Calcium influx during striatal upstates (Evans et al. 2013)

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Accession:150912
"... To investigate the mechanisms that underlie the relationship between calcium and AP timing, we have developed a realistic biophysical model of a medium spiny neuron (MSN). ... Using this model, we found that either the slow inactivation of dendritic sodium channels (NaSI) or the calcium inactivation of voltage-gated calcium channels (CDI) can cause high calcium corresponding to early APs and lower calcium corresponding to later APs. We found that only CDI can account for the experimental observation that sensitivity to AP timing is dependent on NMDA receptors. Additional simulations demonstrated a mechanism by which MSNs can dynamically modulate their sensitivity to AP timing and show that sensitivity to specifically timed pre- and postsynaptic pairings (as in spike timing-dependent plasticity protocols) is altered by the timing of the pairing within the upstate. …"
Reference:
1 . Evans RC, Maniar YM, Blackwell KT (2013) Dynamic modulation of spike timing-dependent calcium influx during corticostriatal upstates. J Neurophysiol 110:1631-45 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Striatum;
Cell Type(s): Neostriatum medium spiny direct pathway GABA cell;
Channel(s): I Na,t; I L high threshold; I N; I A; I K; I K,Ca; I A, slow; I Krp; I R;
Gap Junctions:
Receptor(s): AMPA; NMDA; Gaba;
Gene(s): Cav1.3 CACNA1D; Cav1.2 CACNA1C; Cav2.2 CACNA1B;
Transmitter(s):
Simulation Environment: GENESIS;
Model Concept(s): Oscillations; STDP; Calcium dynamics;
Implementer(s): Evans, Rebekah [Rebekah.Evans at nih.gov];
Search NeuronDB for information about:  Neostriatum medium spiny direct pathway GABA cell; AMPA; NMDA; Gaba; I Na,t; I L high threshold; I N; I A; I K; I K,Ca; I A, slow; I Krp; I R;
//genesis

/***************************		MS Model, Version 9.1	*********************
**************************** 	      CaDifshell.g 	*********************
	Avrama Blackwell 	kblackw1@gmu.edu
	Wonryull Koh		wkoh1@gmu.edu
	Rebekah Evans 		rcolema2@gmu.edu
	Sriram 				dsriraman@gmail.com	
******************************************************************************

*****************************************************************************/

//***************************** Begin Local Subroutine ***********************
//old calcium concentration - single time constant of decay
function add_CaConcen (buffername, a, b, cellpath)
	str buffername,cellpath
    float a,b

    str compt
	float len,dia,position
    float Ca_tau,kb   		
	float PI = 3.14159
    float shell_thick={outershell_thickness}
    float Ca_base = {base}

	foreach compt ({el {cellpath}/##[TYPE=compartment]})
	
		//make sure this is the correct compartment type, and determine length and diameter
 		if (!{{compt} == {{cellpath}@"/axIS"} || {compt} == {{cellpath}@"/ax"}}) 
    		dia = {getfield {compt} dia}
    		position = {getfield {compt} position}
     		len = {getfield {compt} len}
    		if ({{getpath {compt} -tail} == "soma"})
              len = dia
            end
   		end

  			//if the compartment is not a spine and its position is between [a,b] 
   		if ({position >= a} && {position < b} ) 
     			// Sabatini's model. Sabatini, 2001,2004
      		create Ca_concen  {compt}/{buffername}  // create Ca_pool here!
      		if({dia} < 0.81e-6)        // this is tertiary dendrites
            		kb = 96
      		elif (dia < 1.5e-6)        // secondary dendrites
            		kb = 96
      		elif (dia < 1.8e-6)        // primary dendrites
            		kb = 96
 		else                       // soma 
      			kb = 200             	// the setting for soma is imaginary
   		end

   			if({dia}	<	15e-6)
   				Ca_tau = 25e-3
   			else 
      				Ca_tau = 100e-3       	// an imaginary setting to fit the model
   			end  
                
   			// set Ca_tau  according to diameters of dendrites      
   			float  shell_dia = dia - shell_thick*2
   			float  shell_vol= {PI}*(dia*dia/4-shell_dia*shell_dia/4)*len
   			float surf = dia*{PI}*dia
		if ({dia}>= 15e-6)
			echo {compt} "shell_vol=" {shell_vol} "+" {len}
			echo "shell_dia="{shell_dia}
			echo "dia=" {dia}
			echo "surface area=" {surf}
		end
		
			setfield {compt}/{buffername} \
               B          {1.0/(2.0*96494*shell_vol*(1+kb))}	\ 
               tau        {Ca_tau}                        		\  
               Ca_base    {Ca_base}   									\
               thick      {shell_thick}  

//
   		end
    end
end

//new calcium concentration - various buffers, pumps and diffusion
function create_difshell (shellName, base, compLen, r, shellThickness, mode)
	str shellName
	float base
	float compLen
	float r, shellThickness
    	str mode

	create difshell {shellName}
	setfield {shellName}	\
		C    {base}	\
        Ceq  {base}	\
        D    {dca}	\ //D_Ca = 2e-6 (cm^2)(s^(-1))
        val  2	\
        leak 0	\
        shape_mode {mode}	\ 
        len {compLen}	\
        dia {r*2}	\	//outer diameter of the shell
        thick {shellThickness}
end

function add_difbuffer_to_difshell (shellName, bname, btotal, kf, kb, d, compLen, r, shellThickness, mode)
	str shellName, bname
	float btotal, kf, kb, d, compLen, r
    	str mode
	create difbuffer {shellName}{bname}

    setfield {shellName}{bname}	\
		activation {base} \
		Btot {btotal}	\
        kBf {kf} \
        kBb {kb} \
        D {d} \
        shape_mode {mode} \
        len {compLen} \
        dia {r*2} \
        thick {shellThickness}

    addmsg {shellName}{bname} {shellName} BUFFER kBf kBb Bfree Bbound
    addmsg {shellName} {shellName}{bname} CONCEN C 
end

function add_mmpump (shellName, surfaceArea, kcat, km)
	str shellName
	float surfaceArea, kcat, km
	str pname = "MMpump"
	
	create mmpump {shellName}{pname}
	setfield {shellName}{pname}	\
        vmax {kcat*surfaceArea}	\ 
		val {2}	\	
        Kd {km}
   	addmsg {shellName}{pname} {shellName} MMPUMP vmax Kd
    addmsg {shellName} {shellName}{pname} CONCEN C
end

function make_fura (compt, totalshells, bufname, calname)
	str compt
	str calname
	str bufname
	int totalshells, i
	create fura2 {compt}/fluorescence
	i=1
	while (i < totalshells+1)
		str bnx = {calname} @ {i}
		//str bn = {bnx}{bufname}
		addmsg {compt}/{bnx}{bufname} {compt}/fluorescence CONCEN Bfree Bbound vol
		i=i+1
	end 
end

function make_volavg (compt, totalshells, calname)
	str compt
	str calname
	int totalshells, i
	create wgtavg {compt}/volavg
	i=1
	while (i < totalshells+1)
		str bnx2 = {calname} @ {i}
		addmsg {compt}/{bnx2} {compt}/volavg ValueWgt C vol
		i=i+1	
	end
end

function make_buffervolavg (compt, totalshells, calname, buffer)
	str compt
	str calname
	str buffer
	int totalshells, i
	create wgtavg {compt}/{buffer}Vavg
	i=1
	while (i < totalshells+1)
		str bnx3 = {calname} @ {i}
		addmsg {compt}/{bnx3}{buffer} {compt}/{buffer}Vavg ValueWgt Bbound vol
		i=i+1	
	end
end

function make_extra_pools (a, b, compt)  //called in mscellshort.g
	str compt
	float a, b

	str NMDApool = "NMDApool"
	str LVApool = "LVApool"
	str HVApool = "HVApool"
	add_CaConcen {NMDApool} {a} {b}   {compt} 
	add_CaConcen {HVApool} {a} {b}   {compt} 
	add_CaConcen {LVApool}  {a} {b}   {compt}

	str allpool = "allpool"
	add_CaConcen {allpool} {a} {b} {compt}
	//making an extra pool to add up all calcium accruing over the upstate, no decay so tau=0
	//add_CaConcen {allpool}  {a} {b}   {compt}
	//setfield {compt}/{allpool} B 0
end

//add_extra_pools is called by MScellshort.g 
function add_extra_pools (compt, NMDACaGHK)
	str compt
	float NMDACaGHK

	addmsg {compt}/CaL12_channelGHK {compt}/HVApool I_Ca Ik
	addmsg {compt}/CaL13_channelGHK {compt}/LVApool I_Ca Ik
	addmsg {compt}/NR2A/GHK {compt}/NMDApool fI_Ca Ik {NMDACaGHK}
	addmsg {compt}/CaR_channelGHK {compt}/HVApool I_Ca Ik
	addmsg {compt}/CaT_channelGHK {compt}/LVApool I_Ca Ik

	addmsg {compt}/CaL12_channelGHK {compt}/allpool I_Ca Ik
	addmsg {compt}/CaL13_channelGHK {compt}/allpool I_Ca Ik
	addmsg {compt}/NR2A/GHK {compt}/allpool fI_Ca Ik {NMDACaGHK}
	addmsg {compt}/CaR_channelGHK {compt}/allpool I_Ca Ik
	addmsg {compt}/CaT_channelGHK {compt}/allpool I_Ca Ik
	
end

//***************************** End Local Subroutines ************************

function add_caconcen_objects (calName, CELLPATH)
	str calName
	str CELLPATH
	str outermostShellName = {calName} @ 1
	str compt 
	float totalshells
	float thickness 

	//use maxshells if you want to set a low number of shells, and the thicknesses will be changed accordingly.  
//If you want the thicknesses to be determined 			

	int setshellnum = 0

	
//0= set thickness; max shell num determined by thickness, 1= set max shell num; thickness determined by max shell num.
	
	//set shell number
	int maxshellnum = 3
	
	//or thickness
	
	foreach compt ({el {CELLPATH}/##[TYPE=compartment]})
			float dia={getfield {compt} dia}
			float r = 0.5*{dia}
			float len = {getfield {compt} len}
			int numShells = 0 //initialize numShells at 0
			
//**********calculate how many shells are needed from the diameter and thickness
//*********when that works, can replace the next four sections of add_difbuffer ... with a single section
		
//If setting the initial thickness, this counts the number of shells for each compartment.  the outer shell is set to 
//equal thickness and then the thickness progressively doubles for each inner shell	
		float testsum = 0	
		if (setshellnum == 0)	
			thickness = {outershell_thickness}
			
			if ({{{r} >= {thickness}} && {r <= {1.1*thickness}}})
				numShells = 0
            else
				while ({r} >= {thickness*thicknessincrease}) 
					//echo "thickness=" {thickness}
					//echo "r=" {r}
					//echo "numshells=" {numShells}
					numShells = numShells + 1 
					r = r - thickness
					testsum = testsum + thickness
					thickness = thickness*thicknessincrease
				end	
				
			//this last thickness=r is to make one last shell that is the thickness of 'whatever is leftover'
				thickness=r
				testsum=testsum+thickness
				totalshells=numShells+1
			end		
			
			//echo "r=" {r}
			//echo "thickness=" {thickness}
			//echo "totalshells=" {totalshells}		
			//echo "testsum=" {testsum}
			r = 0.5*{dia}                //re-initialize r and thickness to make the shells.
			thickness = {outershell_thickness}
		end	
		
//If setting the max number of shells, this calculates the thickness.  
//NOTE: this results in different thicknesses depending on the total size of the compartment. 

		if (setshellnum == 1)
			thickness = {r}/{maxshellnum}
			totalshells = {maxshellnum}
			//echo "r=" {r}
			//echo "thickness=" {thickness}
			//echo "totalshells=" {totalshells}
		end
		
			
//make shells and buffers using the number of shells calculated above.  
	    int i = 1
        while (i < totalshells)
			float shellRadius = {r} 
			str shellname = {calName} @ {i}
			create_difshell {compt}/{shellname} {base} {len} {shellRadius} {thickness} SHELL 
			add_difbuffer_to_difshell {compt}/{shellname} {bname1} {btotal1} {kf1} {kb1} {d1} {len} {shellRadius} {thickness} SHELL
			add_difbuffer_to_difshell {compt}/{shellname} {bname2} {btotal2} {kf2} {kb2} {d2} {len} {shellRadius} {thickness} SHELL 
			add_difbuffer_to_difshell {compt}/{shellname} {bname4} {btotal4} {kf4} {kb4} {d4} {len} {shellRadius} {thickness} SHELL
			if (calciumdye == 1)
				add_difbuffer_to_difshell {compt}/{shellname} {bname3} {btotal3} {kf3} {kb3} {d3} {len} {shellRadius} {thickness} SHELL 
			elif (calciumdye == 2)
				add_difbuffer_to_difshell {compt}/{shellname} {bname5} {btotal5} {kf5} {kb5} {d5} {len} {shellRadius} {thickness} SHELL 
			end
			i = {i} + 1
			//echo "r=" {shellRadius}
			//echo "thickness=" {thickness}
			//echo "shellname=" {shellname}
			r = r-thickness
			if (setshellnum == 0)
				thickness=thickness*thicknessincrease
			end
		end
//make final shell with the 'remaining' radius
		shellRadius={r}
		thickness={shellRadius}
		str shellname = {calName} @ {i}
		//echo "r=" {shellRadius}
		//echo "thickness=" {thickness}
		//echo "shellname=" {shellname}
		create_difshell {compt}/{shellname} {base} {len} {shellRadius} {thickness} SHELL
		add_difbuffer_to_difshell {compt}/{shellname} {bname1} {btotal1} {kf1} {kb1} {d1} {len} {shellRadius} {thickness} SHELL 
		add_difbuffer_to_difshell {compt}/{shellname} {bname2} {btotal2} {kf2} {kb2} {d2} {len} {shellRadius} {thickness} SHELL
		add_difbuffer_to_difshell {compt}/{shellname} {bname4} {btotal4} {kf4} {kb4} {d4} {len} {shellRadius} {thickness} SHELL
		if (calciumdye == 1)
			add_difbuffer_to_difshell {compt}/{shellname} {bname3} {btotal3} {kf3} {kb3} {d3} {len} {shellRadius} {thickness} SHELL
		elif (calciumdye == 2)
			add_difbuffer_to_difshell {compt}/{shellname} {bname5} {btotal5} {kf5} {kb5} {d5} {len} {shellRadius} {thickness} SHELL 
		end

        reset

		//add fura object to each compartment to calc fluorescence
		if (calciumdye == 1)
			make_fura {compt} {totalshells} {bname3} {calName}
		end
		//add wgtavg object to calculated ca concentration without dyes
		make_volavg {compt} {totalshells} {calName}
		//add bound Fluo5F wgtavg object
		if (calciumdye == 2)
			make_buffervolavg {compt} {totalshells} {calName} {bname5}
		end
		

	
		//diffusion between shells
			i = 1
			while (i < totalshells)
				str sn = {calName} @ {i} 
				str innerSn = {calName} @ {i+1}
				addmsg {compt}/{sn} {compt}/{innerSn} DIFF_DOWN prev_C thick
				addmsg {compt}/{innerSn} {compt}/{sn} DIFF_UP prev_C thick
				addmsg {compt}/{sn}{bname4} {compt}/{innerSn}{bname4} DIFF_DOWN prev_free thick
				addmsg {compt}/{innerSn}{bname4} {compt}/{sn}{bname4} DIFF_UP prev_free thick
				i = {i} + 1
			end	
			
			//diffusion between difbuffers
			i = 1
			while (i < totalshells)
				str sn = {calName} @ {i} 
				str innerSn = {calName} @ {i+1}
				addmsg {compt}/{sn}{bname2} {compt}/{innerSn}{bname2} DIFF_DOWN prev_free thick
				addmsg {compt}/{innerSn}{bname2} {compt}/{sn}{bname2} DIFF_UP prev_free thick
				if (calciumdye == 1)
					addmsg {compt}/{sn}{bname3} {compt}/{innerSn}{bname3} DIFF_DOWN prev_free thick
					addmsg {compt}/{innerSn}{bname3} {compt}/{sn}{bname3} DIFF_UP prev_free thick
				elif (calciumdye == 2)
					addmsg {compt}/{sn}{bname5} {compt}/{innerSn}{bname5} DIFF_DOWN prev_free thick
					addmsg {compt}/{innerSn}{bname5} {compt}/{sn}{bname5} DIFF_UP prev_free thick
				end
				i = {i} + 1
			end	
		
			//pump @ outershell
			float surfaceArea = {getfield {compt}/{outermostShellName} surf_up}
			//echo "shell=" {compt}/{outermostShellName}
			//showfield {compt}/{outermostShellName} *
			if ({compt} == "/cell/soma")
				add_mmpump {compt}/{outermostShellName} {surfaceArea} {kcatsoma} {km}
				float CaBase = {getfield {compt}/{outermostShellName} Ceq}
				float vmax = kcatsoma*surfaceArea
				float vol = {getfield {compt}/{outermostShellName} vol}
				float leak = {{vmax*CaBase}/{vol*{CaBase + km}}} // {{kcatsoma*CaBase}/{outershell_thickness*{CaBase + km}}} 
				setfield {compt}/{outermostShellName} leak {leak}
				echo "soma="{kcatsoma}
				echo "soma="{leak}
			elif ({compt} != "/cell/soma")
				add_mmpump {compt}/{outermostShellName} {surfaceArea} {kcatdend} {km}
				float CaBase = {getfield {compt}/{outermostShellName} Ceq}
				float vmax = kcatdend*surfaceArea
				float vol = {getfield {compt}/{outermostShellName} vol}
				float leak = {{vmax*CaBase}/{vol*{CaBase + km}}} // {{kcatdend*CaBase}/{outershell_thickness*{CaBase + km}}} 
				setfield {compt}/{outermostShellName} leak {leak}
			end			
	end
end


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