Exam%3%Outlines%Scaling%of%Functions%1. Scaling%of%body%plans%%a. Area=volume%ratio%is%not%a%linear%relationship.%As%the%size%of%the%% organism%increases,%the%relative%size%of%its%cross%sectional%area%is%% increasing%more%slowly%than%its%mass.%%b. Strength%is%a%squared%function%related%to%area%c. Mass%is%a%cubic%function%related%to%volume%d. Critical%size%–%when%area%is%no%longer%able%to%support%the%mass.%The%% cross%sectional%area%cannot%support%extra%weight.%In%an%organism,%if%% you%take%a%shape%and%expand%it,%it%will%reach%a%point%where%it%cannot%% expand%anymore.%%e. Exchange%rates%over%the%surface%area%of%the%body%is%a%squared%function.%%2. Mathematics%of%Scaling%a. Y=ax^b% or%% log%y=log%a+b(log%x)%b. Graph%of%log%volume%and%log%area%is%a%linear,%direct%relationship.%The%% slope%of%the%line%is%2/3.%%Represents%geometric%similarity%–%where%% shape%does%not%change,%also%called%isometry%–%organismal%shape%does%% not%change.%Extremely%rare%in%organisms.%%c. Allometry%–%where%shape%changes%as%size%changes,%purely%for%physical%% beings.%Ex:%if%you%compare%the%slope%of%the%growth%of%your%body%to%the%% slope%of%the%growth%of%your%skeleton,%you%will % find%that%your%skeleton%% grows%faster%than%your%body.%%3. Allometric%Scaling%–%allows%you%to%reach%larger%sizes.%Changing%shape%% produces%new%combination%of%properties%–%can%be%exploited%by%organisms.%% Allometry%–%where%you%change%shape%as%you%get%older.%%a. Tree%example:%two%trees%have%the%same%height,%but%have%different%% trunk%diameters.%One%trunk%is%increasing%faster%than%you%would%expect%% with%isometric%scaling.%Exhibits%positive%allometry%because%it%is%% increasing%faster%than%we%expect.%%4. Isometry%–%slope%should%scale%multiples%of%1/3,%but%MOST%slopes%scale%to%% multiples%of%¼.%BUT%structures%produced%by%humans%almost%always%scale%as%% multiples%of%~1/3.%%a. Small%animals%have%really%high%heart%rates,%as%you%get%larger%your%% heart%rate%goes%down.%Heart%rate%–%mass^=(1/4).%5. Simple%vs.%Complex%Shapes%a. Fractal%geometry%–%techniques%for%analyzing%complex%shapes.%%b. Measurement%equation:%M=ns^d% % d=dimension% % %% % % % % % % M=measurement% %% % % % % % % s=step%length%% %% % % % % % % n=number%of%steps%c. Simple%shapes%have%integer%dimensions:%d=1%for%length,%d=2%for%area,%% d=3%for%volume%or%mass.%%d. Complex%shapes%have%non=integer%dimensions:%1<d<2%complex%length%% with%area=like%properties,%2<d<4%complex%are%with%volume=like%% properties.%Fractal%objects%have%intermediate%properties.%%e. Fractal%objects%–%self%similar%objects%based%on%iterative%processes.%Ex:%% lung%is%very%complex,%during%development%your%lungs%branch%again%% and%again%and%again.%The%same%process%occurs%over%and%over%again%% and%it%takes%relatively%simple%control%systems%to%do%it.%Simple%set%of%% commands%and%repeat%a%bunch%of%times%to%get%an%organism.%%f. Koch%curve%–%built%by%repeatedly%inserting%the%same%thing%over%and%% over%to%a%line.%%IRATIVE%PROCESS.%Koch%snowflake%has%an%infinite%% perimeter%because%this%process%can%be%carried%out%until%infinity.%But%it%% has%a%finite%area.%A=%(2%rad%(3s^2)/(5).%Fractal%dimension%=%1.26%g. Biological%systems%build%complexity%by%iterative%processes.%Ex:%% mammalian%lungs%are%modular.%%• Lungs%have%no%true%surface%area.%They%are%fractal.%Complex%% surface%with%some%volume=like%properties.%%• d=2.17%(male%human%lung%of%165%lbs)%h. Because%fractal%objects%arise%by%iterative%processes%they%can%fill%% irregular%spaces.%Changing%the%shape%of%the%lung%does%not%change%its%% ability%to%do%its%job.%Helps%with%development.%i. Lungs=%one%side%has%2%lobes%the%other%has%3%lopes%–this%is%because%it%is%% a%fractal%object.%%j. Mammalian%lungs%scale%to%the%¾%power%of%body%mass.%Other%systems%% also%have%a%¾%scale:%metabolic%rate,%oxygen%consumption,%food%% consumption.%This%is%because%they%are%all%related%to%metabolism%and%%% functionally%related%to%the%lungs.%Things%with%this%scaling%are%complex%% in%shape%–%they%are%fractal.%%k. Fractal%scaling%occurs%in%complex%systems.%MAKE%EVERY%% MULTICELLULAR%ORGANISM%POSSIBLE.%l. Allometric%scaling%–%occurs%were%area%volume%processes%are%more%% important%than%fractal%process.%m. Fractal%dimension%–%can%help%detect%cancerous%cells,%predict%heart%% attacks%%Building%Bodies%• Heat%load%–%the%reason%for%the%fundamental%difference%in%leaves.%Leaves%on%the%left%get%far%more%sunlight%and%have%a%larger%heat%load.%The%ones%on%the%right%are%more%in%the%shade.%There%is%a%change%in%fractal%dimension.%• How%is%fractal%dimension%controlled%developmentally?%How%does%the%oak%tree%know%to%have%certain%kinds%of%leaves?%• Diploid%multicelluar%organisms%begin%as%the%zygote.%It%is%totipotent%–%will%produce%everythin%in%the%body.%Full%genetic%potential.%Divides%in%cell%division%–%different%than%mitosis.%Produces%a%cluster%of%cells.%In%this%cluster%there%is%a%process%called%determination%going%on.%%• Determination%–%certain%master%control%genes%are%turned%on.%Sets%the%cell%to%a%certain%path.%Cell%doesn’t%change%appearance%but%its%fate%is%determined.%• Then%we%get%differenetation,%where%the%regulatiroty%genes%that%are%turned%on%now%turn%on%certain%structural%genes%that%differentiate%the%cell%into%what%kind%of%cell%it%is%going%to%be.%Causes%the%cell%to%change%appearance.%%• In%animals,%there%is%the%cell%lineage%effect,%which%as%you%go%through%more%cell%divisions,%the%cells%that%are%there%respond%to%fewer%influences%during%development.%The%cells%become%progressively%less%susceptible%to%a%whole%range%of%regulatory%genes.%%• Differences%that%arise%due%to%mutations%in%regulatory%genes.%%• Gastrulation%–%hollow%ball%of%cells%and%the%cells%at%one%pole%(vegetal%pole)%start%migrating%and%pushing%in%to%form%a%pouch%which%becomes%the%gut%and%endoderm.%The%blastopore%is%what%becomes%the%mouth%(protostomes)%or%the%anus%(dueterostomes).%%• Frog%gastrulation%–%have%a%lot%of%yolk%at%one%part%of%the%cell,%some%cells%are%undernourished,%so%there%is%unequal%divisions.%The%dorsal%lip–%breaks%the%basic%symmetry%of%the%embryo%and%established%some%basic%patterns%for%development.%The%lip%is%very%critical%for%higher%vertebrates%to%survive%gastrulation.%• Induction=%cells%communicate%with%eachother%by%chemical%signals.%Inducers%are%chemical%signials%in%a%developing%embryo.%Trigger%determination%and%differentation.%Whenever%you%have%a%signal%there%is%a%resp onse.%
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