astrocyte_lr_1994.h

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/*
 *  astrocyte_lr_1994.h
 *
 *  This file is part of NEST.
 *
 *  Copyright (C) 2004 The NEST Initiative
 *
 *  NEST is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  NEST is distributed in the hope that it will be useful,
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 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
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 *  You should have received a copy of the GNU General Public License
 *  along with NEST.  If not, see <http://www.gnu.org/licenses/>.
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#ifndef ASTROCYTE_LR_1994_H
#define ASTROCYTE_LR_1994_H
 
#include "config.h"
 
#ifdef HAVE_GSL
 
// C includes:
#include <gsl/gsl_errno.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_odeiv.h>
#include <gsl/gsl_sf_exp.h>
 
// Includes from nestkernel:
#include "archiving_node.h"
#include "connection.h"
#include "event.h"
#include "nest_types.h"
#include "node.h"
#include "recordables_map.h"
#include "ring_buffer.h"
#include "universal_data_logger.h"
 
namespace nest
{
 
extern "C" int astrocyte_lr_1994_dynamics( double, const double*, double*, void* );
 
/* BeginUserDocs: astrocyte
 
Short description
+++++++++++++++++
 
An astrocyte model based on Li & Rinzel (1994)
 
Description
+++++++++++
 
``astrocyte_lr_1994`` is a model of astrocytic calcium dynamics. The model was
first proposed by Li & Rinzel (1994) :footcite:p:`Li1994` and it is based on earlier work of De
Young & Kaiser (1992) :footcite:p:`DeYoung1992`. The input and output of the model are implemented
according to Nadkarni & Jung (2003) :footcite:p:`Nadkarni2003`.
 
The model has three dynamic state variables: the concentration of inositol
1,4,5-trisphosphate in the astrocyte (:math:`\mathrm{[IP3]}`), the calcium
concentration in the astrocytic cytosol (:math:`\mathrm{[Ca^{2+}]}`), and the
fraction of IP3 receptors on the astrocytic endoplasmic reticulum (ER) that are
not yet inactivated by calcium (:math:`h_\mathrm{IP3R}`).
 
In this model, excitatory synaptic inputs to the astrocyte trigger IP3
generation and change in calcium dynamics in the astrocyte. This might induce an
astrocytic output in the form of a slow inward current (SIC), which is dependent
on its calcium dynamics, to its target neurons. The input and output are based
on the equations in :footcite:p:`Nadkarni2003` but with adaptations, as described in the following.
 
Spike input
-----------
 
The astrocyte receives inputs from excitatory (glutamatergic)
synapses. The synaptic inputs directly affect IP3 concentration according to the
following equation:
 
.. math::
 
 \frac{d[\mathrm{IP3}]}{dt} =
 \frac{[\mathrm{IP3}]_0 - [\mathrm{IP3}]}{\tau_\mathrm{IP3}} + \Delta_\mathrm{IP3} \cdot J_\mathrm{syn}(t)
 
In the absence of inputs, :math:`\mathrm{[IP3]}` decays to its baseline value
(:math:`[\mathrm{IP3}]_0`) with the time constant (:math:`\tau_\mathrm{IP3}`). Each time when an
astrocyte receives an excitatory synaptic input, it triggers an instantaneous
increase of :math:`\mathrm{[IP3]}`. In this implementation, the inputs are spike events
sent from neurons or generators. The summed synaptic weight the astrocyte receives at time
:math:`t` is given by :math:`J_\mathrm{syn}(t)`. The parameter
:math:`\Delta_\mathrm{IP3}` scales the impact of synaptic inputs on the
IP3 dynamics.
 
Calcium current input
---------------------
 
In this implementation, a current input to the astrocyte is directly
added to its cytosolic calcium concentration. Generators that send out currents
can be connected to astrocytes to directly generate fluctuations in cytosolic
calcium:
 
.. math::
 
 \frac{d[\mathrm{Ca^{2+}}]}{dt} =
 J_\mathrm{channel} - J_\mathrm{pump} + J_\mathrm{leak} + J_\mathrm{noise}
 
Here, :math:`\mathrm{[Ca^{2+}]}` is the cytosolic calcium concentration, and
:math:`J_\mathrm{noise}` is the current input. :math:`J_\mathrm{channel}`,
:math:`J_\mathrm{pump}`, :math:`J_\mathrm{leak}` are the calcium fluxes defined
as in :footcite:p:`Nadkarni2003`.
 
Output
------
 
If the astrocyte receives excitatory synaptic inputs, it might
output SIC to its target neurons. This current depends on the cytosolic
calcium concentration. This dependency is modeled according to the expressions
first proposed in [3]:
 
.. math::
 
 I_\mathrm{SIC} =  \mathrm{SIC_{scale}} \cdot \mathrm{H}\left(\mathrm{ln}(y)\right) \cdot \mathrm{ln}(y)
 
where
 
.. math::
 
 y = \left( \mathrm{[Ca^{2+}]} - \mathrm{SIC_{th}} \right)/\mathrm{nM}
 
When the cytosolic calcium concentration of the astrocyte exceeds the threshold
value (:math:`\mathrm{SIC_{th}}`), a SIC output (:math:`I_\mathrm{SIC}`) is
generated. This thresholding is modeled as a Heaviside function
(:math:`\mathrm{H(\cdot)}`). In this implementation, the SIC threshold
:math:`\mathrm{SIC_{th}}` as well as the scaling constant
:math:`\mathrm{SIC_{scale}}` are treated as model parameters that can be set
together with other parameters. Nadkarni & Jung (2003) :footcite:p:`Nadkarni2003` proposed values for
these parameters by fitting the equation for SIC to an experimental data set.
 
The output is implemented as SICEvent sent from the astrocyte to its target
neurons through the ``sic_connection``.
 
For the reference implementation of this model, see the
`astrocyte_model_implementation <../model_details/astrocyte_model_implementation.ipynb>`_ notebook.
 
See also :footcite:p:`Li1994`, :footcite:p:`DeYoung1992`, :footcite:p:`Nadkarni2003`.
 
Parameters
++++++++++
 
The following parameters can be set in the status Dictionary.
 
======== ========= =============================================================
**Dynamic state variables**
--------------------------------------------------------------------------------
IP3      µM        Inositol 1,4,5-trisphosphate concentration in the astrocytic
                   cytosol
Ca_astro µM        Calcium concentration in the astrocytic cytosol
h_IP3R   unitless  Fraction of IP3 receptors on the astrocytic ER that are not
                   yet inactivated by calcium
======== ========= =============================================================
 
=============== ========= =====================================================
**Parameters**
-------------------------------------------------------------------------------
Ca_tot          µM        Total free astrocytic calcium concentration in terms
                          of cytosolic volume
IP3_0           µM        Baseline value of astrocytic IP3 concentration
Kd_IP3_1        µM        First astrocytic IP3R dissociation constant of IP3
Kd_IP3_2        µM        Second astrocytic IP3R dissociation constant of IP3
Kd_act          µM        Astrocytic IP3R dissociation constant of calcium
                          (activation)
Kd_inh          µM        Astrocytic IP3R dissociation constant of calcium
                          (inhibition)
Km_SERCA        µM        Half-activation constant of astrocytic SERCA pump
SIC_scale       unitless  Parameter determining the scale of astrocytic SIC
                          output
SIC_th          µM        Threshold that determines the minimal level of
                          astrocytic cytosolic calcium sufficient to induce
                          SIC
delta_IP3       µM        Parameter determining the increase in astrocytic IP3
                          concentration induced by synaptic input
k_IP3R          1/(µM*ms) Astrocytic IP3R binding constant for calcium
                          inhibition
rate_IP3R       1/ms      Maximum rate of calcium release via astrocytic IP3R
rate_L          1/ms      Rate constant of calcium leak from astrocytic ER to
                          cytosol
rate_SERCA      µM/ms     Maximum rate of calcium uptake by astrocytic SERCA
                          pump
ratio_ER_cyt    unitless  Ratio between astrocytic ER and cytosol volumes
tau_IP3         ms        Time constant of the exponential decay of astrocytic
                          IP3
=============== ========= =====================================================
 
References
++++++++++
 
.. footbibliography::
 
Sends
+++++
 
SICEvent
 
Receives
++++++++
 
SpikeEvent, DataLoggingRequest
 
See also
++++++++
 
aeif_cond_alpha_astro, sic_connection
 
Examples using this model
+++++++++++++++++++++++++
 
.. listexamples:: astrocyte_lr_1994
 
EndUserDocs */
 
void register_astrocyte_lr_1994( const std::string& name );
 
class astrocyte_lr_1994 : public Node
{
 
public:
  astrocyte_lr_1994();
  astrocyte_lr_1994( const astrocyte_lr_1994& );
  ~astrocyte_lr_1994() override;
 
  using Node::handle;
  using Node::handles_test_event;
  using Node::sends_secondary_event;
 
 
  void handle( SpikeEvent& ) override;
  void handle( CurrentEvent& ) override;
  void handle( DataLoggingRequest& ) override;
 
  size_t handles_test_event( SpikeEvent&, size_t ) override;
  size_t handles_test_event( CurrentEvent&, size_t ) override;
  size_t handles_test_event( DataLoggingRequest&, size_t ) override;
 
  void
  sends_secondary_event( SICEvent& ) override
  {
  }
 
  void get_status( Dictionary& ) const override;
  void set_status( const Dictionary& ) override;
 
private:
  void init_buffers_() override;
  void pre_run_hook() override;
 
  // bool update_( Time const&, const long, const long, const bool );
 
  void update( Time const&, const long, const long ) override;
 
  // END Boilerplate function declarations ----------------------------
 
  // Friends --------------------------------------------------------
 
  // make dynamics function quasi-member
  friend int astrocyte_lr_1994_dynamics( double, const double*, double*, void* );
 
  // The next two classes need to be friend to access the State_ class/member
  friend class RecordablesMap< astrocyte_lr_1994 >;
  friend class UniversalDataLogger< astrocyte_lr_1994 >;
 
  // ----------------------------------------------------------------
 
  struct Parameters_
  {
    // parameters based on Nadkarni & Jung (2003)
    double Ca_tot_;     
    double IP3_0_;      
    double Kd_IP3_1_;   
    double Kd_IP3_2_;   
    double Kd_act_;     
    double Kd_inh_;     
    double Km_SERCA_;   
    double SIC_scale_;  
    double SIC_th_;  
    double delta_IP3_;     
    double k_IP3R_;        
    double rate_IP3R_;     
    double rate_L_;        
    double rate_SERCA_;    
    double ratio_ER_cyt_;  
    double tau_IP3_;       
 
    Parameters_();  
 
    void get( Dictionary& ) const;              
    void set( const Dictionary&, Node* node );  
  };
 
public:
  // ----------------------------------------------------------------
 
  struct State_
  {
 
    enum StateVecElems
    {
      IP3 = 0,
      Ca_astro,  // 1
      h_IP3R,    // 2
      STATE_VEC_SIZE
    };
 
    double y_[ STATE_VEC_SIZE ];
 
    State_( const Parameters_& );  
    State_( const State_& );
 
    State_& operator=( const State_& );
 
    void get( Dictionary& ) const;
    void set( const Dictionary&, const Parameters_&, Node* );
  };
 
  // ----------------------------------------------------------------
 
  struct Buffers_
  {
    Buffers_( astrocyte_lr_1994& );                   
    Buffers_( const Buffers_&, astrocyte_lr_1994& );  
 
    UniversalDataLogger< astrocyte_lr_1994 > logger_;
 
    RingBuffer spike_exc_;
    RingBuffer currents_;
 
    gsl_odeiv_step* s_;     
    gsl_odeiv_control* c_;  
    gsl_odeiv_evolve* e_;   
    gsl_odeiv_system sys_;  
 
    // Since IntergrationStep_ is initialized with step_, and the resolution
    // cannot change after nodes have been created, it is safe to place both
    // here.
    double step_;             
    double IntegrationStep_;  
 
    double J_noise_;
 
    // values to be sent by SIC event
    std::vector< double > sic_values;
  };
 
  // ----------------------------------------------------------------
 
  // Access functions for UniversalDataLogger -------------------------------
 
  template < State_::StateVecElems elem >
  double
  get_y_elem_() const
  {
    return S_.y_[ elem ];
  }
 
  // ----------------------------------------------------------------
 
  Parameters_ P_;
  State_ S_;
  Buffers_ B_;
 
  static RecordablesMap< astrocyte_lr_1994 > recordablesMap_;
};
 
 
inline size_t
astrocyte_lr_1994::handles_test_event( SpikeEvent&, size_t receptor_type )
{
  if ( receptor_type != 0 )
  {
    throw UnknownReceptorType( receptor_type, get_name() );
  }
  return 0;
}
 
inline size_t
astrocyte_lr_1994::handles_test_event( CurrentEvent&, size_t receptor_type )
{
  if ( receptor_type != 0 )
  {
    throw UnknownReceptorType( receptor_type, get_name() );
  }
  return 0;
}
 
inline size_t
astrocyte_lr_1994::handles_test_event( DataLoggingRequest& dlr, size_t receptor_type )
{
  if ( receptor_type != 0 )
  {
    throw UnknownReceptorType( receptor_type, get_name() );
  }
  return B_.logger_.connect_logging_device( dlr, recordablesMap_ );
}
 
inline void
astrocyte_lr_1994::get_status( Dictionary& d ) const
{
  P_.get( d );
  S_.get( d );
 
  d[ names::recordables ] = recordablesMap_.get_list();
}
 
inline void
astrocyte_lr_1994::set_status( const Dictionary& d )
{
  Parameters_ ptmp = P_;      // temporary copy in case of errors
  ptmp.set( d, this );        // throws if BadProperty
  State_ stmp = S_;           // temporary copy in case of errors
  stmp.set( d, ptmp, this );  // throws if BadProperty
 
  // We now know that (ptmp, stmp) are consistent. We do not
  // write them back to (P_, S_) before we are also sure that
  // the properties to be set in the parent class are internally
  // consistent.
 
  // if we get here, temporaries contain consistent set of properties
  P_ = ptmp;
  S_ = stmp;
}
 
}  // namespace
 
#endif  // HAVE_GSL
#endif  // ASTROCYTE_LR_1994_H