Models::Acetate Struct Reference

Acetate model with explicit oxygen limitation. More...

#include <acetate.hpp>

Public Types
enum class	particle_var : int {   length = 0 , l_max , a_p , a_max ,   a_e , a_go , a_fe , a_ao ,   phi_s , phi_o2 , phi_a , __COUNT__ }
enum	species_index : std::size_t { S = 0 , O2 = 1 , Ac = 2 , N_N = n_c }
	Species indices, O2 has to stay at index 1 (gas/liquid transfer) More...
enum	reaction_index : std::size_t {   i_go = 0 , i_fe = 1 , i_ov = 2 , i_ao = 3 ,   N_R = 4 }
	Reaction indices. More...
using	uniform_weight = std::true_type
using	Self = Acetate
using	FloatType = float
using	Config = std::nullopt_t
using	SelfParticle = MC::ParticlesModel<Self::n_var, Self::FloatType>
using	SelfContribs = MC::ParticlesContribs<Self::n_c, Self::FloatType>
using	reaction_rates = Kokkos::Array<FloatType, N_R>
using	uptake_rates = Kokkos::Array<FloatType, N_N>

Static Public Member Functions
static KOKKOS_INLINE_FUNCTION void	init (const MC::pool_type &random_pool, std::size_t idx, const SelfParticle &arr)
static KOKKOS_INLINE_FUNCTION MC::Status	update (const MC::pool_type &random_pool, FloatType d_t, std::size_t idx, const SelfParticle &arr, const SelfContribs &arr_contribs, std::size_t position_index, const MC::LocalConcentration &c)
static KOKKOS_INLINE_FUNCTION void	division (const MC::pool_type &random_pool, std::size_t idx, std::size_t idx2, const SelfParticle &arr, const SelfParticle &buffer_arr)
static KOKKOS_INLINE_FUNCTION reaction_rates	metabolism (const uptake_rates &phi, FloatType nu_p, FloatType &nu)
	Distribute the available uptake fluxes over the four reactions.
static KOKKOS_INLINE_FUNCTION double	mass (std::size_t idx, const SelfParticle &arr)
static std::array< std::string_view, Self::n_var >	names ()
static std::array< std::string_view, Self::n_c >	species ()

Public Attributes
MODEL_CONSTANT FloatType	a_max_m = 2e-6 / 3600.
MODEL_CONSTANT FloatType	l_max_m = 2e-6
MODEL_CONSTANT FloatType	l_min_m = l_max_m / 2.
MODEL_CONSTANT FloatType	d_m = 0.6e-6
MODEL_CONSTANT FloatType	lin_density = c_linear_density(static_cast<FloatType>(1000), d_m)
MODEL_CONSTANT FloatType	k_s = 1e-3
	Monod affinity constants [kg/m^3].
MODEL_CONSTANT FloatType	k_o = 1e-5
MODEL_CONSTANT FloatType	k_a = 1e-4
MODEL_CONSTANT FloatType	y_x_go = 0.5F
	gX/gS
MODEL_CONSTANT FloatType	y_x_fe = 0.15F
	gX/gS
MODEL_CONSTANT FloatType	y_x_ov = 0.0F
	overflow does not grow
MODEL_CONSTANT FloatType	y_x_ao = 0.33F
	gX/gAc
MODEL_CONSTANT FloatType	y_o2_go
	gO2/gS, 0.384
MODEL_CONSTANT FloatType	y_o2_ao
	gO2/gAc
MODEL_CONSTANT FloatType	y_ac_fe
	gAc/gS produced by fermentation, 0.808
MODEL_CONSTANT FloatType	y_ac_ov
	gAc/gS produced by overflow. C6H12O6 -> 3 C2H4O2 balances as is, so 1
MODEL_CONSTANT FloatType	f_o2_max = 1.2
MODEL_CONSTANT FloatType	f_ac_max = 1. / 3.
	Acetate uptake capacity relative to the glucose one.
MODEL_CONSTANT FloatType	phi_s_max = a_max_m * lin_density / y_x_go
MODEL_CONSTANT FloatType	x_c_max = 30.
MODEL_CONSTANT FloatType	f_pos = 2.
	One explicit step removes at most 1/f_pos of the local concentration.
MODEL_CONSTANT FloatType	d_t_floor = 1e-30
	Only there so that d_t = 0 does not divide by zero.
MODEL_CONSTANT FloatType	a_p_min = 1e-3F * a_max_m
MODEL_CONSTANT FloatType	a_p_recovery = 0.25F
MODEL_CONSTANT auto	l_max_dist
MODEL_CONSTANT auto	l_dist

Static Public Attributes
static constexpr std::size_t	n_var = INDEX_FROM_ENUM(particle_var::__COUNT__)
static constexpr std::string_view	name = "acetate"
static constexpr std::size_t	n_c = 3
	Liquid species: glucose, dioxygen, acetate.

Detailed Description

Acetate model with explicit oxygen limitation.

Derived from Models::SimpleAcetate, this model adds dissolved oxygen as a third liquid species.

Warning

The transfer kernel hardcodes the oxygen row of the kla matrix to index 1, so the species ordering (S, O2, Ac) must not be changed.

Four lumped reactions, by decreasing priority:

• i_go S + O2 -> X + CO2 respiration
• i_ao Ac + O2 -> X + CO2 acetate re-uptake
• i_ov S -> Ac overflow, no growth
• i_fe S -> X + Ac + CO2 fermentation

Mass balance

Acetate moves according to the two limitations of the cell and to nothing else:

• a_p. The glucose that oxygen could have supported but that the growth capacity cannot handle leaves as acetate through i_ov. This is the classic overflow, active even at oxygen saturation.
• O2. The glucose that the growth capacity could have handled but that oxygen cannot support is fermented through i_fe, which also releases acetate.
• Acetate is taken back up by i_ao alone, on the oxygen and on the growth capacity left over by i_go. Both residuals are zero as soon as the cell overflows or ferments, so acetate is never produced and consumed in the same step.

As in SimpleAcetate the internal currency is the elongation rate a [m/s], converted to a mass flux through the linear density.

Member Typedef Documentation

Config

using Models::Acetate::Config = std::nullopt_t

FloatType

using Models::Acetate::FloatType = float

reaction_rates

using Models::Acetate::reaction_rates = Kokkos::Array<FloatType, N_R>

Self

using Models::Acetate::Self = Acetate

SelfContribs

using Models::Acetate::SelfContribs = MC::ParticlesContribs<Self::n_c, Self::FloatType>

SelfParticle

using Models::Acetate::SelfParticle = MC::ParticlesModel<Self::n_var, Self::FloatType>

uniform_weight

using Models::Acetate::uniform_weight = std::true_type

uptake_rates

using Models::Acetate::uptake_rates = Kokkos::Array<FloatType, N_N>

Member Enumeration Documentation

particle_var

enum class Models::Acetate::particle_var : int

strong

Enumerator
length
l_max
a_p
a_max
a_e
a_go
a_fe
a_ao
phi_s
phi_o2
phi_a
__COUNT__

reaction_index

enum Models::Acetate::reaction_index : std::size_t

Reaction indices.

Enumerator
i_go
i_fe
i_ov
i_ao
N_R

species_index

enum Models::Acetate::species_index : std::size_t

Species indices, O2 has to stay at index 1 (gas/liquid transfer)

Note

Plain enumerators, not MODEL_CONSTANT: they are used as runtime subscripts of Kokkos::Array in the device kernels and nvcc rejects a static constexpr scalar there ("undefined in device code"). An enumerator has no storage, so it is always usable on the device.

Enumerator
S
O2
Ac
N_N

Member Function Documentation

division()

KOKKOS_INLINE_FUNCTION void Models::Acetate::division ( const MC::pool_type & random_pool, std::size_t idx, std::size_t idx2, const SelfParticle & arr, const SelfParticle & buffer_arr )

static

init()

KOKKOS_INLINE_FUNCTION void Models::Acetate::init ( const MC::pool_type & random_pool, std::size_t idx, const SelfParticle & arr )

static

mass()

KOKKOS_INLINE_FUNCTION double Models::Acetate::mass ( std::size_t idx, const SelfParticle & arr )

inlinestatic

metabolism()

KOKKOS_INLINE_FUNCTION Acetate::reaction_rates Models::Acetate::metabolism ( const uptake_rates & phi, FloatType nu_p, FloatType & nu )

static

Distribute the available uptake fluxes over the four reactions.

Parameters

phi	uptake potentials [kg/s] indexed by species
nu_p	potential growth rate of the cell [kgX/s]
nu	out: growth rate effectively realised [kgX/s]

Returns

the reaction fluxes [kg of substrate/s]

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names()

std::array< std::string_view, Self::n_var > Models::Acetate::names ( )

inlinestatic

species()

std::array< std::string_view, Self::n_c > Models::Acetate::species ( )

inlinestatic

update()

KOKKOS_INLINE_FUNCTION MC::Status Models::Acetate::update ( const MC::pool_type & random_pool, FloatType d_t, std::size_t idx, const SelfParticle & arr, const SelfContribs & arr_contribs, std::size_t position_index, const MC::LocalConcentration & c )

static

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Member Data Documentation

a_max_m

MODEL_CONSTANT FloatType Models::Acetate::a_max_m = 2e-6 / 3600.

a_p_min

MODEL_CONSTANT FloatType Models::Acetate::a_p_min = 1e-3F * a_max_m

Lowest admissible growth capacity [m/s]. a_p has to stay strictly positive: it is the only thing that lets a starved lineage grow again, and log(a_p) is taken at every division.

a_p_recovery

MODEL_CONSTANT FloatType Models::Acetate::a_p_recovery = 0.25F

Regression of the newborn capacity toward its own a_max at division. a_e <= a_p holds by construction, so a redistribution centred on the performance of the mother alone (0) is a one way ratchet: the capacity of a lineage can only decrease and collapses to 0 over the generations.

d_m

MODEL_CONSTANT FloatType Models::Acetate::d_m = 0.6e-6

d_t_floor

MODEL_CONSTANT FloatType Models::Acetate::d_t_floor = 1e-30

Only there so that d_t = 0 does not divide by zero.

f_ac_max

MODEL_CONSTANT FloatType Models::Acetate::f_ac_max = 1. / 3.

Acetate uptake capacity relative to the glucose one.

f_o2_max

MODEL_CONSTANT FloatType Models::Acetate::f_o2_max = 1.2

Oxygen uptake capacity, as a multiple of the stoichiometric demand of a fully respired glucose uptake. Above 1 the cell is never limited by its own uptake machinery, only by the dissolved oxygen available.

Note

the fermentation onset does not depend on y_o2_go: the respirable glucose is min(phi_S, f_o2_max * phi_s_max * monod(O2)), the yield cancels between the capacity and the phi[O2]/y_o2_go bound.

f_pos

MODEL_CONSTANT FloatType Models::Acetate::f_pos = 2.

One explicit step removes at most 1/f_pos of the local concentration.

k_a

MODEL_CONSTANT FloatType Models::Acetate::k_a = 1e-4

k_o

MODEL_CONSTANT FloatType Models::Acetate::k_o = 1e-5

Anane et. al 2017 (Biochem. Eng. J). The sharp switch this gives is what the uptake cap of positivity makes affordable explicitly.

k_s

MODEL_CONSTANT FloatType Models::Acetate::k_s = 1e-3

Monod affinity constants [kg/m^3].

l_dist

MODEL_CONSTANT auto Models::Acetate::l_dist

Initial value:

= MC::Distributions::TruncatedNormal<FloatType>(
        l_max_m * 0.75, l_max_m / 10., 0.7 * l_min_m, l_max_m * 1.3)

l_max_dist

MODEL_CONSTANT auto Models::Acetate::l_max_dist

Initial value:

= MC::Distributions::TruncatedNormal<FloatType>(
            l_max_m, l_max_m / 10., l_max_m * 0.7, 1.3 * l_max_m)

l_max_m

MODEL_CONSTANT FloatType Models::Acetate::l_max_m = 2e-6

l_min_m

MODEL_CONSTANT FloatType Models::Acetate::l_min_m = l_max_m / 2.

lin_density

MODEL_CONSTANT FloatType Models::Acetate::lin_density = c_linear_density(static_cast<FloatType>(1000), d_m)

n_c

std::size_t Models::Acetate::n_c = 3

staticconstexpr

Liquid species: glucose, dioxygen, acetate.

n_var

std::size_t Models::Acetate::n_var = INDEX_FROM_ENUM(particle_var::__COUNT__)

staticconstexpr

name

std::string_view Models::Acetate::name = "acetate"

staticconstexpr

phi_s_max

MODEL_CONSTANT FloatType Models::Acetate::phi_s_max = a_max_m * lin_density / y_x_go

x_c_max

MODEL_CONSTANT FloatType Models::Acetate::x_c_max = 30.

Highest biomass concentration the reactor is expected to reach [kg/m^3]. Sizes the cap below, no influence on the metabolism; overestimating it only makes the cap engage a little earlier.

y_ac_fe

MODEL_CONSTANT FloatType Models::Acetate::y_ac_fe

Initial value:

= static_cast<FloatType>(
        Stoichiometry::y_ac_fer(Stoichiometry::m_cmol_glucose,
                                Stoichiometry::gamma_glucose,
                                y_x_fe))

gAc/gS produced by fermentation, 0.808

y_ac_ov

MODEL_CONSTANT FloatType Models::Acetate::y_ac_ov

Initial value:

= static_cast<FloatType>(
        Stoichiometry::y_ac_fer(Stoichiometry::m_cmol_glucose,
                                Stoichiometry::gamma_glucose,
                                y_x_ov))

gAc/gS produced by overflow. C6H12O6 -> 3 C2H4O2 balances as is, so 1

y_o2_ao

MODEL_CONSTANT FloatType Models::Acetate::y_o2_ao

Initial value:

= static_cast<FloatType>(
        Stoichiometry::y_o2_ox(Stoichiometry::m_cmol_acetate,
                               Stoichiometry::gamma_acetate,
                               y_x_ao))

gO2/gAc

y_o2_go

MODEL_CONSTANT FloatType Models::Acetate::y_o2_go

Initial value:

= static_cast<FloatType>(
        Stoichiometry::y_o2_ox(Stoichiometry::m_cmol_glucose,
                               Stoichiometry::gamma_glucose,
                               y_x_go))

gO2/gS, 0.384

y_x_ao

MODEL_CONSTANT FloatType Models::Acetate::y_x_ao = 0.33F

gX/gAc

y_x_fe

MODEL_CONSTANT FloatType Models::Acetate::y_x_fe = 0.15F

gX/gS

y_x_go

MODEL_CONSTANT FloatType Models::Acetate::y_x_go = 0.5F

gX/gS

y_x_ov

MODEL_CONSTANT FloatType Models::Acetate::y_x_ov = 0.0F

overflow does not grow

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The documentation for this struct was generated from the following file:

• apps/libs/models/public/models/acetate.hpp