I was educated at a well-reputed secondary school, gaining 5 A-levels at grade A. I went on to achieve a Distinction in an MEng degree in Mechanical Engineering from Cambridge University, where I specialised in the manufacturing and design of devices using semiconductor and nano-materials, also taking modules in bioscience and physiology. Obtaining a Distinction for my final grade, I was awarded a scholarship to study at a prestigious university in Tokyo, Japan, undertaking post-graduate research in the mechanical study and analysis of protein structures in red blood cells using Atomic Force Microscopy. A fluent speaker of Japanese and French, I have been employed for several years as a translator of technical documentation, and is comfortable writing on a wide range of topics in the mechanical and material sciences, from traditional topics in mechanical engineering through to semiconductor engineering, nanotechnology and biomaterials. I also have a significant IT background with professional experience in software development. I am currently looking to enter a professional career in consulting on a technical field.

Sample

Monte Carlo Simulation Study of a Red Blood Cell Cytoskeleton under AFM loading.

Abstract
We have developed a finite element model capturing non-linear elasticity and stochastic topology variation to support experimental measurements of mechanical properties of the cytoskeleton, a network of protein fibers in the Red Blood Cell that plays a key role in its mechanical behavior at large deformations. The model has been used to run Monte Carlo simulations of AFM tensile tests, results of which indicate AFM probe separation force to be sensitive to probe position. The statistical relationship established should enable modification of the AFM method to obtain precise measurements of inter-protein bond strengths which control deformation behavior in the cytoskeleton.

Background
The ability of the red blood cell (RBC) to pass through capillaries much narrower than its nominal 8µm diameter (Li et al [1]) comes from lack of an internal structure and the apparent hyperelasticity of its cytoskeleton, a 2-dimensional network of spectrin protein tetramers interconnected by actin nodes which reinforces the cell membrane (Fig. 1). Deformation of the cytoskeleton under applied stress is characterised by a combination of two non-linear mechanisms: simple extension and compression of the composite tetramers, and dissociation of chemical bonds within the structure, increasing flexibility (Gov and Safran [2]). Whilst the force-extension response of individual spectrin tetramers is known with reasonable accuracy from numerous studies (Mirijanian and Voth [3]), the strength of Van der Waals bonds connecting spectrin tetramers to actin nodes has yet to be directly measured. This bond strength is known to depend on the chemical environment (An et al. [4]), in particular the concentration of protein 4.1 (which strengthens the bond) and concentration of ATP (which increases chemical energy available for bond dissociation). Since the mechanical behavior of the cell under large deformations is thought to be highly sensitive to such changes in bond strength [2-4], it is a mechanism by which diseases such as Sickle Cell Malaria and other biochemical factors can have significant (potentially negative) effects on blood flow. A method of evaluating changes in bond strength could therefore be very useful to biomedical research.

However, due to the extremely low force range in which individual bonds typically dissociate (0-100 pN), experimental methods are limited. We are performing tensile tests by Atomic Force Microscopy (AFM), using a V-shaped probe treated to bind to proteins in the cytoskeleton of an RBC with its cell membrane chemically removed (Fig. 2). The method allows precise measurement of the mechanical response of the cell under tension; in particular, the maximum cantilever force F prior to dissociation is a useful indicator of the strength of bonds connecting proteins attached to the probe surface. However, results are widely distributed (Fig. 3), due to the distribution of both bond dissociation force (a thermodynamic property), and experimental conditions (random variables changing between repeat measurements). We have used a numerical modeling approach by which experimental factors can be precisely controlled, and sensitivity to each can be evaluated. In this paper, position of the probe tip on the surface is identified as a significant source of variability.

Figure 1. Schematic of the RBC cytoskeleton with spectrin tetramers bound and unbound to actin nodes.

Figure 2. AFM Force distance curve illustration.

Figure 3. Typical distribution of maximum separation force F.

Methods
The model developed is effectively an implementation of the Finite Element Method comprising both non-linear elastic and stochastic effects. It consists of a 3-dimensional network containing b = 75010 1-d cable-type elements representing spectrin tetramers in the cytoskeleton (Fig. 4); the mechanical response of each element is modeled after various studies [2, 3] by the Worm-Like-Chain model [2] with a persistence length p of 6.5 nm and contour (maximum) length l_c of 200 nm.

Figure 4. The model in its initial unstressed equilibrated state.

Figure 5. Force-extension response of an individual tetramer element with length x∙l_c.

The highly non-linear force-extension response (Fig. 5) follows from entropy considerations as extension reduces the tetramer’s potential to assume convoluted shapes; the corresponding potential energy of a tetramer of length x∙l_c is:

Dissociation of any bond in the structure is modeled as a transition across a single activation energy barrier Ea; Ea therefore characterises the bond strength and is the primary parameter of interest, initially taken to be 100kcal∙mol-1 [4]. Modeling the transition from the bonded to the free state as a first-order Markov process [3], the average frequency V is given by equation (2), where A is a constant comprising various physical parameters, and E is the mechanical potential energy of the bound tetramer evaluated from integration of equation (1).

                                                                                (2)

From equation (1), the probability of survival of a bond i up to time t is given by:

                                                             (3)

In the subsequent Monte Carlo simulations, randomness is accounted for by assigning each element a “strength coefficient” si (i = 1→ b) in the range 0-1. During the simulation, if pi(t) ≥ si for any element i, that element is regarded as having a dissociated bond at one of its ends; its force is then set to zero. Within the time-frame of the tensile test simulation, the probability of re-association is neglected. The model can thus be used to capture force and deformation history of the entire structure as a function of an input vector si. These input vectors are chosen such that values are uniformly randomly distributed in the range 0-1, and used to perform each simulation up to the point at which all 6 elements directly connected to the probe tip dissociate and the cantilever force falls to zero; the force F at this point is then recorded and the values obtained used to compile a distribution which may be compared directly with experimental data.

The model was used to run Monte Carlo simulations of the AFM tensile test targeting points on the surface. The distance from the central axis of the cell was divided by the maximum cell radius, to give a normalised radial displacement, r (0 - 1). A total of 931 simulations were carried out, the positions chosen to be approximately uniform across the surface of the cell.

Results and discussion
The standardised results (Fig. 6) demonstrate a marked dependence of F on the position of the probe tip: F is much lower and has a narrower distribution near the edge of the cell than at the centre.

Figure 6. Monte Carlo Simulation results.

This is explained by examining distribution of the probe force in the attached tetramers (Fig. 7). When the tensile force is applied at the centre it is evenly distributed through the surrounding tetramers, resulting in maximum strength. When the force is applied near the edge, force is concentrated in the outside surface under high strain, resulting in progressive separation of the tetramers at lower force – a “weakest link” effect.

Figure 7. Illustration of the model with tensile force applied (a) centrally, (b) near the edge.

The Monte Carlo data can be compiled in histogram form as in Fig. 6 to give a discrete probability matrix, A(r, F). Based on A, a least-squares solution can be used to obtain the expected distribution d(r) of radial displacements resulting in measured experimental data n(F). With the dimensions of A and n chosen to match, the solution is in the standard form:

                                                        (4)

Results for d obtained from inputting the experimentally-obtained n distribution are given in Fig. 8(a). It suggests a wide level of distribution in radial displacement, focused more toward the edge of the cell than the centre. Furthermore, comparison of the fitted line corresponding to this d distribution with the experimental data (Fig. 8(b)) shows that the Monte Carlo results cannot account for high experimental values in the range F > 120pN. These results are believed to be due simultaneous attachment of the probe tip to multiple nodes; future studies will account for this possibility and allow for numerical correction.

(a)

(b)

Conclusions
Based on the Monte Carlo simulation data, a significant dependence of results on position has been identified. Based on this data, reverse fitting of a radial displacement distribution has been made, suggesting significant variation in probe position. It is also clear that the results cannot be fully accounted for by the current model, suggesting the need to account for other experimental factors such as multiple attachments to the probe tip. Subsequent modeling efforts will allow sensitivity to these factors to be assessed and numerically corrected for. This should allow biochemical parameters such as the bond activation energy Ea to be evaluated without previous repeatability issues.

References
Li., J, Lykotrafitis, G., Dao, M., Suresh, S., Pro. Nat. Ac. Sci., Vol. 104, No. 12, pp. 4937–4942, 2007

Zhu, Q., Vera, C., Asaro, R.J., Sche, P., Sung, L.A., Biophys. J., Vol. 15, No. 93(2), pp. 386–400, 2007.

Gov, N.S., and Safran, S.A., Biophys. J., Vol. 88, pp. 1859–1874, 2005.

Mirijanian, D.T., and Voth, G.A., PNAS, Vol. 105, No. 4, pp.1204–1208, 2008.

An, X.; Lecomte, M.C., Chasis, J.A., Mohandas, N., Gratzer, W., J. Biol. Chem, Vol. 277, Issue 35, pp. 31796-31800, 2002