## 2 Materials and Methods
### Biofuling Model  
The presence of a biofilm on a microplastic particle changes its density. According to [49], we calculate the density of a spherical particle as follows:  
\[\rho_{p}=\rho_{0}\frac{R_{0}^{3}}{\left(R_{0}+BT\right)^{3}}+\rho_{b}\Bigg{[} 1-\frac{R_{0}^{3}}{\left(R_{0}+BT\right)^{3}}\Bigg{]}, \tag{3}\]  
where \(R_{0}\) is the initial radius of the particle (m), \(\rho_{0}\) is the density of the polymer (kg/m\({}^{3}\)), \(\rho_{b}\) is equals= to 1170 kg/m\({}^{3}\) (as proposed in [50]), and \(BT\) is the thickness of the biofilm (m). The evolution of biofilm thickness is determined separately for particles frozen into ice and particles floating freely in the ocean. In ice, \(BT\) is determined based on the seasonal variability in sea-ice algal biomass (mg/m\({}^{2}\)), the model estimation of which is graphically presented in [51]. The study shows pan-Arctic results obtained from a Sea Ice Model for Bottom Algae (SIMBA), with the algal bloom being triggered by light and showing a latitudinal dependency. We have fitted a function \(f_{ice}\) reflecting the main features of sea-ice algal biomass behavior over the year (see Supplementary Materials, Formula (S1)). We assume that a biofilm exists at the same concentration on a particle in the ice, so the biofilm thickness is  
\[BT=\frac{f_{ice}}{\rho_{b}}\cdot 10^{-6} \tag{4}\]  
and corresponds to the graphs illustrated in Figure 2.  
For particles floating in the ocean, the biofilm thickness is determined from the total volume of the particle \(V_{tot}\) (m\({}^{3}\)) and the size of the clean particle:  
\[BT=\left(\frac{3}{4\pi}V_{tot}\right)^{1/3}-R_{0}, \tag{5}\]  
\[V_{tot}=V_{0}+V_{b}, \tag{6}\]  
\[V_{0}=\frac{4}{3}\pi R_{0}^{3}, \tag{7}\]  
\[V_{b}=V_{A}AS_{0}. \tag{8}\]  
Here, \(V_{0}\) is the volume of a spherical microplastic particle (m\({}^{3}\)), \(V_{b}\) is the volume of biofilm (m\({}^{3}\)), which depends on the number of algae cells \(A\) (no./m\({}^{2}\)) attached to the unit surface area of the particle. Each algae cell has a volume \(V_{A}=2\times 10^{-16}\) m\({}^{3}\) (average value from the data evaluated in [52]), and the total surface area of the particle is \(S_{0}=4\pi R_{0}^{2}\). Modeling of attached algae dynamics is based on the method proposed in [PERSON] et al., 2017 [42]. The simulated change in the number of attached algae cells per unit area of plastic particle over time, dA/dt, is determined based on two biomass accumulation processes (collision of MPs with algae in surrounding water and attached algae growth) and two biomass loss processes (mortality and respiration of attached algae):  
\[\frac{dA}{dt}=\frac{\beta_{A}A_{w}}{S_{0}}+\mu_{A}A-m_{A}A-Q_{10}^{(T-20)/10}R _{A}A, \tag{9}\]  
where \(A_{w}\) is the surrounding water algae concentration (no./m\({}^{3}\)), \(\beta_{A}\) is the collision rate (m\({}^{3}\)/day), \(\mu_{A}\) is the attached algae growth rate (1/day), \(m_{A}\) is the grazing or mortality rate (1/day), \(R_{A}\) is the respiration rate (1/day), and the coefficient \(Q_{10}\), depending on water temperature \(T\) (\({}^{\circ}\)C), indicates how much the respiration rate increases when the temperature increases by 10 \({}^{\circ}\)C.  
Figure 2: Seasonal evolution of biofilm thickness for particles embedded into the ice. To obtain the concentration of algae in the surrounding water, \(A_{w}\), we follow an approach that was also used in the Kooi model [42]. \(A_{w}\) is estimated by converting the chlorophyll-a concentration into carbon:  
\[Chl\;a:C=0.003+1.0154e^{0.050T}e^{-0.059I_{z}/10^{6}}\mu^{\prime}, \tag{10}\]  
and then converting the carbon into the number of algae cells per unit volume using a constant value:  
\[BT=\frac{f_{ice}}{\rho_{b}}\cdot 10^{-6} \tag{4}\]0  
In Equation (10), \(I_{z}\) is the light intensity (\(\mu\text{E}/\text{m}^{2}/\text{day}\)) at a certain depth, which is determined according to the exponential decrease in the water column of a radiation beam transmitted through the ocean surface.