Self-oscillating endoplasmic motility study in a strand of plasmodium P. Polycephalum T.I. Avsievich, S.N. Abdulkareem, S.G. Proskurin Biomedical engineering Tambov State Technical University

Endoplasmic motility is an example of auto oscillation, which is inherent to a wide class of cells from single-celled amoebas to cancer cells in multicellular organisms. INTRODUCTION Examples: Belousov - Zhabotinsky reaction; mechanisms in cardiac muscle contraction; nervous impulse propagation; activity in cells from single-celled amoeboid to fibroblasts, leukocytes and tumor cells in multicellular organisms; amoeboid motility P. Polycephalum Autowaves in Belousov - Zhabotinsky reaction

To analyse time-dependent velocity V(t) of self-oscillating motility of endoplasm in the isolated strand of plasmodium Physarum Polycephalum upon exposure to inhibitors of cellular respiration. PURPOSE of the STUDY OBJECTIVES 1. Registration of self-oscillating motility in the strand in normal conditions (buffer solution) and after the inhibitors’ treatment; 2. Fourier analysis of the time dependences V(t) of the endoplasm; 3. Mathematical model describing the registered oscillations.

potassium cyanide (KCN): cytochrome pathway inhibitor salicylhydroxamic acid (SHAM): alternative respiration inhibitor 1) 10 mm strand was isolated out of plasmodium and placed in buffer solution pH=7.2; 2) Strand was treated with KCN and SHAM (5 and 7 µM, respectively) which leads to a cessation of protoplasmic motility; 3)Further inhibitors were removed and strand was placed in the buffer solution. Resumption of endoplasmic motility, V(t) recording for 10 min after. 1) inhibition of aerobic ATP synthesis 2) cessation of breathing 3) cessation of endoplasmic motility MATERIALS and METHODS P. Polycephalum Slime mold Network of cylindrical bands µm in diameter and length up to 2 cm Model organism for many studies involving amoeboid motility

potassium cyanide (KCN) salicylhydroxamic acid (SHAM) MATERIALS and METHODS P. Polycephalum Detector Laser Strand of plasmodium with shuttle endoplasmic motility inside Laser Doppler anemometer Velocity time dependence

RESULTS Spectral analysis (Fast Fourier Transform - FFT) (length 600 s) from 0 and 600 s Solid lines - Gaussian approximations to the peaks Figure 1. Fourier spectra of the time dependence V(t) of protoplasmic motility from 0 to 600 s (blue) and 600 to 1200 s (pink) in the buffer solution. Figure 2. Similar spectra after KCN and SHAM treatment Proskurin S. G., Avsievich T. I., Biophysics, 2014 (in press)

RESULTS ω1ω1 ω2ω2 After removal of respiratory inhibitors During first 10 min increases activity of the first peak and the complete suppression of the second one. On 12th minute, system begins to return to the normal state with two harmonic components. Influence of inhibitors Respiratory inhibitors affect on both sources of oscillation, but one of them (ω 1 ) recovers faster. Proskurin S. G., Avsievich T. I., Biophysics, 2014 (in press)

Buffer solution ( pH=6,8) Spectral analysis reveals two distinct harmonic signals. Despite the frequencies differ in first and second signals, the ratio ω 2 /ω 1 =1.96±2% in each of them remains constant. RESULTS ω 1 and ω 2 remains constant during 20 min: ω 1 =0.013± Hz ω 2 =0.0254± Hz ω 2 /ω 1 = SD 2.6 % at first 10 min just one source of oscillations ω 1 is present, in the next 10 min noted the appearance of a second frequency peak ω 2 : ω 1 =0.0198± Hz ω 2 =0.0388± Hz ω 2 /ω 1 = SD 1.8 % In buffer after treatment by KCN and SHAM

RESULTS Analytical calculation of the self-oscillation frequencies of harmonics: where E - Young's modulus of ectoplasm elasticity, k 1, k 2, k 4 - rate constants, n - harmonic number, l, r – length and radius of the strand, μ – endoplasm viscosity [2]. Theoretical frequencies: ω 1 = Hz, ω 2 = Hz ω 2 /ω 1 =1.89

b) R 2 =0.971 RESULTS Significant correlation between the model and experimental data is observed Time dependences of endoplasmic motility in plasmodium strand before (a) and after removing the respiration inhibitors (b) a) R 2 =0.943

RESULTS Significant correlation between mathematical model and experimental data up to 800 s is observed. Additional parameters are required to describe transition to the normal state. 1 harmonic ω 1 appearance of a second harmonic ω 2 R 2 =0.971

RESULTS Directed motion of endoplasm S+S+ S-S- S+S+ S-S- Directed motion of the strand is different for the first and the second signal Area under the graph is changed S + - above X axis S – - under X axis S + / S - ≈ 0, 6 S + / S - ≈ 1, 6

DISCUSSION and CONCLUSIONS 1)Sign-sensitive laser Doppler velocimetry allows to register shuttle endoplasmic motility in plasmodium strands with diameter up to 0.5 mm; 2)Fourier analysis of velocity time dependences of the endoplasm allows obtaining two distinct harmonic components in both signals; 3)Influence of KCN and SHAM leads to a complete cessation of endoplasmic motility. After removal of the inhibitors the respiratory system becomes normal, gradually restoring the activity of both harmonic oscillation sources; 4)Significant correlation between mathematical model and experimental data were demonstrated.

1.Proskurin S.G., Avsievich T.I., Spectral analysis of self-oscillation motility in isolated plasmodium strand of Physarum Polycephalum // Biophysics (in press). 2. Teplov V.A., Mitrofanov V.V., Romanovsky Y.M., Synchronization of mechanochemical auto-oscillations within the Physarum polycephalum plasmodium by periodical external actions // Biophysics. 2005, T. 50, № 4. p REFERENCES

Self-oscillating endoplasmic motility study in a strand of plasmodium P. Polycephalum T.I. Avsievich, S.N. Abdulkareem, S.G. Proskurin Biomedical engineering Tambov State Technical University