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The 'chemesis' library of GENESIS objects

'chemesis' is a library of objects for creating models of biochemical reactions, second messengers, and calcium dynamics.

This library is based on chemesis version 2.5, and was developed and contributed to the GENESIS 2.4 libraries by K. T. (Avrama) Blackwell. The main website for the latest chemesis source code, tutorials, simulation scripts, and lecture slides is http://krasnow1.gmu.edu/CENlab/software.html.

Demonstration scripts and tutorials may be found in genesis/Scripts/chemesis. The source code for these objects and their data structure is given in genesis/src/chemesis.

chemesis provides the following objects:

cicr: computes state variables associated with calcium release channels, either the ryanodine or ip3 receptor channel

cicrflux: computes ion flow through ip3 or Ryr receptor channel from the smooth endoplasmic reticulum (SER) and the cytosol.

conservepool: calculates concentration & quantity in a compartment by subtracting the conc/quantity of all other forms of the molecule

diffusion: calculates flux across the shared/connected surface areas

enzyme: implements a reaction pool, and the two coupled reactions implementing and enzyme reaction

feedback: calculates enhancement or reduction in an enzyme activity by another substrance

mmenz: simplified michaelis-menton enzyme reaction

mmpump2: Michaelis-Menten pump. unlike mmpump, this object calculates flux due to the pump

ncx: implements two different forms of a sodium-calcium exchanger

reaction: computes kf*substrates and kb*products for nth order reactions.

rhodopsin: quite a complicated object for calculating stochastic activation and inactivation of rhodopsin molecules

rxnpool: accumulates changes in quantity and concentration from many other chemesis objects and then calculates the new concentration This object is similar to pool (kinetikit) and functions similar to compartment, which accumulates current fluxes.

wgtavg: An object to calculate a weighted average, such as mean calcium in a set of shells.

Note that chemesis does not require you to work in SI units, but if you don't, you need to set various units fields on all the objects, and you must use a set of consistent units.

Documentation for the objects is given below:

Object Type:      cicr
datatype          IP3R_type
function          cicrpool()
class             [ gate ] [ segment ] 
size              224 bytes
author            A. Blackwell ERIM Aug 96; revised GMU Aug 99

VALID ACTIONS

CHECK RESET PROCESS INIT

VALID MESSAGES

      [5] CONSERVE      xconc     /* fraction of other states */
      [4] CALCIUM       caconc     /* concentration of calcium */       
      [3] IP3           ip3conc   /* concentration of ip3 */    
      [2] GSTATE        kbgamma conc /* back rate const and conc in gamma dir */
      [1] BSTATE        kbbeta conc  /* back rate const and conc in beta dir */
      [0] ASTATE        kbalpha conc /* back rate const and conc in alpha dir */

FIELDS

             activation                
             fraction        fraction of channel in state        
             previous_state            
             alpha           forward rate constant in alpha direction        
             beta            forward rate constant in beta direction        
             gamma           forward rate constant in gamma direction        
             alpha_state     if ip3 is bound (1) or not (0) for this state       
             beta_state      if calcium is bound (1) or not (0) to open part for this state       
             gamma_state     if calcium is bound(1) or not (0) to closed part for this state       
             conserve        flag indicating a conserve pool       
             xinit           initial value       
             xmin            minimum value, typically 0      
             xmax            maximum value, typically 1

DESCRIPTION

cicr computes state variables associated with calcium release channels, either the ryanodine or ip3 receptor channel. Create one element for each receptor state, thus ip3 receptor of DeYoung and Keizer requires 8 cicr elements. cicr calculates the fraction of receptors in each state, the flux is calculated using a cicrflux element. Transitions between ASTATE are dependent on IP3 concentration (a required message for cicr) thus only BSTATE and GSTATE elements, which transitions are calcium dependent, are created for ryanodine receptor channel.


Object Type:      cicrflux
datatype          flux_type
function          cicrflux()
class             [ channel ] [ segment ] 
size              184 bytes
author            A. Blackwell ERIM Aug 96; revised GMU Dec 99; GMU Mar 02

VALID ACTIONS

CHECK RESET PROCESS INIT

VALID MESSAGES

      [2] IP3R              ip3r  //fraction of open channels
      [1] CONC2             conc2 
      [0] CONC1             conc1 

FIELDS

             activation                
             maxflux        single channel flux (cm/time) * number of channels * Surface area (cm^2)       
             deltaflux1     maxflux*openfraction*(conc1-conc2), send value to A of rxnpool 2        
             deltaflux2     maxflux*openfraction*(conc2-conc1), send value to A of rxnpool 1        
             power          exponent; fraction open = ip3r^power       
             units          1 for moles, 1e-3 for mmoles, 1e-6 for umoles       

DESCRIPTION

cicrflux computes ion flow through ip3 or Ryr receptor channel from the smooth endoplasmic reticulum (SER) and the cytosol. This requires at least two rxnpools, one tracking calcium in the SER and one tracking calcium in the cytosol. All three messages are required. the IP3R message is really just the fraction field from whichever cicr element is the conducting state

return messages as follows:
addmsg from cicrflux object to pool 1 RXN0MOLES deltaflux2 addmsg from cicrflux object to pool 2 RXN0MOLES deltaflux1


Object Type:      conservepool
datatype          conserve_type
function          conservepool()
class             [ concentration ] [ segment ] 
size              248 bytes
author            A. Blackwell ERIM Aug 96; revised GMU Dec 99; GMU Mar 02

VALID ACTIONS

CHECK RESET PROCESS INIT

VALID MESSAGES

      [2] VOLUME            volume /* volume of compartment */
      [1] MOLES             moles /* quantity of other forms */
      [0] CONC              conc /* concentration of other forms */

FIELDS

             activation                
             previous_state            
             Conc            concentration of molecule       
             quantity        quantity of molecules
             Qinit           initial quantity of molecule        
             Qtot            total quantity of this and other forms of molecule       
             Cinit           initial concentration       
             Cmin            minimum concentration       
             Ctot            total concentration of this and other forms of molecule        
             volume          used to convert from concentration to quantity and vice versa        
             type            whether specifying quantity or concentration of molecule       
             units           1 for moles, 1e-3 for mmoles, 1e-6 for umoles      
             Dunits          1 for meters, 1e-4 for cm, etc       
             VolUnitConv     Dunits^3, converts volume to SI       

DESCRIPTION

Implementation of pool for conserved molecules. If type = 0, computes concentration of molecule which is the total conc less the conc in all other states. If type = 1, computes quantity of molecule which is the total quantity less the quantity in all other states. Then computes concentration by dividing by volume.


Object Type:      diffusion
datatype          diffusion_type
function          diffusion()
class             [ channel ] [ segment ] 
size              184 bytes
author            A. Blackwell GMU Dec 97; revised GMU Dec 99; GMU Mar 02

VALID ACTIONS

CHECK RESET PROCESS INIT

VALID MESSAGES

      [1] POOL2             len2 area2 conc2 /* pool 1 dimensions & Conc */
      [0] POOL1             len1 area1 conc1 /* pool 2 dimensions & Conc*/

FIELDS

             D                diffusion constant    
             difflux1         D*area/len*conc21 send value to A field of pool 2      
             difflux2         D*area/len*conc2, send value to A field of pool 1    
             units            1 for moles, 1e-3 for mmoles, 1e-6 for umoles       
             Dunits           1 for meters, 1e-4 for cm, etc       

DESCRIPTION

Diffusion is an object used to computes flux of molecules due to diffusion through shared surface between two rxnpools. This object can implement both 1-D and 2-D diffusion, and sums the fluxes between each pair of rxnpools. 2D diffusion is implemented among a set of cylindrical shells, with the surface area of the side of the cylinder stored in SAside, and surface area of inside and outside of the shell stored in SAout and SAin of the rxnpool (desribed below). Thus, diffusion helps the rxnpool to implements the equation:

Sum over i (Conc1i-Conc2i)*Mean(area1i,area2i)/((len1i+len2i)/2)

Each diffusion element calculates
(Conc1i-Conc2i)*Mean(area1i,area2i)/((len1i+len2i)/2) for a pair of adjacent rxnpools. Their shared surface areas do not need to be identical. The mean surface area is calculated as geometric mean, not arithmetic mean.

Each diffusion needs a pair of messages, one from each rxnpool (pool1 and pool2). Each message must contain the appropriate surface area (i.e. the area of the surface facing the other rxnpool), the length of the rxnpool, and the concentration. Each diffusion object then sends a pair of messages back to the rxnpools,

         addmsg diffusionElement pool2 RXN0MOLES difflux2
         addmsg diffusionElement pool2 RXN0MOLES difflux1 

Object Type: enzyme

datatype      enzyme_type
function      enzyme()
class         [ segment ] 
author        A. Blackwell ERIM Aug 96; revised GMU Dec 99; revised GMU Mar 02

VALID ACTIONS

CHECK SET RESET PROCESS INIT

VALID MESSAGES

      [4] VOLUME            vol SAin SAout              /* volume and SAin input */
      [3] RHODOPSIN         mrho vol SAin SAout /* effective rhodopsin, volume and SAin input from rhodopsin */ 
      [2] SUBSTRATE         conc                        /* conc. of substrate */     
      [1] FEEDBACK          feedback rateconst /* concentration of feedback molecule, which rate const to modify. */
      [0] ENZ               conc                   /* concentration or quantity of enzyme */  

FIELDS

             conc            concentration (integrated)         
             quant           quantity in molecules         
             complex_conc              
             complex_quant             
             previous_state            
             Cmin            minimum concentration         
             Cinit           initial concentration        
             Qinit           initial quantity in molecules        
             len             length of cylindrical pool        
             radius          radius of cylindrical or spherical pool         
             vol             volume of pool       
             SAside          side surface area of cylinder       
             SAout           outer surface area of spherical shell        
             SAin            inner surface area of spherical shell        
             units           1 for moles, 1e-3 for mmoles, 1e-6 for umoles      
             type             whether pool integrates concentration (0) or quantity (1)      
             kf               forward rate  constant.  Kf units must be consistent with substrate units.       
             kb               backward rate constant. units are per time.      
             kcat              catalytic rate constant. units are per time.      
             deltacat          change in product of whole reaction  = kcat*EScomplex
             deltaenz          change in free enzyme conc = (kb+kcat)*EScomplex
             kbprod            change in substrate conc = kb * EScomplex conc
             kfsubs             kf * Enz * Subs     
             feedback          computed feedback value      
             rateconst         which rate const is modified by feedback      
             fbconc            concentration of feedback substance     
             thresh            above or below this no feedback computed.      
             pow               raise fb to this power      
             form              0 for hyperbolic, 1 for sigmoid increase, 2 for sigmoid decrease
             sign              -1 for feedback below threshold, +1 for fb above thresh
             halfmax           parameter for sigmoid form of feedback      
             Dunits            1 for meters, 1e-4 for cm, etc      
             VolUnitConv       Dunits^3, converts volume to SI units   

DESCRIPTION

enzyme implements a reaction pool (thus has many of the same fields as rxnpool), and the two reactions of an enzyme reaction. In the first reaction, enzyme binds to substrate. In the second reaction, product is formed and the enzyme is regenerated. Thus, this object tracks the enzyme concentration, but two additional rxnpools are needed - one for substrate and one for product.

Eqn: Michaelis-Menton enzyme kinetics. Vmax = kcat; Km = (Kcat+kb)/kf

                                kf      kcat
        [Enzyme] + [Substrate] <-> [E-S] -> [Enzyme] + [Product]
                                kb

        Computes dprod/dt =  kcat*E-Scomplex
        Solves for E-Scomplex concentration from: dES/dt = -(kcat+kb)*ES + kf*E*S

        dProduct/dt units are quantity (not concentration)
        addmsg from enz object to rxnpool RXN0MOLES product.

It also has fields to allow modulation (change in rate constants) of the enzyme activity by any molecule. Feedback message requires feedback concentration and rate const: 0 for kf, 1 for kb, 2 for kcat.

using hyperbolic form: feedback is proportional to: 1 / conc(feedback substance) for negative feedback

feedback is proportional to: conc (feeback substance) for positive feedback.

Sigmoid form: feedback is proportional to: conc/conc + halfmax (for inc feedback)

feedback is proportional to: halfmax / conc + halfmax (for dec feedback)


Object Type:      feedback
datatype          feedback_type
function          feedback()
class             [ segment ] 
size              184 bytes
author            A. Blackwell GMU feb 02

VALID ACTIONS

SET RESET PROCESS INIT

VALID MESSAGES

[0] CONC conc // concentration of feedback substance

FIELDS

             thresh           above or below this no feedback computed      
             pow              raise fb to this power       
             form             0 for hyperbolic, 1 for sigmoid increase, 2 for sigmoid decrease
             sign             -1 for feedback below threshold, +1 for fb above thresh        
             halfmax          parameter for sigmoid form of feedback         
             feedback         output value of feedback        

DESCRIPTION

An object for computing modification of rate constants caused by feedback of some substance, e.g. calcium, sent as message.

hyperbolic form: feedback is proportional to: 1 / conc(feedback substance) for negative feedback

feedback is proportional to: conc (feeback substance) for positive feedback.

Sigmoid form: feedback is proportional to: conc/conc + halfmax (for inc feedback) feedback is proportional to: halfmax / conc + halfmax (for dec feedback)


Object Type:      mmenz
datatype          mmenz_type
function          mmenz()
class             [ segment ] 
size              208 bytes
author            A. Blackwell ERIM Aug 96; revised GMU Dec 99

VALID ACTIONS

SET RESET PROCESS INIT

VALID MESSAGES

      [2] SUBSTRATE         conc /* conc. of substrate */
      [1] FEEDBACK          conc /* conc. of feedback substance */
      [0] ENZ               conc /* amount of enzyme */

FIELDS

             activation                
             Vmax           maximal rate of reaction, units of per time        
             Km             combination rate constant: (kf2+kb1)/kf1        
             product        quantity of product produced.  Units will the the same enzyme units       
             thresh         below this conc, positive feedback, above the concentration implement negative feedback        
             pos_pow        raise positive feedback to this power         
             pos_form       0 for hyperbolic, 1 for sigmoid         
             pos_halfmax    param for sigmoid feedback         
             neg_pow        raise negative feedback to this power        
             neg_form       0 for hyperbolic, 1 for sigmoid          
             neg_halfmax    parameter for sigmoid feedback         
             feedback       computed value of feedback          
             subs_rate

DESCRIPTION

Simplified Michaelis-Menton enzyme kinetics. Can assume constant substrate, or can compute effect of substrate on reaction rate. Vmax = kf2; Km = (Kf2+kb1)/kf1

                       kf1     kf2
[Enzyme] + [Substrate] <-> [E-S] -> [Enzyme] + [Product]
                       kb1

Under assumptions of M-M dynamics, Solves dprod/dt = kf1*Enzyme*Subs/(Subs + Km)

Vmax units are quantity per time, where quantity units are the same as the enzyme units (input from enzyme rxnpool). Substrate and Km must have units of Conc. Product (quantity units, same as enzyme) = Vmax * E * S/ (S+Km).

Use addmsg from enz object to rxnpool RXN0MOLES product. For more accurate MM kinetics, enzyme OR enz object in kinetikit. Feedback allows decrease in enzyme activity as function of concentration of feedback substance.

hyperbolic form: feedback is proportional to: 1 / conc(feedback substance) for negative feedback

feedback is proportional to: conc (feeback substance) for positive feedback.

Sigmoid form: feedback is proportional to: conc/conc + halfmax (for inc feedback) feedback is proportional to: halfmax / conc + halfmax (for dec feedback)


Object Type:      mmpump2
datatype          pump_type
function          mmpump2()
class             [ channel ] [ segment ] 
size              200 bytes
author            A. Blackwell ERIM Aug 96; revised GMU Dec 99; GMU Mar 02

VALID ACTIONS

SET RESET PROCESS INIT

VALID MESSAGES

[0] CONC conc

FIELDS

             activation      
             max_rate  Maximum Pump Rate   
             half_conc concentration at which pump rate is half maximal   
             half_conc_pow   
             moles_in  State variable for return message to pools   
             moles_out State variable for return message to pools   
             power     exponent applied to Concentration   
             units     1 for moles, 1e-3 for mmoles, 1e-6 for umoles   

DESCRIPTION

A Michaelis-Menton type of formulation of pump. Either SERCA ATPase pump or Na-Ca ATPase cytosolic pump. Requires input message in concentration units. Computes right hand side of dC/dt = (+/-)max_rate * Ca^n / (Ca^n + half_conc^n). Output Messages

        addmsg from mmpump2 to cytosol-rxnpool  RXN0MOLES moles_out.  
        addmsg from mmpump2 to ER or extracellular rxnpool RXN0MOLES moles_in. 

Note that mmpump is another implementation of a Michaelis-Menton pump.


Object Type:      ncx
datatype          exchange_type
function          ncx()
class             [ channel ] [ segment ] 
author            A. Blackwell GMU Sept 02

VALID ACTIONS

CHECK SET RESET PROCESS INIT

VALID MESSAGES

      [4] VM                Vm   /* membrane potential*/
      [3] NAEXT             conc /* Na external Concentration */
      [2] NAINT             conc /* Na internal Concentration */
      [1] CAEXT             conc /* Ca external Concentration */
      [0] CAINT             conc /* Ca internal concentration */

FIELDS

             activation                
             Ca_int         internal calcium concentration         
             Ca_ext         external calcium concentration         
             Na_int         internal calcium concentration         
             Na_ext          external calcium concentration       
             Vm             membrane potential        
             Vnaca          reveral potential of ncx        
             naterm         Na_ext^stoic, used for Jafri formula        
             caterm         Ca_ext ^hill, used for Gall formula         
             chi            F/RT        
             Kmca           affinity for calcium        
             Kmna           affinity for sodium        
             kmhill         km^hill        
             naicao         nai^hill*cao        
             gamma          partition coefficient        
             T              temperature in Kelvin         
             I              current        
             Gbar           maximal conductance        
             Gcurrent       conductance for compartment       
             ksat           another constant used by jafri        
             Vunits         units of membrane potential        
             valence        calcium charge        
             hill           hill coefficient        
             stoich         stoichiometry of pump (how many sodium for calcium)
             Na_msg            whether sodium conc messages are being passed
             ncxtype           whether using Gall (0) or Jafri (1) formula

DESCRIPTION

Sodium calcium exchanger equations.

if ncxtype = 0 uses Gall formula:
I = K * Cai^Hill/(Cai^Hill + Kmca^H) * (Vm - Vnaca) where Vnaca = RT/F(stoic*ln(Nao/Nai) - ln(Cao/Cai))

if ncxtype = 1 uses jafri formula:

I = K* (Cao*Nai^stoich*exp(gamma*FV/RT) - Cai*Nao^stoich*exp((1-gamma*FV/RT)) divided by
(Kmna^stoich+nao^stoich)*(Kmca+cao)*(1+ksat*exp(1-gamma)FV/RT))

if Na_msg = 0 then Na concentrations are initialized, no Na messages required. if Na_msg = 1, then Na messages are required. In all cases input messages of calcium are required. The calcium and sodium input message in concentration units.

Requires Vm message, units indicated with Vunit field addmsg from ncx to rxnpool CURRENT valence current.


Object Type:      reaction
datatype          react_type
function          reaction()
class             [ segment ] 
author            A. Blackwell ERIM Aug 96 ; revised GMU Dec 99

VALID ACTIONS

SET RESET PROCESS INIT

VALID MESSAGES

      [1] PRODUCT           conc  /* concentration or quantity of products */
      [0] SUBSTRATE         conc  /* concentration or quantity of substrates */

FIELDS

             kb               backward rate constant      
             kf               forward rate constant      
             kbprod           kb * products       
             kfsubs           kf * substrates      

DESCRIPTION

An element to compute kf*substrates and kb*products for nth order reactions. dC/dt = kf * substrate * substrate * ... - kb*product* ...

For each substrate and product in reaction, a message must be received (n times, if n moles required). Input and rate constants both must be in units of concentration, (use RXN2 to send message to rxnpool) or both must be in units of moles (use RXN2MOLE).

addmsg from reaction to substrate rxnpool RXN2 (or RXN2MOLES) kbprod kfsubs addmsg from reaction to product rxnpool RXN2 (or RXN2MOLES) kfsubs kbprod


Object Type:      rhodopsin
datatype          rhodopsin_type
function          rhodopsin()
class             [ segment ] 
size              7128 bytes
author            A. Blackwell GMU March 02

VALID ACTIONS

CHECK SET RESET PROCESS INIT

VALID MESSAGES

      [1] INACT             inactivation 
      [0] ISOM              isomerization 

FIELDS

             input_slice               
             slice                     
             isom                      
             last_isom                 
             villus                    
             total_villi               
             slice_villi               
             villi_isom                
             isom_time                 
             total_time                
             active_villi    
             villus_vol      
             villus_xarea    
             villus_sa       
             slice_vol       
             slice_xarea     
             slice_sa        
             factor          
             total_isom      
             depletion       
             effective       
             villi_list      
             inact_const     
             inact_rate      
             inact           
             last_inact      
             total_inact     
             units           
             conc            
             quantity        
             len             
             radius          

DESCRIPTION

Quite a complicated object for calculating stochastic activation of rhodopsin molecules and includes stochastic inactivation by Rhodopsin Kinase or Arrestin. It keeps track of:

Number of rhodopsin molecules per villi, which allows decrease effectiveness with additional villi

time of rhodopsin activation, which allows decrease effectiveness over time due to depletion


Object Type:      rxnpool
datatype          rxnpool_type
function          rxnpool()
class             [ concentration ] [ segment ] 
size              280 bytes
author            A. Blackwell ERIM Aug 96; revised GMU Dec 99; GMU Mar 02

VALID ACTIONS

RESTORE2 SAVE2 CHECK RESET PROCESS INIT

VALID MESSAGES

      [6] VOLUME            vol SAin SAout //This input will change the volume and surface area of the compartment      
      [5] RXN0MOLES         A             //The input value causes quantity independent increase in molecules
      [4] CURRENT           charge current  //Two input values - the current, and the valence of the ion flowing
      [3] RXN2MOLES         A B         //Two input values provided from reactions between elements that track quantity
      [2] RXN2              A B //The input value is a rate constant, multiplied by the existing molecule conc or quantity
      [1] RXN1              B           //The input value is a rate constant, multiplied by the existing molecule conc or quantity
      [0] RXN0              A   //The input value causes concentration independent increase in molecules

FIELDS

             Conc            concentration         
             quantity        quantity in molecules       
             previous_state            
             Cmin            minimum concentration       
             Cinit           initial concentration        
             Qinit           initial quantity in molecules         
             len             length of cylindrical pool        
             radius          radius of cylindrical or spherical pool        
             vol             volume of pool        
             SAside          side surface area of cylinder       
             SAout           outer surface area of spherical shell       
             SAin            inner surface area of spherical shell       
             type            whether pool integrates concentration (0) or quantity (1)        
             units           1 for moles, 1e-3 for mmoles, 1e-6 for umoles        
             Iunits          1e-12 to convert from nA, msec to A,sec       
             Dunits          1 for meters, 1e-4 for cm, etc       
             VolUnitConv     Dunits^3, converts volume to SI units     

DESCRIPTION

Rxnpool is an object used to keep track of molecule concentration and quantity; thus it interacts with reactions, diffusion, pumps,current, and calcium release objects. Regardless of the source of the molecules, it accumulates fluxes into variables A (rate of change independent of concentration) and B (rate of change proportional to concentration) and solves d[C]/dt = A - B*[C].

Inputs of concentration for 0th, 1st and 2nd order reactions are provided through the messages RXN0, RXN1 and RXN2. Inputs of Moles are provided through the messages RXN0MOLES or RXN2MOLES. Inputs of current (uses physiologists convention - that means a negative current is inward, e.g. a negative calcium current increases calcium concentration. To provide input from tabchannels which use modelers conventation, provide a charge (valence) of -2 for calcium (instead of +2). To provide input from either diffusion, CICRflux, an enzyme reaction or a pump, use RXN0MOLES, because these calculate flux between compartments (rxnpools) with unequal volume. Thus, the change in concentration is different for the two different compartments

rxnpool and all other chemesis objects allow for any consistent set of units. Iunits is a value that specifies which units are used, thus if currents are in units of nanoAmps, then Iunits should be 1e-9. If current is in nA and the clocks units are msec, then Iunits = 1e-12

Dunits indicates the units used for length (needed for diffusion). units is a value that specifies which units for quantity (e.g. moles, mmoles, etc) are used. type indicates whether to do the calculations in units of concentation or quantity. If type = 0, converts molecule inputs to concentration and then integrates; if type = 1, converts concentration inputs to molecules and then integrates.


Object Type:      wgtavg
datatype          wgtavg_type
function          wgtavg()
class             [ segment ] 
size              168 bytes
author            A. Blackwell GMU Oct 2011

VALID ACTIONS

RESET PROCESS INIT

VALID MESSAGES

[0] ValueWgt Value wgt

FIELDS

             totValue        total weighted value"      
             totwgt          total of weights      
             meanValue       weighted mean      

DESCRIPTION
An object to calculate a weighted average. Divides total weighted value by total weights. Can calculate the mean calcium from unequal size calcium shells by using volume as weight.


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