN40 network was obtained by randomly removing 40% of the edges in the original network. The FP40 network was obtained by adding 40% new random edges to the original network. And the Rewire40 network was obtained by shuffling 40% edges of the original network so that the degree distribution of the original network was preserved. Among these noisy networks as well, the quality of the majority of clusters remains significantly higher in RRW, proving its robustness against network noise, as seen from Tables 4, 5, and 6.Table 3 Results for the WI-PHI networkFull size tableTable 4 Results for the FP40 networkFull size tableTable 5 Results for the FN40 networkFull size tableTable 6 Results for the Rewire40 networkFull size tableTable 7 shows the precision, recall, and accuracy values for the local clusters found in the S. cerevisiae network. The precision of RRW is again confirmed to be much higher than the other methods, emphasizing the quality of the clusters found. This precision in clustering is especially important in biological domains such as protein networks, as it enables more accurate predictions for proteins with unknown cellular function. The recall for RRW, however, is found to be low compared to both MCL and naïve. This means that, though the clusters found by RRW are highly precise, they may not find all proteins within a category, or may split single categories into multiple separate clusters. Comparing the average created cluster size of 5.72 for RRW, 9.82 for MCL, and 10.9 for the naïve method, it can indeed be seen that RRW created smaller clusters, leading to a lower recall rate. However, despite this, the overall accuracy measure of the RRW clusters are still higher than those found in both the MCL and naïve methods across all the networks.Table 7 Precision, recall, and accuracy on pre-selected MIPS clustersFull size tableComparison to known biological processesIn addition to MIPS complexes, proteins that are known to function in the same biological process were also used as a separate gold standard to further confirm that found clusters relate to biologically functional modules. A list of 295 significant GO biological process terms was used as given by Myers et al. [33] to specify the biological processes in a cell. We used the GO annotations [34] for yeast (May 23, 2009 version) to identify sets of proteins annotated with the same GO biological process term. 158 of the significant biological process terms were found to be annotated to at least 5 proteins. Hierarchical information was accounted for in this step by allowing proteins with an annotation lower in the tree to match with a parent annotation. These 158 terms, and the sets of proteins annotated with these terms, were then used as a gold standard. All proteins matching the same term were assumed to function together. Comparing the returned clusters in a manner similar to that used with the MIPS standard, it can be seen from Tables 8, 9, 10, and 11 that again the quality of clusters reported by RRW were significantly higher than most of those reported by MCL or the naïve method.Table 8 Results for the WI-PHI networkFull size tableTable 9 Results for the FP40 networkFull size tableTable 10 Results for the FN40 networkFull size tableTable 11 Results for the Rewire40 networkFull size tableAnalysis of select clusters for biological significanceTo further validate the biological significance of the clusters discovered by RRW, we next discuss several statistically significant clusters discovered by our technique that are also biologically meaningful. One high scoring cluster found by RRW, and not created by either MCL or the naïve method, consisted of the proteins YML049c, YMR240c, YMR288w, YOR319w, and YPR094w. Though not all listed within the same MIPS complex, these 5 proteins were among the 7 found to interact in the yeast SF3b U2 snRNP subunits that associate with the pre-mRNA branchpoint region [35]. Another cluster found consisted of 5 proteins: YBL097w, YDR325w, YFR031c, YLR086w, and YLR272c. The MIPS complex catalogue did not list any of these five together in the same physical complex. However, their corresponding genes exactly match the 5 subunit S. cerevisiae condensin complex [36], essential for chromosome segregation during mitosis, demonstrating the ability of RRW to discover significant functional complexes as well as physical. Another 5 protein cluster discovered contained YDR200c, YFR008w, YLR238w, YMR029c, and YMR052w. Again, though not all contained within the same MIPS complex, these proteins have all been found to be part of a six-member group of interacting proteins that prevent recovery from pheremone arrest in yeast [37].ConclusionIn this paper, we proposed a novel algorithm based on repeated random walks on graphs for discovering functional modules within genome-scale protein networks. We applied the RRW on an interaction network of yeast genes by Kiemer et al. [29] and efficiently identified statistically significant clusters of proteins. We validated the biological significance of the results by comparison to known complexes in both the MIPS complex catalogue database [27] and GO functional annotations [34], as well as to existing clustering techniques. The repeated random walk technique offers significant improvements in precision over existing clustering techniques by making use of the strength of functional associations as well as the network topology and providing clusters of desired overlap ratio. Overlapping clusters proved a more accurate model of real biological networks with multifunctional proteins. In summary, our technique discovers biologically more significant clusters in a genome-wide protein interaction network using global connectivity and supporting evidence information accurately and efficiently.MethodsThe Random Walk and the Repeated Random Walk algorithmsFigure 1 gives the algorithm for finding the stationary vector of a Random Walk with restarts from a single starting node. The complexity of the algorithm is O(w·|V|2), where w is the number of iterations to converge. The value of w is determined by the structure of the network and the restart probability α. In general, the ratio of the first two eigenvalues of a transition matrix specifies the rate of convergence to the stationary probability [38].The Repeated Random Walk (RRW) and Random Walk starting from a cluster (ClusterRWSimulation) algorithms are given in Figures 2 and 3. For the RRW algorithm, starting from every node in the network, sets of strongly connected proteins are found by expanding the clusters repeatedly using the ClusterRWSimulation method. Clusters of size ≤ k are inserted into a priority queue ordered by their statistical significance. For expanding a cluster C, the ClusterRWSimulation method is run and the closest protein in its stationary vector recorded. This neighbor protein is added to C, as long as its weight is within the early cutoff, λ, of the previously added protein to the cluster, resulting in one new cluster to be further expanded. The complexity is linear with the maximum cluster size, O (|V|·k).
An implementation of the RRW algorithm is available for download at
http://cs.ucsb.edu/~kpm/RRW/
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Download referencesAcknowledgementsThis work was supported in part by NSF grant IIS-0612327. Tolga Can is partially supported by the Scientific and Technological Research Council of Turkey (TUBITAK) Career Program Grant #106E128.Author informationAuthors and AffiliationsDepartment of Computer Science, University of California, Santa Barbara, CA, 93106, USAKathy Macropol & Ambuj K SinghDepartment of Computer Engineering, Middle East Technical University, 06531, Ankara, TurkeyTolga CanAuthorsKathy MacropolView author publicationsYou can also search for this author in
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Kathy Macropol.Additional informationAuthors' contributionsKM implemented the Repeated Random Walk algorithm and performed the experiments. TC implemented the Random Walk algorithm (starting from a single node) and provided the datasets used in the experiments. AS worked on the underlying algorithms. All authors read and approved the document.Authors’ original submitted files for imagesBelow are the links to the authors’ original submitted files for images.Authors’ original file for figure 1Authors’ original file for figure 2Authors’ original file for figure 3Rights and permissions
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Reprints and permissionsAbout this articleCite this articleMacropol, K., Can, T. & Singh, A.K. RRW: repeated random walks on genome-scale protein networks for local cluster discovery.
BMC Bioinformatics 10, 283 (2009). https://doi.org/10.1186/1471-2105-10-283Download citationReceived: 23 January 2009Accepted: 09 September 2009Published: 09 September 2009DOI: https://doi.org/10.1186/1471-2105-10-283Share this articleAnyone you share the following link with will be able to read this content:Get shareable linkSorry, a shareable link is not currently available for this article.Copy to clipboard
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KeywordsRandom WalkProtein Interaction NetworkSignificant ClusterOriginal NetworkBiological Process Term
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