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README
¶
Docs: GoDoc
Package chem provides basic chemistry simulation algorithms, including:
-
React-- chemical reaction where 2 components bind into a compound, characterized by forward and backward rate constants, Kf, Kb. -
Enz-- enzyme-catalyzed reaction based on the Michaelis-Menten kinetics that transforms S = substrate into P product via SE bound C complex. -
Buffer-- provides a soft buffering driving deltas relative to a target N which can be set by concentration and volume. -
Integrate-- performs basic forward Euler integration, usingIntegrateDtrate constant. -
CoFmNandCoToNconvert concentration to / from numbers of molecules given a volume (just multiplication and division, but useful for documenting the purpose).
In general, all of this code just computes deltas (discrete derivatives) for moving numbers of molecules around -- complex systems of reactions can be constructed and all the different deltas summed up, and applied in a step-wise fashion. At bottom, it is really very simple, involving massive simplifications that nevertheless seem sufficient to capture the relevant phenomena. In effect, the all-important rate constants absorb and compensate for all of those simplifications.
Kinetikit
This code is based on Kinetikit by Upinder S. Bhalla and implemented in the Genesis simulation tool. See:
- Bhalla, U. S., & Iyengar, R. (1999). Emergent Properties of Networks of Biological Signaling Pathways. Science. https://doi.org/10.1126/science.283.5400.381
See the axon urakubo model of LTP / LTD for a re-implementation of the Urakubo et al, 2008 model using this code.
- Urakubo, H., Honda, M., Froemke, R. C., & Kuroda, S. (2008). Requirement of an allosteric kinetics of NMDA receptors for spike timing-dependent plasticity. The Journal of Neuroscience, 28(13), 3310–3323. http://www.ncbi.nlm.nih.gov/pubmed/18367598
Here's another paper that Urakubo builds upon:
- Dupont, G., Houart, G., & De Koninck, P. (2003). Sensitivity of CaM kinase II to the frequency of Ca2+ oscillations: A simple model. Cell Calcium, 34(6), 485–497. https://doi.org/10.1016/S0143-4160(03)00152-0
Reactions
React models a basic chemical reaction:
Kf
A + B --> AB
<-- Kb
where Kf is the forward and Kb is the backward time constant. The source Kf and Kb constants are in terms of concentrations μM-1 and sec-1 but calculations take place using N's, and the forward direction has two factors while reverse only has one, so a corrective volume factor needs to be divided out to set the actual forward factor.
Enzymes
Enz models an enzyme-catalyzed reaction based on the Michaelis-Menten kinetics that transforms S = substrate into P product via SE bound C complex:
K1 K3
S + E --> C(SE) ---> P + E
<-- K2
S = substrate, E = enzyme, C = SE complex, P = product. The source K constants are in terms of concentrations μM-1 and sec-1 but calculations take place using N's, and the forward direction has two factors while reverse only has one, so a corrective volume factor needs to be divided out to set the actual forward factor.
Documentation
¶
Index ¶
Constants ¶
This section is empty.
Variables ¶
var IntegrationDt = 5.0e-5
IntegrationDt is the time step of integration for Urakubo et al, 2008: uses 5e-5, 2e-4 is barely stable, 5e-4 is not The AC1act dynamics in particular are not stable due to large ATP, AMP numbers
Functions ¶
Types ¶
type Buffer ¶
type Buffer struct {
// rate of buffering (akin to permeability / conductance of a channel)
K float64 `desc:"rate of buffering (akin to permeability / conductance of a channel)"`
// buffer target concentration -- drives delta relative to this
Target float64 `desc:"buffer target concentration -- drives delta relative to this"`
}
Buffer provides a soft buffering driving deltas relative to a target N which can be set by concentration and volume.
func (*Buffer) SetTargVol ¶
type Diffuse ¶
type Diffuse struct {
// A -> B forward diffusion rate constant, sec-1
Kf float64 `desc:"A -> B forward diffusion rate constant, sec-1"`
// B -> A backward diffusion rate constant, sec-1
Kb float64 `desc:"B -> A backward diffusion rate constant, sec-1"`
}
Diffuse models diffusion between two compartments A and B as a function of concentration in each and potentially asymmetric rate constants: A Kf -> B and B Kb -> A computes the difference between each direction and applies to each
type Enz ¶
type Enz struct {
// S+E forward rate constant, in μM-1 msec-1
K1 float64 `desc:"S+E forward rate constant, in μM-1 msec-1"`
// SE backward rate constant, in μM-1 msec-1
K2 float64 `desc:"SE backward rate constant, in μM-1 msec-1"`
// SE -> P + E catalyzed rate constant, in μM-1 msec-1
K3 float64 `desc:"SE -> P + E catalyzed rate constant, in μM-1 msec-1"`
// Michaelis constant = (K2 + K3) / K1
Km float64 `inactive:"+" desc:"Michaelis constant = (K2 + K3) / K1"`
}
Enz models an enzyme-catalyzed reaction based on the Michaelis-Menten kinetics that transforms S = substrate into P product via SE-bound C complex
K1 K3
S + E --> C(SE) ---> P + E
<-- K2
S = substrate, E = enzyme, C = SE complex, P = product The source K constants are in terms of concentrations μM-1 and sec-1 but calculations take place using N's, and the forward direction has two factors while reverse only has one, so a corrective volume factor needs to be divided out to set the actual forward factor.
func (*Enz) SetKmVol ¶
SetKmVol sets time constants in seconds using Km, K2, K3 dividing forward K1 by volume to compensate for 2 volume-based concentrations occurring in forward component (s * e), vs just 1 in back
type EnzRate ¶ added in v1.1.47
type EnzRate struct {
// S+E forward rate constant, in μM-1 msec-1
K1 float64 `desc:"S+E forward rate constant, in μM-1 msec-1"`
// SE backward rate constant, in μM-1 msec-1
K2 float64 `desc:"SE backward rate constant, in μM-1 msec-1"`
// SE -> P + E catalyzed rate constant, in μM-1 msec-1
K3 float64 `desc:"SE -> P + E catalyzed rate constant, in μM-1 msec-1"`
// Michaelis constant = (K2 + K3) / K1 -- goes into the rate
Km float64 `inactive:"+" desc:"Michaelis constant = (K2 + K3) / K1 -- goes into the rate"`
}
EnzRate models an enzyme-catalyzed reaction based on the Michaelis-Menten kinetics that transforms S = substrate into P product via SE bound C complex
K1 K3
S + E --> C(SE) ---> P + E
<-- K2
S = substrate, E = enzyme, C = SE complex, P = product This version does NOT consume the E enzyme or directly use the C complex as an accumulated factor: instead it directly computes an overall rate for the end-to-end S <-> P reaction based on the K constants: rate = S * E * K3 / (S + Km) This amount is added to the P and subtracted from the S, and recorded in the C complex variable as rate / K3 -- it is just directly set. In some situations this C variable can be used for other things. The source K constants are in terms of concentrations μM-1 and sec-1 but calculations take place using N's, and the forward direction has two factors while reverse only has one, so a corrective volume factor needs to be divided out to set the actual forward factor.
func (*EnzRate) SetKmVol ¶ added in v1.1.47
SetKmVol sets time constants in seconds using Km, K2, K3 dividing forward K1 by volume to compensate for 2 volume-based concentrations occurring in forward component (s * e), vs just 1 in back
func (*EnzRate) Step ¶ added in v1.1.47
Step computes delta values based on current S, E values, setting dS, dP and C = rate
type Paramer ¶ added in v1.1.48
type Paramer interface {
// Defaults sets default parameters
Defaults()
// Step computes deltas d based on current values c
Step(c, d Paramer)
}
The Paramer interface defines functions implemented for Params structures, containing chem React, Enz, etc functions. This interface is largely for documentation purposes.
type React ¶
type React struct {
// forward rate constant for N / sec assuming 2 forward factors
Kf float64 `desc:"forward rate constant for N / sec assuming 2 forward factors"`
// backward rate constant for N / sec assuming 1 backward factor
Kb float64 `desc:"backward rate constant for N / sec assuming 1 backward factor"`
}
React models a basic chemical reaction:
Kf
A + B --> AB
<-- Kb
where Kf is the forward and Kb is the backward time constant. The source Kf and Kb constants are in terms of concentrations μM-1 and sec-1 but calculations take place using N's, and the forward direction has two factors while reverse only has one, so a corrective volume factor needs to be divided out to set the actual forward factor.
func (*React) SetVol ¶
SetVol sets reaction forward / backward time constants in seconds, dividing forward Kf by volume to compensate for 2 volume-based concentrations occurring in forward component, vs just 1 in back
type SimpleEnz ¶
type SimpleEnz struct {
// S->P forward rate constant, in μM-1 msec-1
Kf float64 `desc:"S->P forward rate constant, in μM-1 msec-1"`
}
SimpleEnz models a simple enzyme-catalyzed reaction that transforms S = substrate into P product via E which is not consumed assuming there is much more E than S and P -- E effectively acts as a rate constant multiplier
Kf*E
S ----> P
S = substrate, E = enzyme, P = product, Kf is the rate of the reaction
func (*SimpleEnz) SetVol ¶ added in v1.1.47
SetVol sets reaction forward / backward time constants in seconds, dividing forward Kf by volume to compensate for 2 volume-based concentrations occurring in forward component, vs just 1 in back
type Stater ¶ added in v1.1.48
type Stater interface {
// Init Initializes the state to starting default values (concentrations)
Init()
// Zero sets all state variables to zero -- called for deltas after integration
Zero()
// Integrate is called with the deltas -- each state value calls Integrate()
// to update from deltas.
Integrate(d Stater)
// Log records relevant state variables in given table at given row
Log(dt *etable.Table, row int)
// ConfigLog configures the table Schema to add column(s) for what is logged
ConfigLog(sch *etable.Schema)
}
The Stater interface defines the functions implemented for State structures containing chem state variables. This interface is largely for documentation purposes.
Source Files