Biased or correlated random walk of proteins in the intracellular compartment may shape various cellular responses. We report sensitivity of protein walk to external static magnetic field that is equivalent to subjecting the protein solution to a spin perturbation. We explain this spin-response by super-paramagnetism of individual tryptophan residues present in a set of randomly chosen proteins. The correlated random walk system can thus facilitate magneto-sensing in biological system, a subject that is of some recent interest.


Magnetism Of Tryptophan And Walk Memory Of Proteins

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Figure 1. Magnetic field induced altered phase space of proteins and magnetism of l-tryptophan: Aqueous solution of l-tryptophan was dried in absence (control) and in presence (pre-incubated) of 0.2 Tesla magnetic field. Magnetic analysis was performed using the dried sample. (a) Magnetization vs temperature (M-T) measurement of SMF pre-incubated (red lines) and control (blue lines) l-tryptophan. Solid and broken lines indicate Zero Field Cooling (ZFC) and Field Cooling (FC) profiles. (b) Magnetization vs Field (M-H) plot of l-tryptophan. Black arrows indicate the maximum positive magnetization as well as the threshold external field strength, beyond which reversal of magnetization occurs. From (c) to (k) are the phase space (XY) trajectories of proteins (BSA, ferritin and fibrinogen).

Scattering based imaging was performed before, after 1 minute and after 5 minutes of 0.2 T magnetic field exposure. In each condition video imaging was performed for 1 minute. In each 1 minute video, 3000-3500 particles were imaged. The X, Y coordinates of each particle was used to construct the pseudo-colored images (see material methods for the algorithm). The pseudo-colored images contain 10,000 grids (100X100) and white pixels indicate the temporal evolution of the X, Y coordinates. (c, d, e) are for BSA, before (c), after 1 minute (d) and after 5 minutes (e) of magnetic field exposure. Similarly, in same order (f, g, h) and (i, j, k) are for ferritin and fibrinogen respectively.


The presence of quantum coherence in biological system came as a surprise , as it implied presence of large scale spatio-temporal coherence at physiological conditions. This is unlike the presence of quantum tunnelling like events reported in certain biomolecular interactions [1] or electron hopping in electron transfer reactions [2] , reported decades back. The counterintuitive part of the new and challenging discipline of quantum biology is not centred around whether quantum effects exists in biosystems. It follows rather trivially that the answer to that question is affirmative [3] . What remains unexplained is how large scale quantum events can persist. A strong bias in this perspective is to postulate a few specialized proteins like cryptochromes [4] [5] which can serve as an amplifier of quantum events.

In this paper we have looked into the the matter from an independent perspective. Can correlated random walk serve as an amplifier of small perturbations and behave also as a memorizing machinery. We have studied the random walk patterns of a magnetic and two nonmagnetic proteins and shown how irrespective of their magnetic property they can memorize exposure to static magnetic field (SMF). We propose this as a spin memory of the protein ensemble. The paradigm shift that is needed in explaining the quantum coherence may lie in such correlated random walk of proteins, when they are translated, modified or undergo streaming or degradation in the cell. This view may be alternative to the proposed view that radical pair mechanism or triplet fusion present in some acceptor-donor combine cause the large scale coherence.


The present paper considers the question of magneto sensing and magnetic memory in biomolecular interaction. As our understanding of cellular communication is based on electrical , chemical or even vibrational components , the existence of a new interaction component (superparamagntism) at the level of amino acids may substantiate our insights in biomolecular interaction and cellular communication process.

Results & Discussion

First of all, we measured the magnetic properties of tryptophan with and without magnetic pre-incubation. Figure 1 (a) and (b) shows the super paramagnetic behavior of tryptophan and field dependent dynamic magnetic transition of the same respectively. Figure 1 (a) shows the zero-field (solid line) and with field (broken line) magnetization profile of trp at different temperatures. The super paramagnetic nature of the amino acid is confirmed by presence of a Neel temperature (blocking temperature)

(indicated by arrow in Figure 1a)
[6] at which

changes sign from positive to negative value. The red and blue profiles compare samples pre-exposed and unexposed to SMF. Incidentally, the existence of

for tryptophan (approx 110°K) asserts its super paramagnetic behavior, this being reported for the first time. It may be further noted that blocking temperature for field exposed and unexposed samples are identical. Now,

is a product of magnetic anisotropy and domain volume. As magnetization of the exposed sample (zero field, red line) shows a higher magnetization at

, a higher magnetic anisotropy is expected in the said case, and this has to be compensated by reduction of magnetic volume as result of the SMF exposure. The magnetization vs field (M-H) plot of tryptophan clearly indicates the retention of magnetization at zero field (see gray arrow of Figure 1b). Not only that, but a positive magnetization is also observed up to a threshold value of external field (see black arrow of Figure 1b). After that, negative magnetization is observed.

The basis of the observed transition from positive to negative magnetization with increasing applied field needs further study. In metallic system (gold nanoparticles) this type of field dependent magnetization can be explained by interface effects [7] .We have tried to explain the probable mechanism of such phenomenon in nonmetallic system in the following section. But, our finding may provide the physical basis of a reported phenomenon [8] regarding the magnetic field induced optical memory of tryptophan.

Interestingly, for proteins we did not find such differential optical behavior of tryptophan in response to magnetic field exposure. But, we found differential auto-correlation decay pattern in dynamic light scattering study after magnetic field exposure (data not shown). It was natural to question whether the static field had any effect on the protein structure. Any structural change would lead to changes in auto-correlation decay pattern.

Our studies using Circular Dichroism (CD) or ANS fluorescence showed no structural change in the time scale of the study. This indicates that either such change is absent or the changes if any had an ultra short duration. To get insights we performed scattering based imaging of thin film containing solution of model proteins like Bovine Serum Albumin (BSA), Ferritin and Fibrinogen. BSA and fibrinogen are nonmagnetic in nature. The former one is roughly spherical in shape and later one is rod shaped. On the other hand ferritin is a non-heme magnetic protein perfectly spherical in shape.

We imaged the solution before, after one minute and after five minutes of magnetic field exposure at room temperature. Then for analysis, we constructed an image plane, which is divided into 10,000 grids (100X100), where X-Y trajectories of the proteins are plotted. See materials and methods section for details of the experiment and m-code used to construct the image. Figure 1, (c)-(k) respectively represents the X-Y trajectories of proteins before exposure (c, f and i), after 1 minute exposure (d, g and j) and after 5 minute exposure (e, h and k) of 0.2 Tesla static magnetic field. ‘c’ (before), ‘d’ (after 1 min) and ‘e’ (after 5 min) indicates X-Y trajectories of BSA and similarly in same order (f), (g) and (h) and (i), (j) and (k) are for Ferritin and fibrinogen respectively.

Before magnetic field exposure the phase space is isotropic (space filling [see c, f and i]). A little bit anisotropy in space is observed after 1 minute field exposure (see d, g and j) and after 5 minutes of exposure the effect become more prominent for BSA and Ferritin (see e and h). For Fibrinogen the effect is not so prominent (compare k with e and h), but a rotation in the direction of the trajectories can be clearly observed (compare j and k with i). For quantification of the extent of anisotropic phase space we calculated an index and assigned as Space Inhomogeneity Index (SII).

SII is the ratio of space filled by the proteins and space filled by random distribution of same number of events. The random points generated by rand function of Matlab were used to filled the image plane having same matrix size (100X100). The ratio between the white pixels filling the matrix was assigned as SII. Table 1 shows the SII values of proteins before and after magnetic field exposure. The SMF induced anisotropic phase space can be compared from Table 1. SII value close to 1 means the space is filled homogenously and lower value of SII indicates inhomogeneity in space. That means, SMF induces inhomogeneity in phase space of particle motion (anisotropic movement).

Table 1: Space Inhomogeneity Index (SII) of the proteins (BSA, ferritin and fibrinogen) before, after 1minute and after 5 minute of magnetic field exposure.

Proteins        SII (before magnetic exposure)    SII (1 minute magnetic exposure)      SII (5 minute magnetic exposure)
BSA                                     0.862                                            0.686                                                         0.585
ferritin                                 0.911                                            0.528                                                         0.337
fibrinogen                           0.855                                             0.852                                                         0.789

The effect of SMF on Brownian motion of proteins can be observed in naked eye from the Movie S1, S2 and S3. Effect of SMF on diffusion has been studied theoretically. As the proteins are charged (Q) particles in presence of field the Lorentzian force (Q X V) may restrict their motion. The direction of the force will be perpendicular to applied magnetic field direction and direction of the motion of the particle. Hence, a vortex like streaming may be observed.

The resultant motion is intrinsically linked to the shape of the particle. The energy require to rotate a spherical particle is less that to rotate a particle with higher shape anisotropy. That is why for fibrinogen (rod shaped protein) we found attenuated response. Classically this type of phenomenon is explainable. But, explanation of the memory like effect that is persistence of space anisotropy after field withdrawal needs nonclassical treatment. We observed the phenomenon when the field is not present (after withdrawal of the field).

The phenomenon can be summarized as memory of external spin perturbation within a spin system. So we look for a model which deals with spatial coherence between spin states and that is Ising model. Ernst Ising solved one dimensional equation to explain the spontaneous magnetization of ferromagnetic system. But, recently the model is being used to explain various biological phenomenon like protein aggregation [9] , protein folding [10] , DNA-protein interaction [11] , etc. Ising model has been exploited in explaining various binding processes from last four decades, one important citation being [12] . The minimal Ising lattice, in which the Hamiltonian is given by,

In the equation (1) ‘σ’ can have two values (+/-1) depending on the type of interaction. The first term in the RHS represents the coupling between neighboring spins that can exist in absence of a field. The second term involving ‘β’ is the contribution due to Bohr magneton that exists only in presence of any external magnetic field B. First term is responsible for spontaneous magnetization in a ferromagnetic system in absence of field (B=0). For biomolecules the interaction energy between individual spin is not sufficient for spontaneous magnetization in absence of field.

But, higher order structure (peptide bonds and pi-pi interaction between aromatic amino acids) of biomolecules may form a spin coherent domain. And if we assume these domains as individual spin sates then the interaction between domains may result in very low magnetization as the exchange interaction is not as strong as ferromagnetic interaction. In this context, we also have to assume that the coupling coefficient ‘J’ is a function of ‘H’ (external field) and involve other degrees of freedom (higher order structure) along with spin with a nonlinear expression.

Now, in presence of magnetic field, interaction energy between domains (first term of RHS of Eq (1) and between individual domain and external magnetic field (second term of RHS of Eq 1) competes with each other. The differential contribution of these two types of interactions may result in field dependent differential magnetism of the system. For the first part of RHS of Eq (1), σ =1, as the interaction between domains is energetically favorable and results in three dimensional structures of proteins with global minima. But the value of σ for the second part of RHS of Eq (1) is negative (-1), which is governed by the diamagnetic anisotropy of the system.

At low field the first part predominates over the diamagnetic part and results in a positive magnetization (ferromagnetism) but at high field the diamagnetic contribution predominates and negative magnetization is found (see the M-H plot of tryptophan in Figure 1 b). This field dependent dynamic magnetic property and onset of ferromagnetism (due to coherent interaction between identical domain) is the basis of memory (walk memory of proteins) of magnetic field exposure in biosystems.

The maximum memory found for Ferritin, which is iron oxide containing magnetic protein and shows permanent magnetization (very low magnetic moment at room temperature). This also proves that the observed memory is related to the generation of positive magnetization at low magnetic field. It has been shown that the magnetism of ferritin core changes with iron content within the core [13] . But the physiological significance of such magnetic dynamism of a protein is still not clear. In this context we can say that modulation of intrinsic magnetic property of ferritin may be utilized to control the walk pattern of this protein in vivo.

Our findings highlight that even proteins can be subjected to magnetically controlled behavior, the memory component of the magnetic contribution depending on the protein shape and dimensionality. It may be noted that simple diamagnetic properties would not suffice to explain the memory aspect. The observation may have important implications in another context.

The presence of super paramagnetism in the individual amino acid scale and emergence of a ferromagnet like memory (at low field) manifested in the random walk proteins in solutions and also in protein motion in live cells (revised manuscript under preparation) implies presence of a temporally stable long term spatial coherence in physiological conditions. This inspired a direct exploitation of the Ising model. In addition, it has been shown that the instant response of live cells towards magnetic field is altered sub-cellular streaming.

In quantum biology some approaches have been sensing weak field [14][15] and events triggered by extreme small scale temporal rhythms often termed as quantum beats [16] .Presence of large spatial coherence that is reflected in random walk for a variety of proteins, has rarely been discussed. The observation may therefore be contextual with respect to deciphering many cellular communication processes, where very rarely the importance of spatial coherence is discussed.

Recently, research groups are interested in studying the functional aspects of membrane less protein assemblies within cell [17] . They are being formed by liquid-liquid phase transition. In this context our observation may be helpful to conceptualize the role of magnetic interaction behind the origin of formation and stability of such liquid droplet.


The superparamagnetic behavior of tryptophan is reported for the first time. Protein motion in solution thus show a magnetic field dependent memory of walk pattern. The finding may provide an alternative module of biological magneto-sensing , that is often described by the radical pair mechanism.


The future perspective of the work will be to understand the magnetic response of of normal and cancer cells. As the observed magnetic response is protein specific then the different cell types may also response in different way. If we get insights about the exact mechanism of translating such physical force by live cells, then we will be able to use such forces for therapeutic approaches.

Funding Statement

The work is supported by Centre of Excellence in Systems Biology and Biomedical Engineering, University of Calcutta.


The authors thank Ms. Namrata Jain , Malvern Instrments, India for her excellent technical support.

Ethics Statement

The work was done with commercially available proteins and did not involve any animal or human sample.

No fraudulence is committed in performing these experiments or during processing of the data. We understand that in the case of fraudulence, the study can be retracted by Matters.


L-tryptophan, Ferritin and Fibrinogen were purchased from Sigma. The Bovine Serum Albumin (BSA) was purchased from SRL. Millipore water was used to prepare stock solution and dilution. Protein solutions were prepared using 100 mM phosphate buffer of pH 7.22. The permanent Neodymium magnets were purchased from Rare Earth Magnetics, India. The field strength was measured using a locally made Gaussmeter (Neoequipments, India).

Magnetic measurement of tryptophan:

20 mg L-tryptophan was dissolved in 10 ml of MilliQ water (basic). The prepared 10 ml tryptophan solution was divided into two parts and dried using a lyophillizer, one part in absence of magnetic field and other one in presence of 0.2 Tesla magnetic field. Then the magnetic measurement of the dried sample was performed in Vibrational Sample Magnetometer (Quantum Design, MPMS 7).

Both samples were heated to 300K in presence of 100 Oesterd field and then cooling up to 4K was performed in presence (field cooling, FC) and in absence (zero field cooling, ZFC) of magnetic field. Magnetization vs Field (M-H) study was performed at 298 K using externally applied oscillatory magnetic field varying from -1 to +1 Tesla. In Figure 1b -0.4 t0 +0.4 T (or -4000 to +4000 (X1000/4) Am/m) field range has been shown.

Scattering based imaging of proteins motion:

Scattering based imaging of proteins (BSA, ferritin and fibrinogen) were performed using Nanoparticle Tracking Analysis (NTA) system (NanoSight NS300, Malvern, United Kingdom) equipped with a high sensitivity CMOS camera and 532 nm laser. All measurements were performed at room temperature. NTA 2.3 software was used to store the imaging data as ASCI file as well as in AVI video format.

The ASCI file contains particle number (ID), X, Y coordinates of that particle and the time of the particle tracking. 0.1 mg/ml protein solution was imaged before, after 1 minute and after 5 minutes of magnetic field exposure. At first we took the sample in a thin film sample holder and imaged for 1 minute. Then we kept a magnet on the top of the sample film for 1 minute and again imaged for 1 minute after removing the magnet. We performed the same step with 5 minutes magnetic incubation. We used the ASCI files for our analysis. We constructed a gray scale phase space trajectories of the proteins using Matlab (Mathworks, USA).

function z=raja_grid(x,y,m,n);
% m & n are sizes of the matrix (100X100)
ik=find(x<0); x(ik)=[]; y(ik)=[];
ik=find(y<0); x(ik)=[]; y(ik)=[];
x=x/max(x); y=y/max(y); z=zeros(m,n);
for i=1:m-1; for j=1:n-1 kk=find (x>=xl(i) & x<=xl(i+1) & y>=yl(j) & y<=yl(j+1) );
if isempty(kk)~=1 z(i,j)=z(i,j)+1; z(i,j)=255*(sum(I(kk))./max(I(kk)));
z=uint8(z); w(:,:,1)=z;w(:,:,2)=z;w(:,:,3)=z;
%w is the gray scale output image.