Apparent Anomalous Diffusion in the Cytoplasm of Human Cells: The

Subscriber access provided by UNIVERSITY OF THE SUNSHINE COAST

Article

Apparent Anomalous Diffusion in the Cytoplasm of Human Cells: The Effect of Probes’ Polydispersity Tomasz Kalwarczyk, Karina Kwapiszewska, Krzysztof Szczepanski, Krzysztof Sozanski, Jedrzej Szymanski, Bernadeta Michalska, Paulina Patalas-Krawczyk, Jerzy Duszynski, and Robert Holyst J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b07158 • Publication Date (Web): 28 Sep 2017 Downloaded from http://pubs.acs.org on October 3, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Apparent Anomalous Diffusion in the Cytoplasm of Human Cells: The Effect of Probes’ Polydispersity Tomasz Kalwarczyk,∗,†,¶ Karina Kwapiszewska,∗,†,¶ Krzysztof Szczepanski,† Krzysztof Sozanski,† Jedrzej Szymanski,‡ Bernadeta Michalska,‡ Paulina Patalas-Krawczyk,‡ Jerzy Duszynski,‡ and Robert Holyst∗,† †Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland ‡Nencki Institute of Experimental Biology of the Polish Academy of Sciences, 3 Pasteur Street 02-093 Warsaw, Poland ¶Contributed equally to this work E-mail: [email protected]; [email protected]; [email protected]

1 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract This work, based on in vivo and in vitro measurements, as well as in silico simulations, provides a consistent analysis of diffusion of polydisperse nanoparticles in cytoplasm of living cells. Using the example of fluorescence correlation spectroscopy (FCS) we show the effect of polydispersity of probes on the experimental results. Although individual probes undergo normal diffusion, in the ensemble of probes an effective broadening of the distribution of diffusion times occurs - similar to anomalous diffusion. We introduced fluorescently labeled dextrans into cytoplasm of HeLa cells and found that cytoplasmic hydrodynamic drag, exponentially dependent on probe size, extraordinary broadens the distribution of diffusion times across the focal volume. As a result the in vivo FCS data were effectively fitted with anomalous subdiffusion model while for monodisperse probe the normal diffusion model was most suitable. Diffusion time obtained from anomalous diffusion model corresponds to a probe whose size is determined by the weight average molecular weight of the polymer. The apparent anomaly exponent decreases with increasing polydispersity of the probes. Our results and methodology can be applied in intracellular studies of mobility of nanoparticles, polymers, or oligomerizing proteins.

Introduction Polydispersity is an ubiquitous characteristics of nanoparticle populations. 1 It is common in natural systems such as biosynthesized polymers 2 or proteins with oligomerization functionality 3 and is also unavoidable in artificial synthesis of nanoobjects or polymers. 4 Moreover, technicalities 5

of current fractionation and purification procedures make complete monodispersity impossible to obtain for probes commonly used in living cells, i.e. dextrans. 5 Therefore, any physical model applied for description of nanoparticle-based experiments should be reconsidered according to possible polydispersity. Determination of rheological properties of living cells’ interior is one of the fields of inter-

10

est of contemporary biophysics and an area where nanoscopic probes find their broad applica2 ACS Paragon Plus Environment

Page 2 of 23

Page 3 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


tion. Fluorescently labeled particles are introduced into a cell and their diffusion coefficients are non-invasively measured by the means of e.g. fluorescence correlation spectroscopy (FCS) or fluorescence recovery after photobleaching (FRAP). 6,7 In the literature one can find only several approaches to the analysis of FCS data for polydisperse probes at in vitro* conditions. 8–10 In vivo 15

studies, however, are still missing, yet highly required. Researchers working in the field of single cell biophysics face numerous impediments resulting from complex structure of the cell interior. Eucaryotic cells consist of a dynamic structure of vesicles, cytoskeleton and numerous intracellular compartments separated by membranes. The cytosol itself is a complex liquid of reported heterogeneity. 11 On the other hand when membrane affinitive

20

probes are used they can attach and disattach of the membrane. Such dynamics causes that the effectively observed probes’ motion is a combination of normal 3D diffusion and 2D diffusion in the membrane, 12 or can be attributed to the attaching/disattaching reaction kinetics. 13 Additionally, we have recently shown that diffusion coefficients D of probes in the cytoplasm do not scale directly with the reciprocal of the probe radius rp .† In fact, D is a stretched exponential function of the

25

length-scale of the flow around the probe. The latter quantity is comparable to rp . 16–20 According to this length-scale dependent hydrodynamic drag (LSD) concept, the hydrodynamic drag ( f (rp )) is inversely proportional to the diffusion coefficient and is given by the following equation:  !   ξ 2 ξ 2 −a/2  f (rp) D0  , = = C exp  2 + 2 f0 D Rh r p

(1)

where D0 stands for the diffusion coefficient of a given particle in a buffer; f0 is the hydrodynamic drag of a buffer‡ ; C ∼ 1; ξ and Rh are two length-scale characteristic for a given system, and a is 30

an exponent smaller than 1. In this paper we present the joint effect of probes’ polydispersity and of the hydrodynamic drag of the HeLa cell cytoplasm on the in vivo FCS measurement results. Taking into account cellular * For the purpose of this paper we will use ”in vivo ” term as ”in cytoplasm of a living cell (cultured in Petri dish)”, while ”in vitro ” will refer to ”in the buffer”. † Such dependence would be expected from the Stokes-Sutherland-Einstein (SSE) relation, D = kT/6πηrp , 14,15 where k is the Boltzmann constant, T is the absolute temperature, and η denotes the constant viscosity of the medium. ‡ f0 = 6πη0 rp , where η0 denotes viscosity of the buffer.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 23

heterogeneity, we focus only on the cytosol. We used non-cytotoxic 21 probe, dextran, which is suspected to be non-interacting with membranes in order to avoid influence of attractive interactions 35

between probe and membranes. We show that, according to the LSD model, polydispersity of the probe is more pronounced in the cytosol than in vitro while for monodisperse probes the effect is not visible. The outcome of this paper provides simple methodology for the interpretation of the fluorescence correlation spectroscopy data for polydisperse probes diffusing inside cytoplasm of living cells (Figure 1). Our approach is based on the anomalous subdiffusion model describing the

40

FCS autocorrelation function. We performed in vivo (human HeLa cells) and in vitro experiments as well as in silico calculations on model polydisperse probes. On the basis of experimentally obtained distributions of molecular weights of polymers, we calculated distributions of diffusion times across the focal volume. The results were further compared with the data obtained by FCS for the in vitro and in vivo environments. For in vitro measurements the anomalous subdiffu-

45

sion model is experimentally indistinguishable from the single-component model. The effect of polydispersity is clearly visible, however, at in vivo conditions. We reveal that the LSD of cell cytoplasm causes unusual broadening of the distribution of diffusion times. We also indicate that the expected distributions of diffusion times amplitudes are in agreement with the diffusion times measured experimentally and interpreted in terms of the anomalous subdiffusion model. Finally,

50

we use numerical calculations to predict how the anomalous exponent, α, changes with the polydispersity of the probes. The predictions are also compared with the experimentally measured α exponents at in vivo conditions, proving consistency of the model.

Theory The general form of the FCS autocorrelation function can be expressed as: .

G (τ) = 1 +

n 1X Ai N i=1

1 τ 1+ τD,i

1 !α s

1+

1 τ κ2 τD,i


!α

(2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


G (τ)

Page 5 of 23

τ G (τ) ∼

D f rp

D

1 α 1+ ττ D

Lag time

f rp

Mw

rp

Molecular weight Figure 1: A scheme of the procedure allowing to determine the length-scale dependent hydrodynamic drag of the cytoplasm (see Equation (1)) using polydisperse probes. From the anomalous subdiffusion fit of the FCS autocorrelation curve the diffusion time, τD, of an average probe can be obtained, and thus the diffusion coefficient of the average probe D f rp can be determined (according to D = ω2 /4τD , where ω denotes the width of the waist of the focal volume). Simultaneously on the basis of the known weight average molecular weight of probes Mw , from the molecular weight distribution, the size of the average probe, rp , is determined. Both D and rp give the f rp dependence on rp . In this work we used a back-engineering method. We knew the f rp dependence and we compared the results with those predicted on the basis of Mw . 55

Here N stands for the average number of fluorescent probes inside the focal volume, τD is the time of diffusion of an average probe across the focal volume, Ai corresponds to the amplitude of i-th component, and κ is the aspect ratio of the focal volume. The simplest case when only one type of diffusing species is present in the sample can be characterized by Equation (2) for 5 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

n = 1, A = 1, and α = 1. This model was used for in vivo analysis of such probes as coumarin, 7 60

8-Hydroxypyrene-1,3,6-trisulfonate, 22 nanodiamonds, 23 DNA, 24 or adenylate kinase tagged with EGFP. 25 It was previously shown 12 that the FCS data for probes resembling affinity to membranes can be analyzed as a sum of two models: the normal diffusion model and two dimensional diffusion model. More often, in vivo data are fitted with a multicomponent variant of the model, where n > 1 and α = 1. 26–32 Due to the character of the probe and/or cytoplasm, a two- or even three- compo-

65

nent model describes the FCS data obtained in vivo well, but usually without satisfying physical justification of the origin of each component. 29,30 Another model that is frequently used to describe in vivo FCS data is the anomalous subdiffusion model. 27,28,31,33–36 In this model n = 1 and A = 1, but α < 1. By definition, diffusion is considered anomalous when the dependence of the mean square displacement h∆x (t)i2 on time

70

t becomes nonlinear: h∆x (t)i2 ∝ tα ; α , 1. Subdiffusion (α < 1) is believed to result from hindering of the probe’s motion, which most likely occurs in the complex matrix of cytoplasm 37 or stems from the heterogeneity of the cellular structure. 11 Validity of the usage of the anomalous subdiffusion model in such cases is still debated. The major weakness of that model is the lack of understanding of the factors causing the anomality. Moreover, there are works indicating that the

75

theory of anomalous subdiffusion contains mathematical contradiction 38 when considered in terms of FCS experiments. Nevertheless, models aiming to elucidate the anomalous diffusion concept are being developed. 39 One of the possible explanation of the observed apparent subdiffusive behavior is the polydispersity of the probes. 38,40 In such case each probe moves via normal Brownian diffusion (i.e. with α = 1), but the lack of size homogeneity in the probe’s population broadens

80

the distribution of the probe diffusion coefficients. This inhomogeneity affects the autocorrelation curve – which constitutes a certain average over the whole probe population – in a similar manner as expected for subdiffusive motion of the probe. Taking into account the diversity of models used for description of FCS data, it is clear that thorough characterization of probes used in the experiments is required for proper interpretation

85

of the data. As a consequence the information about the probes’ size, shape, and chemistry is


Page 6 of 23

Page 7 of 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


mandatory to avoid experimental artifacts and misinterpretations. 41

Materials and Methods Characteristics of fluorescently labeled dextrans Commercially available dextrans (Sigma-Aldrich) labeled with tetramethylrodamine isothiocyanate 90

(TRITC) were used for experiments. Molecular weights of dextrans ranged from 4.4kDa to 155kDa. The dextrans were characterized by means of gel permeation chromatography (GPC) using TSK gel columns. As a result, distributions of molecular weights were obtained (Figure S1 in the Supporting Information, SI). On the basis of those distributions the weight average molecular weight, Mw , and the number average molecular weight, Mn , were calculated (Table 1 ).

95

Average hydrodynamic radii, rp , of the polymers were found experimentally in FCS measurements conducted in pure water. On that basis the dependence of rp on molecular weight of dextrans was established based on the log-log fit of the rp vs. Mw :

rp = r0

Mw Mw0

!ν

(3)

,

where r0 = 0.043 ± 0.017 (in nm), ν = 0.42 ± 0.04, Mw is given in g/mol, and Mw0 = 1 g/mol. Table 1: Characteristics of the polymeric probes used in the experiments. Sample Name Dex-4.4kDa Dex-20kDa Dex-40kDa Dex-75kDa Dex-155kDa

Mn [g/mol] 3,550 26,250 56,000 122,480 252,970

Mw [g/mol] 4,740 35,950 72,890 176,900 366,720

PDI 1.334 1.370 1.301 1.444 1.450

rp [nm] 1.3 ± 0.2 3.8 ± 0.3 4.9 ± 0.5 5.6 ± 0.5 8.6 ± 0.7

Mn - number average molecular weight; Mw - weight average molecular weight; PDI - polydispersity index defined by the Mw /Mn ratio; rp - hydrodynamic radius of the probes measured in water by means of FCS.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Cell culture and microinjection 100

HeLa cells were cultivated in monolayer cultures using Dulbecco’s modified Eagle’s medium (purchased from the Institute of Immunology and Experimental Technology, Wrocław, Poland) supplemented with 10%vol fetal bovine serum, penicillin (100 mg/ml) and streptomycin (100 mg/ml) (Sigma-Aldrich). Cells were maintained at 37°C in a 5% CO2 humidified atmosphere. For microinjection procedure cells were grown on 35 mm glass bottom CELLview™ Cell Cul-

105

ture Dish (Greiner Bio One) to approximately 30% of confluence. Microinjection was performed by Femtojet® system (Eppendorf), with glass capillaries of diameters

Apparent Anomalous Diffusion in the Cytoplasm of Human Cells: The

Recommend Documents