Transcript reserve
Metabolism I contributions from : Tânia Sousa Gonçalo Marques and Bas Kooijmann A Theory of Metabolism What is metabolism? A Theory of Metabolism What is metabolism? “Using resources (energy and materials) to make new cells, to repair old ones, and to get rid of wastes requires the assemblage of biochemical pathways that we call metabolism. Metabolism is a universal feature of life that links organisms with their environment, and with each other.” A Theory of Metabolism What is metabolism? “Using resources (energy and materials) to make new cells, to repair old ones, and to get rid of wastes requires the assemblage of biochemical pathways that we call metabolism. Metabolism is a universal feature of life that links organisms with their environment, and with each other.” What should a theory of metabolism look like? A Theory of Metabolism What is metabolism? What should a theory of metabolism look like? It should be a qualitative and quantitative description of how organisms use mass and energy to do the things they need to do to stay alive A Theory of Metabolism What is metabolism? What should a theory of metabolism look like? It should be a qualitative and quantitative description of how organisms use mass and energy to do the things they need to do to stay alive Which type of questions can a theory of metabolism help you with? A Theory of Metabolism Which type of questions can a theory of metabolism help you with? Why do weak accids have an effect on the growth of yeasts? What is the minimum amount of food (and habitat) a panda needs to survive? If the temperature of ocean increases by 0.5ºC what will happen to the survival of the sardine larvae? Environmental Applications Toxicology Environmental Applications Toxicology Which is the toxicity of the environmental concentration of a compound? Which are the toxic effects of a compound? Climate Change Environmental Applications Toxicology Which is the toxicity of the environmental concentration of a compound? Which are the toxic effects of a compound? Climate Change Will an increase in 1ºC have a drastic impact on the distribution range of a species? Waste water treatment plant Environmental Applications Toxicology Which is the toxicity of the environmental concentration of a compound? Which are the toxic effects of a compound? Climate Change Will an increase in 1ºC have a drastic impact on the distribution range of a species? Waste water treatment plant What are the necessary conditions to mantain an healthy microbian comunity in the biological reactors? Fisheries Management Environmental Applications Toxicology Which is the toxicity of the environmental concentration of a compound? Which are the toxic effects of a compound? Climate Change Will an increase in 1ºC have a drastic impact on the distribution range of a species? Waste water treatment plant What are the necessary conditions to mantain an healthy microbian comunity in the biological reactors? Fisheries Management What is the sustainable fishing quota? DEB – a theory for Metabolism It captures the quantitative aspects of metabolism at the individual level for all species DEB – a theory for Metabolism It captures the quantitative aspects of metabolism at the individual level for all species Why the hope for generality? universality of physics and evolution Entropy production is >=0 cell universality: cells are metabolically very similar, independently of the organism or its size widespread biological empirical patterns A widespread biological empirical fact: Von Bertalanffy growth Growth as a function of time L(t ) L ( L Lb ) e rB t Depends on length at birth, maximum length and growth rate It was proposed in 1929 by Putter and in 1938 by Von Bertalanffy A widespread biological empirical fact: Kleiber’s Law Metabolism (respiration or heat production) as a function of mass M aW b Metabolism increases with weight raised to the power 3/4 Max Kleiber originally formulated this basic relationship back in the 1930s. What is the relationship between specific metabolism and weight? A widespread biological empirical fact: Kleiber’s Law Relationship between specific metabolism and weight? Basic Concepts in DEB Theory Consistency with other scientific knowledge (thermodynamics, evolution, etc) Consistency with empirical data Life-cycle approach: embryo, juvenile and adult Occam’s razor: the general model should be as simple as possible (and not more) Occam’s biological razor: organisms increased their control over metabolism during evolution Basic Concepts in DEB Theory The individual: time and spatial scales A DEB organism: the State Variables Metabolism in a DEB individual. The boundary of the organism Rectangles are state variables DEB model: the State Variables What defines a DEB organism? Biomass V - Structure E - Reserve Life-Cycle approach: different life stages EH – Maturity level (it doesn’t contribute to the organisms mass) What about other possibles state variables such as age? Why not age as a state variable? Trichopsis vittatus These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake Notation General Indices for compounds Indices for transformations DEB model: Reserve and Structure Strong homeostasis Reserve & structure have constant aggregated chemical composition DEB model: Reserve and Structure Strong homeostasis Reserve & structure have constant aggregated chemical composition Why more than 1 state variable to define the biomass? The aggregated chemical composition of organisms is not constant – it changes with the growth rate What does a variable aggregated chemical composition impliy? Why not more than 2 state variables to define biomass? Two are sufficient (in animals and bacteria) to capture the change in aggregated chemical composition with the growth rate Strong homeostasis → higher control over metabolism Why not use thousands of chemical species and chemical reactions to define the organism? Metabolism at the chemical level is very complex It is not possible to impose mass conservation without modeling all chemical reactions (which is impossible). “Knowledge on motors of cars is of little help to solve queuing problems” DEB model: Reserve and Structure Weak homeostasis At constant food organisms tend to constant aggregated chemical composition DEB model: Reserve and Structure Weak homeostasis At constant food organisms tend to constant aggregated chemical composition What has to be the relationship between V and E to ensure a constant aggregated chemical composition? Empirical support: growing biomass tends to constant chemical composition at constant food Weak homeostasis -> higher control over metabolism DEB model: Maturity Life Stages (dark blue) and transitions (light blue) embryo fertilization juvenile birth adult puberty death DEB model: Maturity Life Stages (dark blue) and transitions (light blue) embryo fertilization baby birth juvenile adult infant weaning puberty death Essential switch points for metabolic behavior Birth (start of feeding) Puberty (start of allocation to reproduction) Switch points sometimes in reversed order (aphids) EHb- threshold of maturity at birth EHp- threshold of maturity at puberty Life-stages: Metamorphosis Life-stages: Metamorphosis Venturia cannescens Larva Embryo Puppa Adult EHb - Extremes in relative maturity at birth Didelphus marsupiales (Am opossum) ♂, ♀ 0.5 + 0.5 m, 6.5 kg At birth: <2 g; ab = 8-13 d 10-12 (upto 25) young/litter, 2 litters/a Ommatophoca rossii (Ross Seal) ♂ 1.7-2.1 m, 129-216 kg ♀ 1.3-2.2 m, 159-204 kg At birth: 1 m, 16.5 kg; ab = 270 d A DEB organism – energy description Metabolism in a DEB individual. The boundary of the organism Rectangles are state variables Why is the chemical potential of reserve a parameter? A DEB organism – energy description Metabolism in a DEB individual. The boundary of the organism Rectangles are state variables Chemical and thermodynamic properties of the structure and 𝐸 = 𝑀𝐸 𝜇𝐸 reserve are constant (strong homeostasis) 𝜇𝐸 - chemical potential of reserve 𝜇𝑉 - chemical potential of structure EHb- threshold of maturity at birth EHp- threshold of maturity at puberty 𝐸𝐻 = 𝑀𝐻 𝜇𝐸 𝐸𝑉 = 𝑀𝑉 𝜇𝑉 MHb- threshold of maturity at birth MHp- threshold of maturity at puberty A DEB organism Metabolism in a DEB individual. Rectangles are state variables Arrows are flows of food pX, reserve pA, pC, pS, pT , pG, pR, pJ or structure pVG. Circles are transformations Notation General Indices for compounds Indices for transformations Notation for mass flows 1 Feeding & Assimilation 2/3 𝑝𝑋 = 𝑓(𝑋) 𝑝𝑋𝑚 𝑉 Feeding: the uptake of food Assimilation: conversion of substrate (food, nutrients, light) into reserve(s) 𝑝𝐴 = 𝜅𝑋 𝑝𝑋 = 𝑓(𝑋) 𝑝𝐴𝑚 𝑉 2/3 Depend on substrate availability & structural surface area (e.g. surface area of the gut) 𝑝𝑋𝑚 - surface maximum feeding rate 𝑝𝐴𝑚 - surface maximum assimilation rate 𝜅𝑋 - efficiency of food assimilation Are all these parameters independent? Feeding & Assimilation 2/3 𝑝𝑋 = 𝑓(𝑋) 𝑝𝑋𝑚 𝑉 Feeding: the uptake of food Assimilation: conversion of substrate (food, nutrients, light) into reserve(s) 𝑝𝐴 = 𝜅𝑋 𝑝𝑋 = 𝑓(𝑋) 𝑝𝐴𝑚 𝑉 2/3 Depend on substrate availability & structural surface area (e.g. surface area of the gut) 𝑝𝑋𝑚 - surface maximum feeding rate 𝑝𝐴𝑚 - surface maximum assimilation rate 𝜅𝑋 - efficiency of food assimilation Are all these parameters independent? Empirical pattern: the heat increment of feeding suggests that there are processes only associated with food processing Consistency with other fields: mass transfer (needed for acquisition, digestion and food processing) is proportional to area Why is the efficiency of food assimilation of reserve on food a parameter? Feeding & Assimilation 2/3 𝑝𝑋 = 𝑓(𝑋) 𝑝𝑋𝑚 𝑉 Feeding: the uptake of food Assimilation: conversion of substrate (food, nutrients, light) into reserve(s) 𝑝𝐴 = 𝜅𝑋 𝑝𝑋 = 𝑓(𝑋) 𝑝𝐴𝑚 𝑉 2/3 Depend on substrate availability & structural surface area (e.g. surface area of the gut) 𝑝𝑋𝑚 - surface maximum feeding rate 𝑝𝐴𝑚 - surface maximum assimilation rate 𝜅𝑋 - efficiency of food assimilation Empirical pattern: the heat increment of feeding suggests that there are processes only associated with food processing Strong homeostasis imposes a fixed conversion efficiency Consistency with other fields: mass transfer (needed for acquisition, digestion and food processing) is proportional to area Feeding rate Filtration rate, l/h If food availability is constant (or abundant) feeding increases proportional to area or L2 (for isomorphs) Mytilus edulis Data: Winter 1973 Length, cm Intra-taxon predation: efficient conversion κX a high efficiency of food assimilation Hemiphractus fasciatus is a frog-eating frog Beroe sp is a comb jelly-eating comb jelly Euspira catena is a snail-eating snail Coluber constrictor is a snake-eating snake Solaster papposus is a starfish-eating starfish Chrysaora hysoscella is a jelly fish-eating jelly fish Intra-taxon predation: efficient conversion κX a high efficiency of food assimilation Asplanchna girodi is a rotifer-eating rotifer Falco peregrinus is a bird-eating bird Didinium nasutum is a ciliate-eating ciliate Acinonyx jubatus is a mammal-eating mammal Esox lucius is a fish-eating fish Enallagma carunculatum is a insect-eating insect Feeding & Assimilation Proportionality between assimilation and ingestion rate for Mytilus Edulis for different sizes A DEB organism Metabolism in a DEB individual. Rectangles are state variables Arrows are flows of food pX, reserve pA, pC, pS, pT , pG, pR, pJ or structure pVG. Circles are transformations 𝑝𝑋 = 𝑓(𝑋) 𝑝𝑋𝑚 𝑉 2/3 How do we obtain the mass description? 𝑝𝐴 = 𝜅𝑋 𝑝𝑋 = 𝑓(𝑋) 𝑝𝐴𝑚 𝑉 2/3 𝑝𝑋𝑚 - surface maximum feeding rate 𝑝𝐴𝑚 - surface maximum assimilation rate 𝜅𝑋 -efficiency of food assimilation A DEB organism – energy description Metabolism in a DEB individual. Rectangles are state variables Arrows are flows of food JXA, reserve JEA, JEC, JEM, JET , JEG, JER, JEJ or structure JVG. Circles are transformations 𝐽𝑋𝐴 = 𝑓(𝑋) 𝐽𝑋𝐴𝑚 𝑉 2/3 𝑝𝑋 = 𝐽𝑋𝐴 𝜇𝑋 = 𝑓(𝑋) 𝑝𝑋𝑚 𝑉 2/3 𝐽𝐸𝐴 = 𝑦𝐸𝑋 𝐽𝑋𝐴 = 𝑓(𝑋) 𝐽𝐸𝐴𝑚 𝑉 2/3 𝑝𝐴 = 𝐽𝐸𝐴 𝜇𝐸 = 𝑓(𝑋) 𝑝𝐴𝑚 𝑉 2/3 𝐽𝑋𝐴𝑚 - surface maximum feeding rate 𝐽𝐸𝐴𝑚 - surface maximum assimilation rate 𝑦𝐸𝑋 - yield of reserve on food 𝑝𝑋𝑚 = 𝜇𝑋 𝐽𝑋𝐴𝑚 𝑝𝐴𝑚 = 𝜇𝐸 𝐽𝐸𝐴𝑚 Notation General Indices for compounds Indices for transformations A DEB organism – parameters Primary parameters Auxiliary parameters 𝜅𝑋 𝜇𝑋 , 𝜇𝐸 , 𝜇𝑉 𝑝𝐴𝑚 𝑑𝑋 , 𝑑𝐸 , 𝑑𝑉 𝑤𝑋 , 𝑤𝐸 , 𝑤𝑉 A DEB organism Mobilization Metabolism in a DEB individual. Rectangles are state variables Arrows are flows of food pX, reserve pA, pC, pS, pT , pG, pR, pJ or structure pVG. Circles are transformations Mobilization of Reserve The mobilization of reserve is used to fuel the organism’s activities 𝑝𝐶 = 𝑝𝑆 +𝑝𝐺 +𝑝𝐽 + 𝑝𝑅 𝑣 𝐸 𝑑𝐿 𝑝𝐶 = 𝐸 −𝑟 = 𝑣−3 𝐿 𝐿 𝑑𝑡 𝑣 - energy conductance Mobilization of Reserve The mobilization of reserve is used to fuel the organism’s activities 𝑝𝐶 = 𝑝𝑆 +𝑝𝐺 +𝑝𝐽 + 𝑝𝑅 𝑣 𝐸 𝑑𝐿 𝑝𝐶 = 𝐸 −𝑟 = 𝑣−3 𝐿 𝐿 𝑑𝑡 𝑣 - energy conductance Empirical pattern: organisms are capable of spending energy on growth, maintenance and reproduction in the absence of food Empirical pattern: eggs spend energy on maturation but do not feed. Mobilization from reserve -> higher control over the metabolism (independence from the environment) Mobilization is uncoupled from assimilation & feeding: makes evolution easier Weak homeostasis & strong homeostasis & independence of mobilization from the environment mobilization is proportional to C-moles of reserve per unit of length What are the units of 𝑣? Notation General Indices for compounds Indices for transformations Notation 3 Notice that some symbols have more than one meaning: V as symbol stands for volume, and without index for volume of structure, as index stands for the compound structure E as symbol stands for energy, and without index for energy in reserve, as index stands for the compound reserve C, H, O, N as indices stand for mineral compounds as well as chemical elements the context defines the meaning Dots are used to • distinguish rates from states (dimension check) • allow scaling of time without the need to introduce new symbols if time is scaled to a dimensionless quantity, the dot is removed Mobilization of Reserve Some populations of humpback whale Megaptera novaeangliae (36 Mg) migrate 26 Mm anually without feeding, A 15 m mother gets a 6 m calf in tropical waters, gives it 600 l milk/d for 6 months and together return to cold waters to resume feeding in summer A DEB organism – energy description Metabolism in a DEB individual. Rectangles are state variables Arrows are flows of food pX, reserve pA, pC, pS, pT , pG, pR, pJ or structure pVG. Circles are transformations 𝑝𝐶 = 𝑝𝑆 +𝑝𝐺 +𝑝𝐽 +𝑝𝑅 𝑝𝐶 = 𝐸 𝑣 −𝑟 𝐿 1 𝑑𝑉 𝑟= 𝑉 𝑑𝑡 Write in the mass framework A DEB organism – energy description Metabolism in a DEB individual. Rectangles are state variables Arrows are flows of food pX, reserve pA, pC, pS, pT , pG, pR, pJ or structure pVG. Circles are transformations 𝑝𝐶 = 𝑝𝑆 +𝑝𝐺 +𝑝𝐽 +𝑝𝑅 𝑝𝐶 = 𝐸 𝑣 −𝑟 𝐿 1 𝑑𝑉 𝑟= 𝑉 𝑑𝑡 Write in the mass framework 𝐽𝐸𝐶 = 𝐽𝐸𝑆 +𝐽𝐸𝐺 +𝐽𝐸𝐽 + 𝐽𝐸𝑅 𝐽𝐸𝐶 = 𝑀𝐸 𝑣 −𝑟 𝐿 𝑟= 1 𝑑𝑀𝑉 𝑀𝑉 𝑑𝑡 A DEB organism The kappa rule – a fixed allocation rule Metabolism in a DEB individual. Rectangles are state variables Arrows are flows of food pX, reserve pA, pC, pS, pT , pG, pR, pJ or structure pVG. Circles are transformations 𝜅 rule A fixed fraction of mobilised reserve is allocated to somatic maintenance and growth, the rest to maturity maintenance and maturation (juveniles) or reproduction (1 − κ)𝑝𝐶 = 𝑝𝐽 +𝑝𝑅 (adults). κ𝑝𝐶 = 𝑝𝑆 +𝑝𝐺 - kappa Empirical pattern: some species do not stop growing after reproduction has started Length, mm Cum # of young Reproduction Growth: d L rB ( L L) dt Von Bertalanffy Age, d Age, d 𝜅 rule Metabolism in a DEB individual. Rectangles are state variables Arrows are flows of food pX, reserve pA, pC, pS, pT , pG, pR, pJ or structure pVG. Circles are transformation The kappa rule (a fixed allocation rule) 𝜅𝑝𝐶 = 𝑝𝑆 + 𝑝𝐺 𝜅𝐽𝐸𝐶 = 𝐽𝐸𝑆 +𝐽𝐸𝐺 (1 − 𝜅) 𝑝𝐶 = 𝑝𝐽 +𝑝𝑅 (1 − 𝜅)𝐽𝐸𝐶 = 𝐽𝐸𝐽 +𝐽𝐸𝑅 A DEB organism – parameters Primary parameters Auxiliary parameters 𝜅𝑋 𝜇𝑋 , 𝜇𝐸 , 𝜇𝑉 𝑝𝐴𝑚 𝑑𝑋 , 𝑑𝐸 , 𝑑𝑉 𝑣 𝜅 𝑤𝑋 , 𝑤𝐸 , 𝑤𝑉 A DEB organism Priority allocation rules Metabolism in a DEB individual. Rectangles are state variables Arrows are flows of food pX, reserve pA, pC, pS, pT , pG, pR, pJ or structure pVG. Circles are transformations The kappa rule (a fixed allocation rule) The priority maintenance rules The priority maintenance rule states that maintenance has priority: from κ 𝑝𝐶 = 𝑝𝑆 +𝑝𝐺 somatic maintenance is paid first and the rest goes to growth A DEB organism Priority allocation rules Metabolism in a DEB individual. Rectangles are state variables Arrows are flows of food pX, reserve pA, pC, pS, pT , pG, pR, pJ or structure pVG. Circles are transformations The kappa rule (a fixed allocation rule) The priority maintenance rules The priority maintenance rule states that maintenance has priority: from κ 𝑝𝐶 = 𝑝𝑆 +𝑝𝐺 somatic maintenance is paid first and the rest goes to growth A DEB organism – somatic maintenance Metabolism in a DEB individual. Rectangles are state variables Arrows are flows of food pX, reserve pA, pC, pS, pT , pG, pR, pJ or structure pVG. Circles are transformations The kappa rule (a fixed allocation rule) The priority maintenance rules Somatic maintenance Collection of processes that maintain the organism alive: protein turnover (synthesis, but no net synthesis) maintaining conc. gradients across membranes (proton leak) (some) product formation (leaves, hairs, skin flakes, moults) movement (usually less than 10% of maintenance costs) Somatic maintenance Reserve compounds have no maintenance needs because they have a limited lifetime Somatic maintenance is paid from flux pC: 𝑝𝑆 = 𝑝𝑀 𝐿3 + 𝑝𝑇 𝐿2 = 𝑝𝑀 𝑉 + 𝑝𝑇 𝑉 2/3 structural volume (most costs) surface area: heating (endotherms), osmo-regulation (fresh water organisms) Specific somatic maintenance costs are constant because the chemical and thermodynamic properties of the structure are constant (strong homeostasis) Empirical pattern: Freshly produced eggs consist primarly of reserve and hardly respire 𝑝𝑀 - volume specific maintenance costs 𝑝𝑇 - surface specific maintenance costs Reserve pays no maintenance embryonic development embryo weight, g yolk time, d O2 consumption, ml/h Carettochelys insculpta Data from Web et al 1986 time, d A DEB organism – parameters Primary parameters Auxiliary parameters 𝜅𝑋 𝜇𝑋 , 𝜇𝐸 , 𝜇𝑉 𝑝𝐴𝑚 𝑑𝑋 , 𝑑𝐸 , 𝑑𝑉 𝑣 𝜅 𝑤𝑋 , 𝑤𝐸 , 𝑤𝑉 𝑝𝑀 𝑝𝑇