Dynamics

Dynamics#

Schema against which LEMS based on these should be valid: LEMS_v0.7.6.xsd. Generated on 18/06/24 from this commit. Please file any issues or questions at the issue tracker here.

Dynamics#

Specifies the dynamical behavior of components build from this ComponentType. Note that all variables in a Dynamics definition are private. If other components need access to them, then the definition should explicitly link them to an Exposure defined in the component class

can contain these elements

supers	Super
derivedVariables	DerivedVariable
conditionalDerivedVariables	ConditionalDerivedVariable
stateVariables	StateVariable
timeDerivatives	TimeDerivative
kineticSchemes	KineticScheme
onStarts	OnStart
onEvents	OnEvent
onConditions	OnCondition
stateScalarFields	StateScalarField
derivedScalarFields	DerivedScalarField
derivedPunctateFields	DerivedPunctateField
regimes	Regime

Schema

<xs:complexType name="Dynamics">
  <xs:sequence>
    <xs:element name="StateVariable" type="StateVariable" minOccurs="0" maxOccurs="unbounded"/>
    <xs:element name="DerivedVariable" type="DerivedVariable" minOccurs="0" maxOccurs="unbounded"/>
    <xs:element name="ConditionalDerivedVariable" type="ConditionalDerivedVariable" minOccurs="0" maxOccurs="unbounded"/>
    <xs:element name="TimeDerivative" type="TimeDerivative" minOccurs="0" maxOccurs="unbounded"/>
    <xs:element name="OnStart" type="OnStart" minOccurs="0" maxOccurs="1"/>
    <xs:element name="OnEvent" type="OnEvent" minOccurs="0" maxOccurs="unbounded"/>
    <xs:element name="OnCondition" type="OnCondition" minOccurs="0" maxOccurs="unbounded"/>
    <xs:element name="Regime" type="Regime" minOccurs="0" maxOccurs="unbounded"/>
    <xs:element name="KineticScheme" type="KineticScheme" minOccurs="0" maxOccurs="1"/>
  </xs:sequence>
</xs:complexType>

Usage: XML

<Dynamics>
    <StateVariable name="t" dimension="time"/>
</Dynamics>

<Dynamics>
    <StateVariable name="x" dimension="none"/>
    <DerivedVariable name="ex" dimension="none" value="exp(x)"/>
    <DerivedVariable name="q" dimension="none" value="ex / (1 + ex)"/>
    <DerivedVariable name="rf" dimension="per_time" select="Forward/r"/>
    <DerivedVariable name="rr" dimension="per_time" select="Reverse/r"/>
    <TimeDerivative variable="x" value="(1 + ex)^2 / ex * (rf * (1 - q) - rr * q)"/>
    <DerivedVariable name="fcond" dimension="none" exposure="fcond" value="q^power"/>
</Dynamics>

<Dynamics>
    <StateVariable name="q" dimension="none"/>
    <DerivedVariable dimension="per_time" name="rf" select="Forward/r"/>
    <DerivedVariable dimension="per_time" name="rr" select="Reverse/r"/>
    <TimeDerivative variable="q" value="rf * (1 - q) - rr * q"/>
    <DerivedVariable name="fcond" dimension="none" exposure="fcond" value="q^power"/>
</Dynamics>

<Dynamics>
    <OnStart>
        <StateAssignment variable="v" value="v0"/>
    </OnStart>
    <DerivedVariable name="totcurrent" dimension="current" select="populations[*]/current" reduce="add"/>
    <StateVariable name="v" exposure="v" dimension="voltage"/>
    <TimeDerivative variable="v" value="(totcurrent + injection) / capacitance"/>
</Dynamics>

<Dynamics>
    <StateVariable name="v" exposure="v" dimension="voltage"/>
    <TimeDerivative variable="v" value="leakConductance * (leakReversal - v) / capacitance"/>
    <OnEvent port="spikes-in">
        <StateAssignment variable="v" value="v + deltaV"/>
    </OnEvent>
</Dynamics>

StateVariable#

Specifies a state variable that stores values that define the state of the system at a point in time. The dynamics of state variables may be defined as Ordinary Differential Equations (ODEs) using the TimeDerivative entity. They can also be discontinuously modified using elements in Dynamics such as OnStarts, OnEvents, and OnConditions. StateVariables may be linked to exposures.

Properties

name	String	Name of the state variable
dimension	String	The dimension, or ‘none’. This should be the name of an already defined dimension element
exposure	String	If this variable is to be accessed from outside, it should be linked to an Exposure that is defined in the ComponentType.
description	String	An optional description of the state variable

Schema

<xs:complexType name="StateVariable">
  <xs:attribute name="name" type="xs:string" use="required"/>
  <xs:attribute name="dimension" type="xs:string" use="optional" default="none"/>
  <xs:attribute name="exposure" type="xs:string" use="optional"/>
  <xs:attribute name="description" type="xs:string" use="optional"/>
</xs:complexType>

Usage: XML

<StateVariable name="t" dimension="time"/>

<StateVariable name="v" exposure="v" dimension="voltage"/>

<StateVariable name="tsince" exposure="tsince" dimension="time"/>

<StateVariable name="tlast" dimension="time"/>

<StateVariable name="q" dimension="none"/>

StateAssignment#

Has ‘variable’ and ‘value’ fields

Properties

variable	String	The name of the variable
value	String	A string defining the value of the element

Schema

<xs:complexType name="StateAssignment">
  <xs:attribute name="variable" type="xs:string" use="required"/>
  <xs:attribute name="value" type="xs:string" use="required"/>
</xs:complexType>

Usage: XML

<StateAssignment variable="v" value="v + deltaV"/>

<StateAssignment variable="tsince" value="0"/>

<StateAssignment variable="tlast" value="t"/>

<StateAssignment variable="v" value="v0"/>

<StateAssignment variable="geff" value="0"/>

TimeDerivative#

First order differential equations, functions of StateVariables and Parameters, for how StateVariables change with time. Has a variable and a value. The value is the rate of change of the variable.

Properties

variable	String	The name of the variable
value	String	A string defining the value of the element

Schema

<xs:complexType name="TimeDerivative">
  <xs:attribute name="variable" type="xs:string" use="required"/>
  <xs:attribute name="value" type="xs:string" use="required"/>
</xs:complexType>

Usage: XML

<TimeDerivative variable="v" value="leakConductance * (leakReversal - v) / capacitance"/>

<TimeDerivative variable="tsince" value="1"/>

<TimeDerivative variable="q" value="rf * (1 - q) - rr * q"/>

<TimeDerivative variable="x" value="(1 + ex)^2 / ex * (rf * (1 - q) - rr * q)"/>

<TimeDerivative variable="v" value="(totcurrent + injection) / capacitance"/>

DerivedVariable#

A quantity that depends algebraically on other quantities in the model. The ‘value’ field can be set to a mathematical expression, or the ‘select’ field to a path expression. If the path expression produces multiple matches, then the ‘reduce’ field says how these are reduced to a single value by taking the sum or product.

Properties

name	String	Name of the derived variable
select	String	A path to the variable that supplies the value. Note that to select a variable from another component, the variable must be marked as an Exposure. Exactly one of ‘select’ and ‘value’ is required
dimension	String	The dimension, or ‘none’. This should be the name of an already defined dimension element
description	String	An optional description of the derived variable
reduce	String	Either ‘add’ or ‘multiply’. This applies if ther are multiple matches to the path or if ‘required’ is false. In the latter case, for multiply mode, multiplicative expressions in this variable behave as if the term was absent. Additive expressions generate an error. Conversely, if set to ‘add’ then additive expressions behave as if it was not there and multiplicative ones generateand error.
exposure	String
required	boolean	Set to true if it OK for this variable to be absent. See ‘reduce’ for what happens in this case
value	String	A string defining the value of the element

Schema

<xs:complexType name="DerivedVariable">
  <xs:attribute name="name" type="xs:string" use="required"/>
  <xs:attribute name="dimension" type="xs:string" use="optional" default="none"/>
  <xs:attribute name="exposure" type="xs:string" use="optional"/>
  <xs:attribute name="description" type="xs:string" use="optional"/>
  <xs:attribute name="select" type="xs:string" use="optional"/>
  <xs:attribute name="value" type="xs:string" use="optional"/>
  <xs:attribute name="reduce" type="xs:string" use="optional"/>
  <xs:attribute name="required" type="xs:string" use="optional"/>
</xs:complexType>

Usage: XML

<DerivedVariable name="tsince" dimension="time" exposure="tsince" value="t - tlast"/>

<DerivedVariable name="r" dimension="per_time" exposure="r" value="rate * exp((v - midpoint)/scale)"/>

<DerivedVariable name="r" dimension="per_time" exposure="r" value="rate / (1 + exp( -(v - midpoint)/scale))"/>

<DerivedVariable name="x" dimension="none" value="(v - midpoint) / scale"/>

<DerivedVariable name="r" dimension="per_time" exposure="r" value="rate * x / (1 - exp(-x))"/>

OnStart#

can contain these elements

stateAssignments	StateAssignment
eventOuts	EventOut
transitions	Transition

Schema

<xs:complexType name="OnStart">
  <xs:sequence>
    <xs:element name="StateAssignment" type="StateAssignment" minOccurs="1" maxOccurs="unbounded"/>
  </xs:sequence>
</xs:complexType>

Usage: XML

<OnStart>
    <StateAssignment variable="v" value="v0"/>
</OnStart>

<OnStart>
    <StateAssignment variable="geff" value="0"/>
</OnStart>

<OnStart>
    <StateAssignment variable="v" value="v0"/>
</OnStart>

<OnStart>
    <StateAssignment variable="v" value="v0"/>
</OnStart>

<OnStart>
    <StateAssignment variable="v" value="v0"/>
</OnStart>

OnCondition#

can contain these elements

stateAssignments	StateAssignment
eventOuts	EventOut
transitions	Transition

Schema

<xs:complexType name="OnCondition">
  <xs:sequence>
    <xs:element name="StateAssignment" type="StateAssignment" minOccurs="0" maxOccurs="unbounded"/>
    <xs:element name="EventOut" type="EventOut" minOccurs="0" maxOccurs="unbounded"/>
    <xs:element name="Transition" type="Transition" minOccurs="0" maxOccurs="1"/>
  </xs:sequence>
  <xs:attribute name="test" type="xs:string" use="required"/>
</xs:complexType>

Usage: XML

<OnCondition test="tsince .gt. period">
    <StateAssignment variable="tsince" value="0"/>
    <EventOut port="a"/>
</OnCondition>

<OnCondition test="t - tlast .gt. period">
    <StateAssignment variable="tlast" value="t"/>
    <EventOut port="a"/>
</OnCondition>

<OnCondition test="v .gt. threshold">
    <EventOut port="out"/>
    <Transition regime="refr"/>
</OnCondition>

<OnCondition test="t .gt. tin + refractoryPeriod">
    <Transition regime="int"/>
</OnCondition>

<OnCondition test="tsince .gt. period">
    <StateAssignment variable="tsince" value="0"/>
    <EventOut port="a"/>
</OnCondition>

OnEvent#

Event handler block

Properties

port

String

the port to listen on

can contain these elements

stateAssignments	StateAssignment
eventOuts	EventOut
transitions	Transition

Schema

<xs:complexType name="OnEvent">
  <xs:sequence>
    <xs:element name="StateAssignment" type="StateAssignment" minOccurs="0" maxOccurs="unbounded"/>
    <xs:element name="EventOut" type="EventOut" minOccurs="0" maxOccurs="unbounded"/>
  </xs:sequence>
  <xs:attribute name="port" type="xs:string" use="required"/>
</xs:complexType>

Usage: XML

<OnEvent port="spikes-in">
    <StateAssignment variable="v" value="v + deltaV"/>
</OnEvent>

<OnEvent port="in">
    <StateAssignment variable="geff" value="geff + deltaG"/>
</OnEvent>

<OnEvent port="in">
    <StateAssignment variable="v" value="v + deltaV"/>
</OnEvent>

<OnEvent port="spikes-in">
    <StateAssignment variable="v" value="v + deltaV"/>
</OnEvent>

EventOut#

Schema

<xs:complexType name="EventOut">
  <xs:attribute name="port" type="xs:string" use="required"/>
</xs:complexType>

Usage: XML

<EventOut port="a"/>

<EventOut port="a"/>

<EventOut port="out"/>

<EventOut port="a"/>

<EventOut port="a"/>

KineticScheme#

Allows the specification of systems that can be in one of a small number of states at any time with probabilistic transitions between states. This includes continuous time Markov processes as are used for stochastic models of ion channels. A kinetic scheme does not itself introduce any new elements or state variables. It is rather a way of connecting quantities in existing components by saying that quantities in the edge elements should be interpreted as transition rates among quantities in the node elements.

Properties

name	String	Name of kinetic scheme
nodes	String	Source of notes for scheme
edges	String	The element that provides the transitions for the scheme
stateVariable	String	Name of state variable in state elements
edgeSource	String	The name of the attribute in the rate element that defines the source of the transition
edgeTarget	String	Attribute tha defines the target
forwardRate	String	Name of forward rate exposure
reverseRate	String	Name of reverse rate exposure

Schema

<xs:complexType name="KineticScheme">
  <xs:attribute name="name" type="xs:string" use="required"/>
  <xs:attribute name="nodes" type="xs:string" use="required"/>
  <xs:attribute name="stateVariable" type="xs:string" use="required"/>
  <xs:attribute name="edges" type="xs:string" use="required"/>
  <xs:attribute name="edgeSource" type="xs:string" use="required"/>
  <xs:attribute name="edgeTarget" type="xs:string" use="required"/>
  <xs:attribute name="forwardRate" type="xs:string" use="required"/>
  <xs:attribute name="reverseRate" type="xs:string" use="required"/>
</xs:complexType>

Usage: XML

<KineticScheme name="ks" nodes="states" stateVariable="occupancy" edges="transitions" edgeSource="from" edgeTarget="to" forwardRate="rf" reverseRate="rr"/>

<KineticScheme name="ks" nodes="states" stateVariable="occupancy" edges="transitions" edgeSource="from" edgeTarget="to" forwardRate="rf" reverseRate="rr" dependency="v" step="deltaV"/>

Regime#

Allows the dynamics of a ComponentType to be expressed via a finite state machine. Each regime has its internal dynamics, and conditions on which transitions between regimes occur are specified using the OnCondition element

Properties

name	String	The name of the regime
initial	String	‘True’ if this is the initial regime of the system

can contain these elements

derivedVariables	DerivedVariable
stateVariables	StateVariable
timeDerivatives	TimeDerivative
onStarts	OnStart
onEntrys	OnEntry
onEvents	OnEvent
onConditions	OnCondition
requiredVars	lemsschema:requiredvar_

Schema

<xs:complexType name="Regime">
  <xs:sequence>
    <xs:element name="TimeDerivative" type="TimeDerivative" minOccurs="0" maxOccurs="unbounded"/>
    <xs:element name="OnEntry" type="OnEntry" minOccurs="0" maxOccurs="1"/>
    <xs:element name="OnCondition" type="OnCondition" minOccurs="0" maxOccurs="unbounded"/>
  </xs:sequence>
  <xs:attribute name="name" type="xs:string" use="required"/>
  <xs:attribute name="initial" type="TrueOrFalse" use="optional"/>
</xs:complexType>

Usage: XML

<Regime name="int" initial="true">
    <TimeDerivative variable="v" value="(current + gleak * (vleak - v)) / capacitance"/>
    <OnCondition test="v .gt. threshold">
        <EventOut port="out"/>
        <Transition regime="refr"/>
    </OnCondition>
    <OnEvent port="in">
        <StateAssignment variable="v" value="v + deltaV"/>
    </OnEvent>
</Regime>

<Regime name="refr">
    <OnEntry>
        <StateAssignment variable="tin" value="t"/>
        <StateAssignment variable="v" value="vreset"/>
    </OnEntry>
    <OnCondition test="t .gt. tin + refractoryPeriod">
        <Transition regime="int"/>
    </OnCondition>
</Regime>

OnEntry#

can contain these elements

stateAssignments	StateAssignment
eventOuts	EventOut
transitions	Transition

Schema

<xs:complexType name="OnEntry">
  <xs:sequence>
    <xs:element name="StateAssignment" type="StateAssignment" minOccurs="1" maxOccurs="unbounded"/>
  </xs:sequence>
</xs:complexType>

Usage: XML

<OnEntry>
    <StateAssignment variable="tin" value="t"/>
    <StateAssignment variable="v" value="vreset"/>
</OnEntry>

Transition#

Schema

<xs:complexType name="Transition">
  <xs:attribute name="regime" type="xs:string" use="required"/>
</xs:complexType>

Usage: XML

<Transition regime="int"/>

<Transition regime="refr"/>

Super#

ConditionalDerivedVariable#

Properties

name	String
dimension	String
exposure	String

can contain these elements

cases

Case

Schema

<xs:complexType name="ConditionalDerivedVariable">
  <xs:sequence>
    <xs:element name="Case" type="Case" minOccurs="1" maxOccurs="unbounded"/>
  </xs:sequence>
  <xs:attribute name="name" type="xs:string" use="required"/>
  <xs:attribute name="dimension" type="xs:string" use="optional" default="none"/>
  <xs:attribute name="exposure" type="xs:string" use="optional"/>
</xs:complexType>

Case#

Properties

value

String

A string defining the value of the element

Schema

<xs:complexType name="Case">
  <xs:attribute name="condition" type="xs:string" use="optional"/>
  <xs:attribute name="value" type="xs:string" use="required"/>
</xs:complexType>

Equilibrium#

can contain these elements

derivedVariables

DerivedVariable

Dynamics

Contents

Dynamics#

Dynamics#

StateVariable#

StateAssignment#

TimeDerivative#

DerivedVariable#

OnStart#

OnCondition#

OnEvent#

EventOut#

KineticScheme#

Regime#

OnEntry#

Transition#

Super#

ConditionalDerivedVariable#

Case#

Equilibrium#

StateScalarField#

DerivedScalarField#

DerivedPunctateField#