ORIGINAL ARTICLE: Hunley, C., Mohsin, M., & Marucho, M. (2022). Electrical impulse characterization along actin filaments in pathological conditions. Computer Physics Communications, 275, 108317. https://doi.org/10.1016/j.cpc.2022.108317
Article Abstract: We present an interactive Mathematica notebook that characterizes the electrical impulses along actin filaments in both muscle and non-muscle cells for a wide range of physiological and pathological conditions. The simplicity of the theoretical formulation, and high performance of the Mathematica software, enable the analysis of multiple conditions without computational restrictions. The program is based on a multi-scale (atomic → monomer → filament) approach capable of accounting for the atomistic details of a protein molecular structure, its biological environment, and their impact on the travel distance, velocity, and attenuation of monovalent ionic wave packets propagating along micro-filaments. The interactive component allows investigators to choose the experimental conditions (intracellular Vs in vitro), nucleotide state (ATP Vs ADP), actin isoform (alpha, gamma, beta, and muscle or non-muscle cell), as well as a conformation model that covers a variety of mutants and wild-type (the control) actin filaments. We used the computational tool to analyze environmental changes such as temperature effects and pH changes of the surrounding solutions, as well as structural changes to an actin monomer due to radius changes. Additionally, we investigated for the first time the electrostatic consequences of actin mutations from different disease conditions. These studies may provide an unprecedented molecular understanding of why and how age, inheritance, and disease conditions induce dysfunctions in the biophysical mechanisms underlying the propagation of electrical signals along actin filaments.

A brief description of the field and our focus

Actin is an abundant biopolymer inside all eukaryotic (animals, plants, and fungi) cells. Actin, along with two other biopolymers, gives cells their shape and rigidity; that is why they are called cytoskeleton (skeleton of cell). Cytoskeleton polymers also help cell division and cellular cargo transport in subcellular compartments. Besides those well-understood biological and biophysical roles, cytoskeleton has an emerging attribute.
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Actin and microtubules have significant negative surface charges. Therefore, these polymers can attract positive ions (sodium, potassium, and calcium) from the cytoplasm. These condensed ions (counter-ions) can then transmit along the cytoskeleton polymer, forming an ionic current and giving cytoskeleton transmission line-like properties. Experimental evidence shows ionic signals can transport, amplify, and oscillate along actin and microtubule. Thus, these filaments have the potential to act as bio-transistors and can take part in information processing in neuronal cells. We can have answers to unknown questions regarding the distinctive formation of memory and conscience, learning and perception. Also, the electrical activities of these conducting polymers can be either used or mimicked to develop biological computers. However, we still need to establish theories and models for explaining the electrical properties of the cytoskeleton, which is crucial for the advancement of the field and for the development of new technologies.
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Our group studies the electrical properties of the cytoskeleton experimentally and develops theories and computational models. We have a multiscale theory for ionic current along actin. Using that theory, we wrote a notebook to analyze the electrical impacts of various environmental factors and mutations of actin filaments.

About the notebook

This notebook can be an excellent resource for studying ionic currents along actin . The notebook can also be a good pedagogical tool for scientific computations, data representations, and Mathematica . The notebook uses graphical user interfaces (GUI) for taking user input and displaying success message . It utilizes advanced plotting techniques in Mathematica to get highly interactive plots and animations . Moreover, the notebook uses advanced programming techniques and coding styles, memoization techniques and packed arrays for memory efficiency, and parallel computing techniques for time efficiency .
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  • Memory required: ~ 0.1GB
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  • Calculation time: ~ 1 minute
    • Button["Click this box to run the notebook. Once prompted insert appropriate inputs and click 'Proceed'. Wait for the message 'The calculations are over.' Use the sliders and check boxes (if available) to change the parameters to see the changes in plots.",​​FrontEndExecute[​​FrontEndToken[​​InputNotebook[],"EvaluateNotebook"​​]​​],​​ImageSize{700,150},​​BaseStyle->"Subsection"]
    Click this box to run the notebook. Once prompted insert appropriate inputs and click 'Proceed'. Wait for the message 'The calculations are over.' Use the sliders and check boxes (if available) to change the parameters to see the changes in plots.
    In[]:=
    ClearAll["Global`*"]
    In[]:=
    Needs["Developer`"]

    1. Mutations

    Here, we create dictionaries (Mathematica associations) of all reported actin mutations and corresponding diseases. The dictionaries are used for user inputs and in later calculations.

    1.1 ACTG2

    In[]:=
    ACTG2mutations={{"Arg36His","Chronic intestinal pseudo obstruction"},{"Arg38Cys","MMIHS"},{"Arg38His","MMIHS"},{"Met43Thr","MMIHS"},{"Arg61Gln","MMIHS"},{"Arg61Gly","MMIHS"},{"Lys117Arg","Visceral myopathy, familial"},{"Tyr132Asn","MMIHS"},{"Gly145Cys","Chronic intestinal pseudo obstruction"},{"Arg146Leu","Chronic intestinal pseudo obstruction"},{"Arg146Ser","Visceral myopathy, familial"},{"Arg176Cys","MMIHS"},{"Arg176His","MMIHS"},{"Arg176Leu","MMIHS"},{"Arg176Ser","MMIHS"},{"Thr193Ile","Chronic intestinal pseudo obstruction"},{"Gly196Asp","MMIHS"},{"Ala203Thr","Micro-colon megacystic syndrome"},{"Arg209Gln","Visceral myopathy, familial"},{"Arg209Term","Severe intestinal pseudo-obstruction"},{"Arg255Cys","MMIHS"},{"Arg255His","Visceral myopathy, familial"}};
    In[]:=
    ACTG2mutationsAssoc=AssociationThread[ACTG2mutations[[All,1]]->ACTG2mutations[[All,2]]];

    1.2 ACTA2

    In[]:=
    ACTA2mutations={{"Glu3Gln","Thoracis aortic disorder"},{"Cys17Arg","Aortic disease"},{"Gly20Ser","Aortic disease"},{"Asp24Tyr","Thoracic aortic aneurysms and dissections"},{"Asp25Gly","Thoracic aortic aneurysms and dissections"},{"Gly36Arg","Thoracic aortic aneurysms and dissections"},{"Arg37Cys","Thoracic aortic aneurysms and dissections"},{"Arg37Gly","Aortic disease"},{"Arg38His","Thoracic aortic disease, coronary artery disease and strokes"},{"Arg37Ser","Aortic dissection, acute"},{"Pro38Ser","Thoracic aortic aneurysms and dissections"},{"His40Asn","Thoracic aortic aneurysms and dissections"},{"Val43Leu","Thoracic aortic aneurysms and dissections"},{"Met44Arg","Patent Ductus Arteriosus"},{"Met47Val","Thoracic aortic aneurysms and dissections"},{"Gly48Val","Aortic disease"},{"Asp56Asn","Aortic dissection, acute"},{"Ala58Glu","Thoracic aortic disorder"},{"Gln59Arg","Thoracic aortic aneurysms and dissections"},{"Arg62Lys","Aortic disease"},{"Leu67Gln","Aortic disease"},{"Pro70Gln","Thoracic aortic aneurysms and dissections"},{"Asp80Glu","Thoracic aortic aneurysms and dissections"},{"Trp86Arg","Aortic disease"},{"Thr106Met","Thoracic aortic aneurysm"},{"Asn111Thr","Thoracic aortic aneurysms and dissections"},{"Asn115Ile","Thoracic aortic aneurysms and dissections"},{"Asn115Ser","Thoracic aortic aneurysms and dissections"},{"Asn115Thr","Thoracic aortic aneurysms and dissections"},{"Arg116Gln","Thoracic aortic aneurysms and dissections"},{"Met132Thr","Aortic dissection"},{"Tyr133His","Thoracic aortic aneurysms and dissections"},{"Ala138Val","Thoracic aortic aneurysms and dissections"},{"Val139Ala","Aortic disease"},{"Tyr143Cys","Thoracic aortic aneurysms and dissections"},{"Gly146Arg","Aortic disease"},{"Arg147Cys","Thoracic aortic aneurysms and dissections"},{"Val152Ala","Thoracic aortic aneurysms and dissections"},{"Gly158Asp","Thoracic aortic aneurysms and dissections"},{"Val159Ala","Aortic aneurysm"},{"His161Gln","Aortic disease"},{"Pro164Thr","Aortic disease"},{"Tyr166Asn","Thoracic aortic aneurysms and dissections"},{"Arg177Cys","Cardiovascular, autonomic and brain anomalies"},{"Arg177His","Multisystem smooth muscle dysfunction"},{"Arg177Leu","Cerebrovascular disease"},{"Arg177Ser","Multisystem smooth muscle dysfunction"},{"Arg183Gln","Thoracic disease and coronary artery disease"},{"Tyr188Ser","Marfan syndrome with aortopathy"},{"Met190Val","Aortic disease"},{"Arg196Cys","Aortic disease"},{"Arg196His","Aortic disease"},{"Val201Ile","Thoracic aortic aneurysms and dissections"},{"Val201Leu","Thoracic aortic disorder"},{"Arg210Gln","Thoracic aortic disease, coronary artery disease and strokes"},{"Glu241Lys","Thoracic aortic aneurysms and dissections"},{"Leu242Phe","Aortic disease"},{"Pro243His","Thoracic aortic disease and strokes"},{"Pro243Leu","Aortic disease"},{"Ile248Leu","Thoracic aortic disease and strokes"},{"Arg254His","Thoracic aortic aneurysms and dissections"},{"Arg256Cys","Thoracic aortic aneurysms and dissections"},{"Arg256His","Thoracic aortic disease and strokes"},{"Gly268Arg","Aortic disease"},{"Gly268Glu","Thoracic aortic aneurysm"},{"Gly273Ala","Thoracic aortic aneurysms and dissections"},{"Thr277Ala","Thoracic aortic disorder"},{"Ile282Asn","Thoracic aortic aneurysms and dissections"},{"Met283Thr","Thoracic aortic disorder"},{"Ser300Ala","Thoracic aortic aneurysms and dissections"},{"Gly302Arg","Thoracic aortic aneurysms and dissections"},{"Gly302Ser","Thoracic aortic disorder, nonsyndromic"},{"Arg312Term","Thoracic aortic aneurysms and dissections"},{"Thr324Asn","Thoracic aortic disease, coronary artery disease and strokes"},{"Lys326Asn","Thoracic aortic aneurysms and dissections"},{"Gly342Ser","Aortic dissection, acute"},{"Leu346Arg","Thoracic aortic aneurysms and dissections"},{"Thr351Asn","Thoracic aortic aneurysms and dissections"},{"Gly366Arg","Schizophrenia"},{"Arg372Cys","Thoracic aortic disorder"}};
    In[]:=
    ACTA2mutationsAssoc=AssociationThread[ACTA2mutations[[All,1]]->ACTA2mutations[[All,2]]];

    1.3 ACTC1
    

    1.4 ACTA1
    

    1.5 ACTG1
    

    1.6 ACTB
    

    2. User inputs
    

    3. Parameters

    This section uses physical constants and inputs from the previous section to calculate quantities like electrical resistance, capacitance, and impedance for intracellular and in-vitro ionic conditions. As these quantities are functions of environmental properties (pH, temperature) and structural properties (length, radius, conformations), we define functions capable of computing those using input parameters.

    3.1 Cylinder and electrolyte Parameters and constants

    3.1.1 cylinder Parameters

    We model the polymer as cylindrical. Here, we evaluate the cylinder parameters: length, radius, and surface charge density. We use user inputs and values extracted from protein databank structures.
    QpHicong=QuantityArray[{23,-82,-154,-184,-222},"ElementaryCharge"];​​isom=Which[isoform=="alpha-skeletal(ACTA1)",0,isoform=="alpha-cardiac(ACTC1)",0,isoform=="alpha-smooth(ACTA2)",0,isoform=="gamma-smooth(ACTG2)",1,isoform=="beta-cytoplasmic(ACTB)",1,isoform=="gamma-cytoplasmic(ACTG1)",1];​​nucl=Which[nucleotide=="ATP",0,nucleotide=="ADP",1];​​state=Which[mut=="wild type",0,mut=="mutant (options in next screen)",1];​​QpHi=QpHicong+14*QuantityArray[{isom+nucl+mutation*state,isom+nucl+mutation*state,isom+nucl+mutation*state,isom+nucl+mutation*state,isom+nucl+mutation*state},"ElementaryCharge"];​​L=Quantity[422.20,"Angstroms"];​​LAF=422.20×
    -10
    10
    ;​​CylRad=Quantity[len,"Angstroms"];​​CylRadd=QuantityMagnitude[UnitConvert[CylRad]];​​denom=2×π×CylRad;​​Lm=Quantity[5.4,"Nanometers"];​​uLm=QuantityMagnitude[UnitConvert[Lm]];​​sSurfCyl=2×π×CylRad×Lm;​​SurfCyl=QuantityMagnitude[UnitConvert[sSurfCyl]];​​rzp=CylRadd;

    3.1.2 Constants

    Here are the physical constants we need for our calculations.
    ϵ0=N[QuantityMagnitude[UnitConvert[Quantity["ElectricConstant"]]]];​​R=QuantityMagnitude[UnitConvert[Quantity["MolarGasConstant"]]];​​F=QuantityMagnitude[UnitConvert[Quantity["FaradayConstant"]]];​​ue=Quantity["ElementaryCharge"];​​e=QuantityMagnitude[UnitConvert[Quantity["ElementaryCharge"]]];​​uKb=Quantity["BoltzmannConstant"];​​Kb=QuantityMagnitude[UnitConvert[Quantity["BoltzmannConstant"]]];​​
    Intracellular
    In-vitro

    4. Theory

    This section uses the multiscale theory developed by our group to calculate voltage signals as functions of position, time, pH, and input voltage. The functions are then used to demonstrate results.

    4.1 Equations

    4.2 Intracellular

    5. Results

    We present the results through interactive plots and animations (Mathematica manipulates). Users have already chosen some parameters in the beginning. Now, they have more control in viewing and analyzing the results. They can select ionic conditions (intracellular or in-vitro) and change pH and input voltage. Our considered range includes physiological, and all reported pathological conditions.

    5.1 Potential profile

    5.2 Ion velocity profile

    5.3 Effective electric conductivity

    5.5 Ion Current density

    Longitudinal

    Transversal

    5.9 Soliton profile animations in Intracellular electrolytes

    Animations show ion signal wave-packet (soliton) propagation in intracellular conditions.

    CITE THIS NOTEBOOK

    Electrical signal propagation along Actin filaments in physiological and pathological conditions​
    by Md Mohsin​
    Wolfram Community, STAFF PICKS, December 1, 2023
    ​https://community.wolfram.com/groups/-/m/t/3075476