Viral infection and B cell response

Following infection, B cell receptors are released as Antibodies targeting specific pathogens (Antigens):

     

Dramatis personae: [Virus, Antigen] vs. [Antibody, B cell]

Viral spikes are keys to binding receptors on target cells:

Spike density of some viruses:

Why is HIV spike density two orders of magnitude lower than other viruses?

Is the desire to evade antibody response an evolutionary factor for viral spike density?

How does the immune system create antibodies?

Affinity Maturation

Antibody maturation occurs takes place in Germinal Centers formed in lymph nodes:

Computational Model:

 

The processes of (hyper)mutation/competition/selection lead to rapid Population Evolution:

Fitness f  governs reproduction rates according to                 

Population mean  is defined by                                          

Mean fitness evolves as                                                     

green bullet Roland Fisher's Fundamental Theorem of Natural Selection

Affinity ω  is a trait correlated with fitness, and (including possibility of mutations) evolves as

green bullet George Price's Equation:                                                

To use the  equations in Affinity Maturation, we need to describe the dependence of fitness on affinity.

Fitness of B cells in Germinal Center

The mutating B cell Receptor (BCR) binds to spikes of presented virus:

Fitness of the maturing B cells depends on receptor affinity ω, and spike density n, qualitatively as:

Approximating the affinity distribution by a Gaussian of mean  and variance , Price's equation leads to

With these approximations, the equations are easily integrated to yield:

where         ,    and      .

In the above calculation, as in a more detailed agent based model, affinity is a non-monotonic function of target density:

   

Optimal affinity is achieved at target (spike) density of less than ~1 per area spanned by the BC:

too few targets at low density to be productive, too many targets at high density to be competitive.

In more detail, B cell attempts to pull in and digest the virus, with one or both hands:

Optimal affinity is achieved at target (spike) density of less than ~1 per area spanned by the B cell receptor.

Virus spike densities

Is evading potent antibody response an evolutionary force in setting viral spike densities?

If so, why is HIV different from other viruses?  

HIV disrupts the process of affinity maturation by depleting the helper T cell population:

 

The competition for reduced helper T cell signal negates the loss of competition at high spike densities:

  

Note that there is no structural reason preventing higher spike density on SIV, and mutant viruses with higher density have been created:

  

However, once injected into host the spike density goes down in subsequent generations.

Synthetic vaccines

Several strategies are in development for vaccination with synthetic nano-particles coated with target antigens:

 

Our results suggest that most potent antibodies are obtained at an optimal target density.

The low spike density of HIV may have evolved because of the effects of T helper cell depletion on affinity maturation

A. Amitai, A.K Chakraborty, and M. Kardar, PLOS Computational Biology (2018) (off-line)

Broadly neutralizing Antibodies.